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Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan
Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan
Turkish Journal of Mathematics
We study hyperelastic curves known as a generalization of elastic curves in $3-$dimensional lightlike cone which is a degenerate hypersurface in Minkowski $4-$space as critical points of the cone curvature energy functional constructed with the $r-$th power of the cone curvature depending on the given boundary conditions for the natural number $r \geq 2$. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according …
Efficient Nyberg-Rueppel Type Of Ntru Digital Signature Algorithm, Ferdi̇ Elverdi̇, Sedat Akleylek, Bariş Bülent Kirlar
Efficient Nyberg-Rueppel Type Of Ntru Digital Signature Algorithm, Ferdi̇ Elverdi̇, Sedat Akleylek, Bariş Bülent Kirlar
Turkish Journal of Mathematics
Message recovery is an important property in Nyberg-Rueppel type digital signature algorithms. However, the security of Nyberg-Rueppel type digital signature algorithms depends on the hard problems which might be vulnerable to quantum attacks. Therefore, quantum resistant Nyberg-Rueppel type digital signature algorithms with message recovery property are needed. Since NTRU-based cryptosystems are one of the best studied quantum-resistant schemes, using traditional NTRU encryption scheme has several advantages on the message recovery property. In this paper, we define Nyberg-Rueppel type of NTRU digital signature algorithm. It is carried out by combining NTRU-based encryption and signature algorithms. In the proposed scheme, efficient message …
A New Subclass Of Certain Analytic Univalent Functions Associated With Hypergeometric Functions, Alaatti̇n Akyar
A New Subclass Of Certain Analytic Univalent Functions Associated With Hypergeometric Functions, Alaatti̇n Akyar
Turkish Journal of Mathematics
The main objective of the present paper is to give with using the linear operator theory and also hypergeometric representations of related functions a new special subclass $\mathcal{TS}_{p}(2^{-r},2^{-1}), r\in \mathbb{ Z }^{+}$ of uniformly convex functions and in addition a suitable subclass of starlike functions with negative Taylor coefficients. Furthermore, the provided trailblazer outcomes in presented study are generalized to certain functions classes with fixed finitely many Taylor coefficients.
Classification Of Some Geometric Structures On 4-Dimensional Riemannian Lie Group, Esmaeil Peyghan, Davood Seifipour
Classification Of Some Geometric Structures On 4-Dimensional Riemannian Lie Group, Esmaeil Peyghan, Davood Seifipour
Turkish Journal of Mathematics
In this paper we study the spectral geometry of a $4$-dimensional Lie group. The main focus of this paper is to study the $2$-Stein and $2$-Osserman structures on a $4$-dimensional Riemannian Lie group. In this paper, we study the spectrum and trace of Jacobi operator and also we study the characteristic polynomial of generalized Jacobi operator on the non-abelian $4$-dimensional Lie group $G$, whenever $G$ is equipped with an orthonormal left invariant Riemannian metric $g$. The Lie algebra structures in dimension four have key role in this paper. It is known that in the classification of $4$-dimensional non-abelian Lie algebras …
On A Solvable System Of Rational Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
On A Solvable System Of Rational Difference Equations Of Higher Order, Merve Kara, Yasi̇n Yazlik
Turkish Journal of Mathematics
In this paper, we present that the following system of difference equations $$ x_{n}=\frac{x_{n-k}z_{n-l}}{b_{n}x_{n-k}+a_{n}z_{n-k-l}}, \ y_{n}=\frac{y_{n-k}x_{n-l}}{d_{n}y_{n-k}+c_{n}x_{n-k-l}}, \ z_{n}=\frac{z_{n-k}y_{n-l}}{f_{n}z_{n-k}+e_{n}y_{n-k-l}}, $$ where $n\in \mathbb{N}_{0}$, $k,l\in\mathbb{N}$, the initial values $x_{-i},y_{-i},z_{-i}$ are real numbers, for $i \in \overline{1,k+l}$, and sequences $\left( a_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( b_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( c_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( d_{n}\right) _{n\in \mathbb{N}_{0}}$, $\left( e_{n}\right) _{n\in \mathbb{N}_{0}}$ and $\left( f_{n}\right) _{n\in \mathbb{N}_{0}}$ are non-zero real numbers, for all $n\in \mathbb{N}_{0}$, which can be solved in closed form. We describe the forbidden set of the initial values using the obtained formulas and also determine the asymptotic behavior of solutions for the case …
Non-Solvable Groups All Of Whose Indices Are Odd-Square-Free, Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman
Non-Solvable Groups All Of Whose Indices Are Odd-Square-Free, Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman
Turkish Journal of Mathematics
Given a finite group $G$ and $x\in G$, the class size of $x$ in $G$ is called odd-square-free if it is not divisible by the square of any odd prime number. In this paper, we show that if $G$ is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of $G$, which is an answer to the dual of the question mentioned by Huppert in [5].
Rough Approximations Based On Different Topologies Via Ideals, Ayşegül Çaksu Güler, Esra Dalan Yildirim, Oya Özbakir
Rough Approximations Based On Different Topologies Via Ideals, Ayşegül Çaksu Güler, Esra Dalan Yildirim, Oya Özbakir
Turkish Journal of Mathematics
In this paper, we generalize the notations of rough sets based on the topological space. Firstly, we produce various topologies by using the concept of ideal, $C_j$-neighbourhoods and $P_j$-neighbourhoods. When we compare these topologies with previous topologies, we see that these topologies are more general. Then we introduce new methods to find the approximations by using these generated topologies. When we compare these methods with the previous methods, we see that these methods are more accurate.
Inverse Coefficient Identification Problem For A Hyperbolic Equation With Nonlocal Integral Condition, Azizbayov Elvin
Inverse Coefficient Identification Problem For A Hyperbolic Equation With Nonlocal Integral Condition, Azizbayov Elvin
Turkish Journal of Mathematics
This paper is concerned with an inverse coefficient identification problem for a hyperbolic equation in a rectangular domain with a nonlocal integral condition. We introduce the definition of the classical solution, and then the considered problem is reduced to an auxiliary equivalent problem. Further, the existence and uniqueness of the solution of the equivalent problem are proved using a contraction mapping principle. Finally, using equivalency, the unique existence of a classical solution is proved.
Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua
Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua
Turkish Journal of Mathematics
In this paper, we consider gradient estimates for positive solutions to the following equation $$\triangle_V u+au^p\log u=0$$ on complete noncompact Riemannian manifold with $k$-dimensional Bakry-Emery Ricci curvature bounded from below. Using the Bochner formula and the Cauchy inequality, we obtain upper bounds of $ \nabla u $ with respect to the lower bound of the Bakry-Emery Ricci curvature.
Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen
Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen
Turkish Journal of Mathematics
It is rigorously proven under certain assumptions that a quasilinear system with discontinuous right-hand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.
On $(A,D)$-Edge Local Antimagic Coloring Number Of Graphs, Rajkumar Sundaramoorthy, Nalliah Moviri Chettiar
On $(A,D)$-Edge Local Antimagic Coloring Number Of Graphs, Rajkumar Sundaramoorthy, Nalliah Moviri Chettiar
Turkish Journal of Mathematics
For any graph $G=(V,E),$ the order and size of G are $p$ and $q$. A bijection $l$ from $V(G)$ to $\{1,2,..,p\}$ is called $(a,d)$-edge local antimagic labeling if for any two adjacent edges are not received the same edge-weight (color) and the set of all edge-weights are formed an arithmetic progression $\{a,a+d,a+2d,\dots,a+(c-1)d\}$, for some integers $a,d>0$ and $c$ is the number of distinct colors used in the proper coloring.} An edge-weight (color) $w(uv)$ is the sum of two end vertices labels, $w(uv)=f(u)+f(v),uv\in E(G).$ The $(a,d)$-edge local antimagic coloring number is the least color (edge-weight) used in any $(a,d)$-edge local …
K−Uniformly Multivalent Functions Involving Liu-Owa Q−Integral Operator, Asena Çeti̇nkaya
K−Uniformly Multivalent Functions Involving Liu-Owa Q−Integral Operator, Asena Çeti̇nkaya
Turkish Journal of Mathematics
In this paper, we introduce $q-$analogue of Liu-Owa integral operator and define a subclass of $k-$uniformly multivalent starlike functions of order $\gamma, (0\leq\gamma< p; p\in\mathbb{N})$ by using the Liu-Owa $q-$integral operator. We examine coefficient estimates, growth and distortion bounds for the functions belonging to the subclass of $k-$uniformly multivalent starlike functions of order $\gamma$. Moreover, we determine radii of $k-$uniformly starlikeness, convexity and close-to-convexity for the functions belonging to this subclass.
Uniformly Convergent Finite Difference Method For Reaction-Diffusion Type Third Order Singularly Perturbed Delay Differential Equation, Rajendran Mahendran, Veerasamy Subburayan
Uniformly Convergent Finite Difference Method For Reaction-Diffusion Type Third Order Singularly Perturbed Delay Differential Equation, Rajendran Mahendran, Veerasamy Subburayan
Turkish Journal of Mathematics
A class of third order reaction-diffusion type singularly perturbed ordinary delay differential equations is considered in this article. A fitted finite difference method on Shishkin mesh is suggested to solve the problem. Moreover, we present a class of nonlinear problems. An error estimation is obtained based on the maximum norm and it is of almost first order convergence. Numerical results are given to support theoretical claims.
Discrete Impulsive Sturm-Liouville Equation With Hyperboliceigenparameter, Turhan Köprübaşi, Yelda Aygar Küçükevci̇li̇oğlu
Discrete Impulsive Sturm-Liouville Equation With Hyperboliceigenparameter, Turhan Köprübaşi, Yelda Aygar Küçükevci̇li̇oğlu
Turkish Journal of Mathematics
Let $L$ denote the selfadjoint difference operator of second order with boundary and impulsive conditions generated in $\ell _{2}\left( %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion \right) $ by \begin{equation*} a_{n-1}y_{n-1}+b_{n}y_{n}+a_{n}y_{n+1}=\left( 2\cosh z\right) y_{n}\text{ },% \text{ }n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion \setminus \left\{ k-1,k,k+1\right\} , \end{equation*}% \begin{equation*} \begin{array}{c} y_{0}=0\text{ }, \\ \left\{ \begin{array}{c} y_{k+1}=\theta _{1}y_{k-1} \\ \bigtriangleup y_{k+1}=\theta _{2}\bigtriangledown y_{k-1} \end{array}% \right. ,\text{ }\theta _{1},\theta _{2}\in %TCIMACRO{\U{211d}}% %BeginExpansion \mathbb{R}, %EndExpansion \end{array}% \end{equation*} where $\left\{ a_{n}\right\} _{n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion },$ $\left\{ b_{n}\right\} _{n\in %TCIMACRO{\U{2115} } %BeginExpansion \mathbb{N} %EndExpansion }$ are real sequences and $\bigtriangleup ,\bigtriangledown $ are respectively forward …
Second Main Theorem For Meromorphic Mappings Intersecting Moving Targets On Parabolic Manifolds, Jiali Chen, Qingcai Zhang
Second Main Theorem For Meromorphic Mappings Intersecting Moving Targets On Parabolic Manifolds, Jiali Chen, Qingcai Zhang
Turkish Journal of Mathematics
In this paper, we establish a new second main theorem for meromorphic mappings from $M$ into $\mathbb{P}(V)$ intersecting moving targets $g_{j}:M\rightarrow\mathbb{P}(V^{\ast}),\ 1\leq j\leq q,$ where $M$ is a parabolic manifold and $V$ is a Hermitian vector space. As an application, we prove the algebraic dependence problem for meromorphic mappings with moving targets in general position.
Product-Type Operators On Weak Vector Valued $\Alpha$-Besov Spaces, Sepideh Nasresfahani, Ebrahim Abbasi
Product-Type Operators On Weak Vector Valued $\Alpha$-Besov Spaces, Sepideh Nasresfahani, Ebrahim Abbasi
Turkish Journal of Mathematics
Let $\psi_1$ and $\psi_2$ be analytic functions on the open unit disk $\mathbb{D}$ and $\phi$ an analytic self map on $\mathbb{D}$. Let $M_\psi$, $C_\phi$ and $D$ denote the multiplication, composition and differentiation operators. We consider operators $M_{\psi_1} C_\phi$, $M_{\psi_2} C_\phi D$ and the Stevi\'c-Sharma operator $T_{\psi_1,\psi_2,\phi}(f)=M_{\psi_1}C_\phi (f)+M_{\psi_2}C_\phi D(f)$ on $\alpha$-Besov space $\mathcal{B}_{p,\alpha}$ and weak vector valued $\alpha$-Besov space $ w\mathcal{B}_{p,\alpha}(X)$ for complex Banach space $X$ and find some equivalent statements for boundedness of these operators. Also, boundedness and compactness of composition operator $C_\phi$ on $\mathcal{B}_{p,\alpha}(\mathbb{D})$ and $w\mathcal{B}_{p,\alpha}(\mathbb{D})$ are given.
Codimensions Of Algebras With Additional Structures, Daniela La Mattina
Codimensions Of Algebras With Additional Structures, Daniela La Mattina
Turkish Journal of Mathematics
Let $A$ be an associative algebra endowed with an automorphism or an antiautomorphism $\varphi$ of order $\leq 2.$ One associates to $A,$ in a natural way, a numerical sequence $c^\varphi_n(A),$ $n=1, 2, \ldots$, called the sequence of $\varphi$-codimensions of $A$ which is the main tool for the quantitative investigation of the polynomial identities satisfied by $A$. In \cite{GLM} it was proved that such a sequence is eventually nondecreasing in case $\varphi$ is an antiautomorphism. Here we prove that it still holds in case $\varphi$ is an automorphism and present some recent results about the asymptotics of $c^\varphi_n(A)$.
Solvability In The Small Of $M$-Th Order Elliptic Equations In Weighted Grand Sobolev Spaces, Bilal Bilalov, Yusuf Zeren, Sabina Sadigova, Şeyma Çeti̇n
Solvability In The Small Of $M$-Th Order Elliptic Equations In Weighted Grand Sobolev Spaces, Bilal Bilalov, Yusuf Zeren, Sabina Sadigova, Şeyma Çeti̇n
Turkish Journal of Mathematics
In this work we consider the Sobolev spaces generated by the norm of the power weighted grand Lebesgue spaces. It is considered $m$-th order elliptic equation with nonsmooth coefficients on bounded domain in $R^{n} $. This space is nonseparable and by using shift operator we define the separable subspace of it, in which infinitely differentiable functions are dense. The investigation needs to establish boundedness property of convolution regarding weighted grand Lebesgue spaces. Then on scheme of nonweighted case we establish solvability (strong sense) in the small of $m$-th order elliptic equations in power weighted grand Sobolev spaces. Note that in …
Quasi $J$-Submodules, Ece Yetki̇n Çeli̇kel, Hani Khashan
Quasi $J$-Submodules, Ece Yetki̇n Çeli̇kel, Hani Khashan
Turkish Journal of Mathematics
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a quasi $J$-submodule if whenever $r\in R$ and $m\in M$ such that $rm\in N$ and $r\notin(J(R)M:M)$, then $m\in M$-$rad(N)$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Furthermore, we provide new classes of modules generalizing presimplifiable modules and justify their relation with (quasi) $J$-submodules. Finally, for a submodule $N$ …
Adjunction Identity To Hypersemigroups, Niovi Kehayopulu
Adjunction Identity To Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
It is shown that some embedding problems on hypersemigroups are actually problems of adjunction. According to the theorem of this paper, for every hypersemigroup $S$ which does not have identity element, an hypersemigroup $T$ having identity element can be constructed in such a way that $S$ is an ideal of $T$. Moreover, if $S$ is regular, intra-regular, right (left) regular, right (left) quasi-regular or semisimple, then so is $T$. If $A$ is an ideal, subidempotent bi-ideal or quasi-ideal of $S$, then it is an ideal, bi-ideal, quasi-ideal of $T$ as well. Illustrative examples are given.
New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei
New Form Of Laguerre Fractional Differential Equation And Applications, Zahra Kavooci, Kazem Ghanbari, Hanif Mirzaei
Turkish Journal of Mathematics
Laguerre differential equation is a well known equation that appears in the quantum mechanical description of the hydrogen atom. In this paper, we aim to develop a new form of Laguerre Fractional Differential Equation (LFDE) of order $2\alpha$ and we investigate the solutions and their properties. For a positive real number $\alpha$, we prove that the equation has solutions of the form $L_{n,\alpha}(x)=\sum_{k=0}^na_kx^k$, where the coefficients of the polynomials are computed explicitly. For integer case $\alpha=1$ we show that these polynomials are identical to classical Laguerre polynomials. Finally, we solve some fractional differential equations by defining a suitable integral transform.
Solving A Class Of Ordinary Differential Equations And Fractional Differential Equations With Conformable Derivative By Fractional Laplace Transform, Mohammad Molaei, Farhad Dastmalchi Saei, Mohammad Javidi, Yaghoub Mahmoudi
Solving A Class Of Ordinary Differential Equations And Fractional Differential Equations With Conformable Derivative By Fractional Laplace Transform, Mohammad Molaei, Farhad Dastmalchi Saei, Mohammad Javidi, Yaghoub Mahmoudi
Turkish Journal of Mathematics
In this paper, we use the fractional Laplace transform to solve a class of second-order ordinary differential equations (ODEs), as well as some conformable fractional differential equations (CFDEs), including the Laguerre conformable fractional differential equation. Specifically, we apply the transform to convert the differential equations into first-order, linear differential equations. This is done by using the fractional Laplace transform of order $\alpha+\beta$ or $\alpha+\beta+\gamma$. Also, we investigate some more results on the fractional Laplace transform, obtained by Abdeljawad.
Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan
Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan
Turkish Journal of Mathematics
In this paper, by using fixed point theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind $$ \phi(x) = \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ and the nonhomogeneous equation $$ \phi(x) = x + \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ for all $x \in [0,1]$ and $0
Existence Of Solutions For An Infinite System Of Tempered Fractional Order Boundary Value Problems In The Spaces Of Tempered Sequences, Khuddush Mahammad, Rajendra Prasad Kapula, Leela Doddi
Existence Of Solutions For An Infinite System Of Tempered Fractional Order Boundary Value Problems In The Spaces Of Tempered Sequences, Khuddush Mahammad, Rajendra Prasad Kapula, Leela Doddi
Turkish Journal of Mathematics
This paper deals with infinite system of nonlinear two-point tempered fractional order boundary value problems $$ \begin{aligned} {}^\mathtt{RL}_{~0}\mathbb{D}^{δ_2,\ell}_\mathtt{z}\Big[\mathtt{p}_\mathtt{j}(\mathtt{z})&{}^\mathtt{RL}_{~0}\mathbb{D}^{δ_1,\ell}_\mathtt{z} \vartheta_\mathtt{j}(\mathtt{z})\Big]=λ_\mathtt{j}\varphi\big(\mathtt{z},\vartheta(\mathtt{z})\big),\, \mathtt{z}\in[0,\mathtt{T}], δ_1,δ_2\in(1,2),\\ &\hskip0.25cm\vartheta_\mathtt{j}(0)=\lim_{\mathtt{z}\to0}\left[{}^\mathtt{RL}_{~0}\mathbb{D}^{δ_1,\ell}_\mathtt{z}(e^{\ell\mathtt{z}}\vartheta_\mathtt{j}(\mathtt{z}))\right]=0,\\ &e^{\ell\mathtt{T}}\vartheta_\mathtt{j}(\mathtt{T})=\lim_{\mathtt{z}\to\mathtt{T}}\left[{}^\mathtt{RL}_{~0}\mathbb{D}^{δ_1,\ell}_\mathtt{z}(e^{\ell\mathtt{z}}\vartheta_\mathtt{j}(\mathtt{z}))\right]=0, \end{aligned} $$ where $\mathtt{j}\in\{1,2,3,\cdot\cdot\cdot\},\,\ell\ge 0,$ ${}^\mathtt{RL}_{~0}\mathbb{D}^{\star,\ell}_\mathtt{z}$ denotes the Riemann--Liouville tempered fractional derivative of order $\star\in\{δ_1,δ_2\}$, $\vartheta(\mathtt{z})=\left(\vartheta_\mathtt{j}(\mathtt{z})\right)_{\mathtt{j}=1}^{\infty},$ $\varphi_\mathtt{j}:[0,\mathtt{T}]\to[0,\mathtt{T}]$ are continuous and we derive sufficient conditions for the existence of solutions to the system via the Hausdorff measure of noncompactness and Meir-Keeler fixed point theorem in tempered sequence spaces.
Global Existence And Energy Decay For A Coupled System Of Kirchhoff Beam Equations With Weakly Damping And Logarithmic Source, Ducival Carvalho Pereira, Carlos Alberto Raposo Da Cunha, Adriano Pedreira Cattai
Global Existence And Energy Decay For A Coupled System Of Kirchhoff Beam Equations With Weakly Damping And Logarithmic Source, Ducival Carvalho Pereira, Carlos Alberto Raposo Da Cunha, Adriano Pedreira Cattai
Turkish Journal of Mathematics
This paper deals with the global solutions and exponential stability for a coupled system of Kirchhoff beam weakly damping and with a logarithmic source. We apply the potential well and establish the global well-posedness by using the Faedo--Galerkin approximations, taking into account that the initial data is located in a suitable set of stability created from the Nehari manifold. Moreover, by using Nakao's lemma, we prove the exponential stability of the solution.
Two Nonzero Weak Solutions For A Quasilinear Kirchhoff Type Problem, Lin Li, Stepan Tersian
Two Nonzero Weak Solutions For A Quasilinear Kirchhoff Type Problem, Lin Li, Stepan Tersian
Turkish Journal of Mathematics
We study the existence of two nonzero solutions for a class of quasilinear Kirchhoff problems. The approach is based on the variational methods. Our nonlinerity is contrast to some previous results is that superlinear growth at infinity.
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
A Sequential Fractional Differential Problem Of Pantograph Type:Existence Uniqueness And Illustrations, Soumia Belarbi, Zoubir Dahmani, Mehmet Zeki̇ Sarikaya
Turkish Journal of Mathematics
In this study, a new class of sequential fractional differential problems of pantograph type is introduced. New existence and uniqueness criteria for the existence and uniqueness of solutions are discussed. Some existence results using Darbo's fixed point and measure of noncompactness are also studied. At the end, two illustrative examples are discussed.
Two Classes Of Permutation Polynomials With Niho Exponents Over Finite Fields With Even Characteristic, Qian Liu
Turkish Journal of Mathematics
In this paper, by transforming the permutation problem into the root distribution problem in the unit circle of certain quadratic and cubic equations, we investigate the permutation behavior of the type $f(x)=x+x^{2^{3m}-2^m+1}+x^{2^{4m}-2^{3m}+2^m}$ over $F_{2^{4m}}$ and $f(x)=x+x^{2^m}+x^{2^{m+1}-1}+ax^{2^{2m}-2^m+1}$ over $F_{2^{2m}}$, respectively.
Berezin Symbol Inequalities Via Grüss Type Inequalities And Related Questions, Rami̇z Tapdigoğlu, Mübari̇z Garayev, Najla Altwaijry
Berezin Symbol Inequalities Via Grüss Type Inequalities And Related Questions, Rami̇z Tapdigoğlu, Mübari̇z Garayev, Najla Altwaijry
Turkish Journal of Mathematics
We prove some new inequalities for Berezin symbols of operators via classical Grüss type inequalities. Some other related questions are also discussed.
Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz
Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz
Turkish Journal of Mathematics
We consider simply connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic symplectic $4$-manifolds in the homeomorphism classes of $\mathbb{C} P^{2}\#8\overline{\mathbb{C} P^{2}}$ and $\mathbb{C} P^{2}\#9\overline{\mathbb{C} P^{2}}$, respectively. From these, we provide upper bounds for the minimal number of singular fibers of such fibrations. In addition, we prove that this number is equal to $18$ for $g=3$ when such fibrations are hyperelliptic. Moreover, we discuss these numbers for higher genera.