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On A Fifth-Order Nonselfadjoint Boundary Value Problem, Eki̇n Uğurlu, Kenan Taş
On A Fifth-Order Nonselfadjoint Boundary Value Problem, Eki̇n Uğurlu, Kenan Taş
Turkish Journal of Mathematics
In this paper we aim to share a way to impose some nonselfadjoint boundary conditions for the solutions of a formally symmetric fifth-order differential equation. Constructing a dissipative operator related with the problem we obtain some informations on spectral properties of the problem. In particular, using coordinate-free approach we construct characteristic matrix-function related with the contraction which is obtained with the aid of the dissipative operator.
Completeness Conditions Of Systems Of Bessel Functions In Weighted $L^2$-Spaces In Terms Of Entire Functions, Ruslan Khats'
Completeness Conditions Of Systems Of Bessel Functions In Weighted $L^2$-Spaces In Terms Of Entire Functions, Ruslan Khats'
Turkish Journal of Mathematics
Let $J_{\nu}$ be the Bessel function of the first kind of index $\nu\ge 1/2$, $p\in\mathbb R$ and $(\rho_k)_{k\in\mathbb N}$ be a sequence of distinct nonzero complex numbers. Sufficient conditions for the completeness of the system $\big\{x^{-p-1}\sqrt{x\rho_k}J_{\nu}(x\rho_k):k\in\mathbb N\big\}$ in the weighted space $L^2((0;1);x^{2p} dx)$ are found in terms of an entire function with the set of zeros coinciding with the sequence $(\rho_k)_{k\in\mathbb N}$.
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Turkish Journal of Mathematics
In this paper, our aim is to investigate a class of first-order nonlinear delay differential equations with several deviating arguments. In addition, we present some sufficient conditions for the oscillatory solutions of these equations. Differing from other studies in the literature, delay terms are not necessarily monotone. Finally, we give examples to demonstrate the results.
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Generating Finite Coxeter Groups With Elements Of The Same Order, Sarah B. Hart, Veronica Kelsey, Peter Rowley
Turkish Journal of Mathematics
Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G)=0$ if $G$ has no such generating sets). This paper investigates $d_k(G)$ when $G$ is a finite Coxeter group either of type $B_n$ or $D_n$, or of exceptional type. Together with the work of Garzoni and Yu, this determines $d_k(G)$ for all finite irreducible Coxeter groups $G$ when $2 \leq k \leq (G)$ ($(G)+1$ when $G$ is of type A$_{n}$).
A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z
A Classification Of 1-Well-Covered Graphs, Zaki̇r Deni̇z
Turkish Journal of Mathematics
A graph is well-covered if all its maximal independent sets have the same size. If a graph is well-covered and remains well-covered upon removal of any vertex, then it is called 1-well-covered graph. It is well-known that $[\frac{n}{2}]+1\leq \alpha(G) + \mu(G) \leq n$ for any graph $G$ with $n$ vertices where $\alpha(G)$ and $\mu(G)$ are the independence and matching numbers of $G$, respectively. A graph $G$ satisfying $\alpha(G) + \mu(G) = n$ is known as König-Egervary graph, and such graphs are characterized by Levit and Mandrescu [14] under the assumption that $G$ is 1-well-covered. In this paper, we investigate connected …
Some Properties Of Second-Order Weak Subdifferentials, Gonca İnceoğlu
Some Properties Of Second-Order Weak Subdifferentials, Gonca İnceoğlu
Turkish Journal of Mathematics
This article deals with second-order weak subdifferential. Firstly, the concept of second-order weak subdifferential is defined. Next, some of its properties are investigated. The necessary and sufficient condition for a second-order weakly subdifferentiable function to have a global minimum has been proved. It has been proved that a second-order weakly subdifferentiable function is both lower semicontinuous and lower Lipschitz.
Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev
Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev
Turkish Journal of Mathematics
In this paper,we define a class of analytic functions $F_{\left( \beta ,\lambda \right) }\left( H,\alpha ,\delta ,\mu \right) ,$ satisfying the following subordinate condition associated with Chebyshev polynomials \begin{equation*} \left\{ \alpha \left[ \frac{zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\delta }+\left( 1-\alpha \right) \left[ \frac{% zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\mu }\left[ 1+% \frac{zG^{^{\prime \prime }}\left( z\right) }{G^{^{\prime }}\left( z\right) }% \right] ^{1-\mu }\right\} \prec H\left( z,t\right) , \end{equation*}% where $G\left( z\right) =\lambda \beta z^{2}f^{^{\prime \prime }}\left( z\right) +\left( \lambda -\beta \right) zf^{^{\prime }}\left( z\right) +\left( 1-\lambda +\beta \right) f\left( z\right) ,$ $0\leq \alpha \leq 1,$ $% 1\leq \delta \leq …
Second Hankel Determinant For Mocanu Type Bi-Starlike Functionsrelated To Shell-Shaped Region, Ni̇zami̇ Mustafa, Gangadharan Murungusundaramoorthy
Second Hankel Determinant For Mocanu Type Bi-Starlike Functionsrelated To Shell-Shaped Region, Ni̇zami̇ Mustafa, Gangadharan Murungusundaramoorthy
Turkish Journal of Mathematics
In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for the analytic bi-univalent function class, which we call Mocanu type bi-starlike functions, related to a shell-shaped region in the open unit disk in the complex plane. Some interesting special cases of the results are also discussed.
General Rotational $\Xi -$Surfaces In Euclidean Spaces, Kadri̇ Arslan, Yilmaz Aydin, Betül Bulca
General Rotational $\Xi -$Surfaces In Euclidean Spaces, Kadri̇ Arslan, Yilmaz Aydin, Betül Bulca
Turkish Journal of Mathematics
The general rotational surfaces in the Euclidean 4-space $\mathbb{R}^{4}$ was first studied by Moore (1919). The Vranceanu surfaces are the special examples of these kind of surfaces. Self-shrinker flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, $\xi -$surfaces are the generalization of self-shrinker surfaces. In the present article we consider $\xi -$surfaces in Euclidean spaces. We obtained some results related with rotational surfaces in Euclidean $4-$space $\mathbb{R}^{4}$ to become self-shrinkers. Furthermore, we classify the general rotational $\xi -$surfaces with constant mean curvature. As an application, we give some …
Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers
Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers
Turkish Journal of Mathematics
A subalgebra $B$ of a Lie algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ is the largest ideal of $L$ contained in $B.$ This is analogous to the concept of weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Turkish Journal of Mathematics
In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …
Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev
Axes In Non-Associative Algebras, Louis Rowen, Yoav Segev
Turkish Journal of Mathematics
Fusion rules are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Hall, Rehren and Shpectorov. Axial algebras, in turn, are closely related to $3$-transposition groups and Vertex operator algebras. In this paper we consider fusion rules for semisimple idempotents, following Albert in the power-associative case. We examine the notion of an axis in the non-commutative setting and show that the dimension $d$ of any algebra $A$ generated by a pair $a,b$ of (not necessarily Jordan) axes of respective types $(λ,δ)$ and $(λ',δ')$ must be at …
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz
On $F$-Kenmotsu $3$-Manifolds With Respect To The Schouten-Van Kampen Connection, Selcen Yüksel Perktaş, Ahmet Yildiz
Turkish Journal of Mathematics
In this paper we study some semisymmetry conditions and some soliton types on $f$-Kenmotsu $3$-manifolds with respect to the Schouten-van Kampen connection.
Crossed Product Of Infinite Groups And Complete Rewriting Systems, Esra Kirmizi Çeti̇nalp, Eylem Güzel Karpuz
Crossed Product Of Infinite Groups And Complete Rewriting Systems, Esra Kirmizi Çeti̇nalp, Eylem Güzel Karpuz
Turkish Journal of Mathematics
The aim of this paper is to obtain a presentation for crossed product of some infinite groups and then find its complete rewriting system. Hence, we present normal form structure of elements of crossed product of infinite groups which yield solvability of the word problem.
Notes On Multivalent Bazilevic Functions Defined By Higher Order Derivatives, Mohamed K. Aouf, Adela O. Mostafa, Teodor Bulboaca
Notes On Multivalent Bazilevic Functions Defined By Higher Order Derivatives, Mohamed K. Aouf, Adela O. Mostafa, Teodor Bulboaca
Turkish Journal of Mathematics
In this paper we consider two subclasses $B(p,q,\alpha,\beta)$ and $B_{1}(p,q,\alpha,\beta)$ of p-valently Bazilevi\'c functions defined by higher order derivatives, and we defined and studied some properties of the images of the functions of these classes by the integral operators $\mathrm{I}_{n,p}$ and $\mathrm{J}_{n,p}$ for multivalent functions, defined by using higher order derivatives.
Repdigits As Sums Of Two Generalized Lucas Numbers, Sai Gopal Rayaguru, Jhon Jairo Bravo
Repdigits As Sums Of Two Generalized Lucas Numbers, Sai Gopal Rayaguru, Jhon Jairo Bravo
Turkish Journal of Mathematics
A generalization of the well-known Lucas sequence is the $k$-Lucas sequence with some fixed integer $k \geq 2$. The first $k$ terms of this sequence are $0,\ldots,0,2,1$, and each term afterwards is the sum of the preceding $k$ terms. In this paper, we determine all repdigits, which are expressible as sums of two $k$-Lucas numbers. This work generalizes a prior result of Şiar and Keskin who dealt with the above problem for the particular case of Lucas numbers and a result of Bravo and Luca who searched for repdigits that are $k$-Lucas numbers.
Banach Algebra Structure On Strongly Simple Extensions, Sara El Kinani
Banach Algebra Structure On Strongly Simple Extensions, Sara El Kinani
Turkish Journal of Mathematics
We consider strongly simple extensions of unitary commutative Banach algebras. We study these Banach algebra structure without assuming the continuity of the canonical injection. The link of the integrality with these extensions is studied. Several algebraic results are also obtained.
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Liftings And Covering Morphisms Of Crossed Modules In Group-Groupoids, Serap Demi̇r Karakaş, Osman Mucuk
Turkish Journal of Mathematics
In this work we introduce lifting and covering of a crossed module in the category of group-groupoids; and then we prove the categorical equivalence of horizontal actions of a double group-groupoid and lifting crossed modules of corresponding crossed module in group-groupoids. These allow us to produce more examples of double group-groupoids.
Good Components Of Curves In Projective Spaces Outside The Brill-Noether Range, Edoardo Ballico
Good Components Of Curves In Projective Spaces Outside The Brill-Noether Range, Edoardo Ballico
Turkish Journal of Mathematics
For all integers $n, d, g$ such that $n\ge 4$, $d\ge n+1$, and $(n+2)(d-n-1)\ge n(g-1)$, we define a good (i.e. generically smooth of dimension $(n+1)d+(3-n)(g-1)$ and with the expected number of moduli) irreducible component $A(d,g;n)$ of the Hilbert scheme of smooth and nondegenerate curves in $\mathbb{P}^n$ with degree $d$ and genus $g$. For most of these $(d,g)$, we prove that a general $X\in A(d,g;n)$ has maximal rank. We cover, in this way, a range of $(d,g,n)$ outside the Brill-Noether range.
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
On The Number Of Non-$G$-Equivalent Minimal Abelian Codes, Fatma Altunbulak Aksu, İpek Tuvay
Turkish Journal of Mathematics
Let $G$ be a finite abelian group. Ferraz, Guerreiro, and Polcino Milies (2014) proved that the number of $G$-equivalence classes of minimal abelian codes is equal to the number of $G$-isomorphism classes of subgroups for which corresponding quotients are cyclic. In this article, we prove that the notion of $G$-isomorphism is equivalent to the notion of isomorphism on the set of all subgroups $H$ of $G$ with the property that $G/H$ is cyclic. As an application, we calculate the number of non-$G$-equivalent minimal abelian codes for some specific family of abelian groups. We also prove that the number of non-$G$-equivalent …
Numerical Investigation Of Viscous Effects On The Nonlinear Burgers Equation, Muhammad Imran Khan, Abdul Rauf, Abdullah Shah
Numerical Investigation Of Viscous Effects On The Nonlinear Burgers Equation, Muhammad Imran Khan, Abdul Rauf, Abdullah Shah
Turkish Journal of Mathematics
This research article presents the numerical solution of the viscous Burgers equation. The diagonally implicit fractional step $\theta$ (DIFST) scheme is used for the time discretization and the space derivative is discretized by the conforming finite element method with quadrilateral mesh. The viscosity effect on the shock wave is calculated with an estimation of the $L_2$ error. For comparison of different time discretization schemes, three test problems are computed. The stability and accuracy of the schemes are given by estimating the $L_2$ error norm. Numerical simulation for one- and two-dimensional problems are given and illustrated graphically. The effect of the …
On Elements Whose Moore-Penrose Inverse Is Idempotent In A ${\Ast}$-Ring, Haiyang Zhu, Jianlong Chen, Yukun Zhou
On Elements Whose Moore-Penrose Inverse Is Idempotent In A ${\Ast}$-Ring, Haiyang Zhu, Jianlong Chen, Yukun Zhou
Turkish Journal of Mathematics
In this paper, we investigate the elements whose Moore-Penrose inverse is idempotent in a ${\ast}$-ring. Let $R$ be a ${\ast}$-ring and $a\in R^\dagger$. Firstly, we give a concise characterization for the idempotency of $a^\dagger$ as follows: $a\in R^\dagger$ and $a^\dagger$ is idempotent if and only if $a\in R^{\#}$ and $a^2=aa^*a$, which connects Moore-Penrose invertibility and group invertibility. Secondly, we generalize the results of Baksalary and Trenkler from complex matrices to ${\ast}$-rings. More equivalent conditions which ensure the idempotency of $a^\dagger$ are given. Particularly, we provide the characterizations for both $a$ and $a^\dagger$ being idempotent. Finally, the equivalent conditions under which …
Operators Between Different Weighted Frechet And (Lb)-Spaces Of Analytic Functions, Ersi̇n Kizgut
Operators Between Different Weighted Frechet And (Lb)-Spaces Of Analytic Functions, Ersi̇n Kizgut
Turkish Journal of Mathematics
We study some classical operators defined on the weighted Bergman Frechet space $A^p_{\alpha+}$ (resp. weighted Bergman (LB)-space $A^p_{\alpha-}$) arising as the projective limit (resp. inductive limit) of the standard weighted Bergman spaces into the growth Frechet space $H^\infty_{\alpha+}$ (resp. growth (LB)-space $H^\infty_{\alpha-}$), which is the projective limit (resp. inductive limit) of the growth Banach spaces. We show that, for an analytic self map $\varphi$ of the unit disc $\mathbb{D}$, the continuities of the weighted composition operator $W_{g,\varphi}$, the Volterra integral operator $T_g$, and the pointwise multiplication operator $M_g$ defined via the identical symbol function are characterized by the same condition …
Preservers Of The Local Spectral Radius Zero Of Jordan Product Of Operators, Mhamed Elhodaibi, Somaya Saber
Preservers Of The Local Spectral Radius Zero Of Jordan Product Of Operators, Mhamed Elhodaibi, Somaya Saber
Turkish Journal of Mathematics
Let $\mathscr{B}(X)$ be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space $X$, and denote by $r_{T}(x)$ the local spectral radius of any operator $T \in \mathscr{B}(X)$ at any vector $x \in X$. In this paper, we characterize surjective maps $\phi$ on $ \mathscr{B}(X)$ satisfying $ r_{\phi(T)\phi(A) + \phi(A)\phi(T)}(x)=0$ if and only if $ r_{TA+AT}(x)=0 $
Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir
Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir
Turkish Journal of Mathematics
In this paper, the existence and uniqueness of the solutions to impulsive coupled system of fractional differential equations with Caputo--Hadamard are investigated. Furthermore, Ulam's type stability of the proposed coupled system is studied. The approach is based on a Perov type fixed point theorem for contractions.
Solvability, Stability, Smoothness And Compactness Of The Set Of Solutions For A Nonlinear Functional Integral Equation, Nguyen Dat Thuc, Le Thi Phuong Ngoc, Nguyen Thanh Long
Solvability, Stability, Smoothness And Compactness Of The Set Of Solutions For A Nonlinear Functional Integral Equation, Nguyen Dat Thuc, Le Thi Phuong Ngoc, Nguyen Thanh Long
Turkish Journal of Mathematics
This paper is devoted to the study of the following nonlinear functional integral equation \begin{equation} f(x)=\sum\limits_{i=1}^{q}\alpha _{i}(x)f(\tau_{i}(x))+\int_{0}^{\sigma_{1}(x)}\Psi \left( x,t,f(\sigma _{2}(t)),\int_{0}^{\sigma_{3}(t)}f(s)ds\right) dt+g(x),\text{ }\forall x\in \lbrack 0,1], \tag{E} \label{E} \end{equation} where $\tau _{i},$ $\sigma _{1},$ $\sigma _{2},$ $\sigma _{3}:[0,1]\rightarrow \lbrack 0,1];$ $\alpha _{i},$ $g:[0,1]\rightarrow \mathbb{R};$ $\Psi :[0,1]\times \lbrack 0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ are the given continuous functions and $f:[0,1]\,\rightarrow \mathbb{R}$ is an unknown function. First, two sufficient conditions for the existence and some properties of solutions of Eq. (E) are proved. By using Banach's fixed point theorem, we have the first sufficient condition yielding existence, uniqueness and stability of the solution. By applying …
Scattering And Characteristic Functions Of A Dissipative Operator Generated By A System Of Equations, Elgi̇z Bayram, Kenan Taş, Eki̇n Uğurlu
Scattering And Characteristic Functions Of A Dissipative Operator Generated By A System Of Equations, Elgi̇z Bayram, Kenan Taş, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper, we consider a system of first-order equations with the same eigenvalue parameter together with dissipative boundary conditions. Applying Lax-Phillips scattering theory and Sz.-Nagy-Foiaş model operator theory we prove a completeness theorem.
On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer
On The Extension Of Hermite-Hadamard Type Inequalities For Co-Ordinated Convex Mappings, Mehmet Zeki̇ Sarikaya, Di̇lşatnur Kiliçer
Turkish Journal of Mathematics
In this paper, we obtain an important inequalities for coordinated convex functions and as a result of these inequalities we give the extension of Hermite-Hadamard type inequalities for Riemann-Liouville fractional integral and logarithmic integral. The inequalities obtained in this study provide generalizations of some result given in earlier works.
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
Turkish Journal of Mathematics
In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.