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On A Class Of Nonlocal Porous Medium Equations Of Kirchhoff Type, Uğur Sert
On A Class Of Nonlocal Porous Medium Equations Of Kirchhoff Type, Uğur Sert
Turkish Journal of Mathematics
We study the Dirichlet problem for the degenerate parabolic equation of the Kirchhoff type \[ u_{t}-a\left(\ u\ _{L^{p}(\Omega)}^{p}\right)\sum\limits_{i=1}^{n}D_{i}\left( \left\vert u\right\vert ^{p-2}D_{i}u\right) +b\left( x,t,u\right)=f\left( x,t\right) \quad \text{in $Q_T=\Omega \times (0,T)$}, \] where $p\geq2$, $T>0$, $\Omega \subset \mathbb{R}^{n}$, $n\geq 2$, is a smooth bounded domain. The coefficient $a(\cdot)$ is real-valued function defined on $\mathbb{R}_+$ and $b(\cdot,\cdot,\tau)$ is a measurable function with variable nonlinearity in $\tau$. We prove existence of weak solutions of the considered problem under appropriate and general conditions on $a$ and $b$. Sufficient conditions for uniqueness are found and in the case $f\equiv0$ the decay rates for $\ u\ …
On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz
On The Extended Zero-Divisor Graph Of Strictly Partial Transformation Semigroup, Emrah Korkmaz
Turkish Journal of Mathematics
Given a commutative ring $R$, the zero-divisor graph of $R$ is an undirected simple graph with vertices the nonzero zero-divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0$. In [8], Redmond presented different versions of zero-divisor graphs of noncommutative rings. The main aim of this paper is to analyse these graphs for the semigroup $\mathcal{SP}_{n}$ of all strictly partial transformations on the set $X_{n}=\{1,2,\dots,n\}$.
Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas
Characterization Of Exponential Polynomial As Solution Of Certain Type Of Nonlinear Delay-Differential Equation, Abhijit Banerjee, Tania Biswas
Turkish Journal of Mathematics
In this paper, we have characterized the nature and form of solutions of the following nonlinear delay-differential equation: $$f^{n}(z)+\sum_{i=1}^{n-1}b_{i}f^{i}(z)+q(z)e^{Q(z)}L(z,f)=P(z),$$ where $b_i\in\mathbb{C}$, $L(z,f)$ are a linear delay-differential polynomial of $f$; $n$ is positive integers; $q$, $Q$ and $P$ respectively are nonzero, nonconstant and any polynomials. Different special cases of our result will accommodate all the results of [J. Math. Anal. Appl., 452(2017), 1128-1144; Mediterr. J. Math., 13(2016), 3015-3027; Open Math., 18(2020), 1292-1301]. Thus our result can be considered as an improvement of all of them. We have also illustrated a handful number of examples to show that all the cases as …
On Minimal Absolutely Pure Domain Of Rd-Flat Modules, Yusuf Alagöz
On Minimal Absolutely Pure Domain Of Rd-Flat Modules, Yusuf Alagöz
Turkish Journal of Mathematics
Given modules $A_{R}$ and $_{R}B$, $_{R}B$ is called absolutely $A_{R}$-pure if for every extension $_{R}C$ of $_{R}B$, $A\otimes B\rightarrow A\otimes C$ is a monomorphism. The class $\underline{\mathfrak{Fl}}^{-1}(A_{R})=$\{$_{R}B$ : $_{R}B$ is absolutely $A_{R}$-pure\} is called the absolutely pure domain of a module $A_{R}$. If $_{R}B$ is divisible, then all short exact sequences starting with $B$ is RD-pure, whence $B$ is absolutey $A$-pure for every $RD$-flat module $A_{R}$. Thus the class of divisible modules is the smallest possible absolutely pure domain of an $RD$-flat module. In this paper, we consider $RD$-flat modules whose absolutely pure domains contain only divisible modules, and we …
Matrix Mappings And Compact Operators For Schröder Sequence Spaces, Muhammet Ci̇hat Dağli
Matrix Mappings And Compact Operators For Schröder Sequence Spaces, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we discuss the domain of a recently defined conservative matrix, constructed by means of the Schröder numbers in the spaces of $p-$absolutely summable sequences and bounded sequences. We determine the $\beta-$duals of the Banach spaces, introduced here, and present characterization of some matrix operators. Moreover, we give the characterization of certain compact operators via the Hausdorff measure of noncompactness.
On Properties Of The Reeb Vector Field Of $(\Alpha,\Beta)$ Trans-Sasakian Structure, Alexander Yampolsky
On Properties Of The Reeb Vector Field Of $(\Alpha,\Beta)$ Trans-Sasakian Structure, Alexander Yampolsky
Turkish Journal of Mathematics
The paper focused on the mean curvature and totally geodesic property of the Reeb vector field $\xi$ on $(\alpha,\beta)$ trans-Sasakian manifold $M$ of dimension $(2n+1)$ as a submanifold in the unit tangent bundle $T_1M$ with Sasaki metric $g_S$. We give an explicit formula for the norm of mean curvature vector of the submanifold $\xi(M)\subset (T_1M,g_S)$. As a byproduct, for the Reeb vector field, we get some known results concerning its minimality, harmonicity and the property to define a harmonic map. We prove that on connected proper trans-Sasakian manifold the Reeb vector field does not give rise to totally geodesic submanifold …
On A Generalization Of Szasz-Mirakyan Operators Including Dunkl-Appell Polynomials, Serdal Yazici, Fatma Taşdelen Yeşi̇ldal, Bayram Çeki̇m
On A Generalization Of Szasz-Mirakyan Operators Including Dunkl-Appell Polynomials, Serdal Yazici, Fatma Taşdelen Yeşi̇ldal, Bayram Çeki̇m
Turkish Journal of Mathematics
In this study, we have introduced a generalization of Szasz-Mirakyan operators including Dunkl-Appell polynomials with help of sequences satisfying certain conditions and have derived some approximation properties of this generalization.
Unitary Equivalence To Truncated Hankel Operators, Xi Zhao, Tao Yu
Unitary Equivalence To Truncated Hankel Operators, Xi Zhao, Tao Yu
Turkish Journal of Mathematics
In this paper, we characterize the operators which are unitarily equivalent to truncated Hankel operators. We show that every rank one operator and every $2\times 2$ matrix is unitarily equivalent to a truncated Hankel operator. Furthermore, we get that certain sum of tenser products of truncated Hankel operators is unitarily equivalent to a truncated Hankel operator.
Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo
Semisymmetric Hypersurfaces In Complex Hyperbolic Two-Plane Grassmannians, Doo Hyun Hwang, Changhwa Woo
Turkish Journal of Mathematics
In this paper, we introduce new notions of symmetric operators such as semisymmetric shape operator and structure Jacobi operator in complex hyperbolic two-plane Grassmannians. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with such notions.
Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh
Equicontinuity And Sensitivity On Countable Amenable Semigroup, Nader Asadi Karam, Mohammad Kbari Tootkaboni, Abbas Sahleh
Turkish Journal of Mathematics
In this paper, we obtain the classification of topological dynamical systems with a discrete action. The equicontinuity and sensitivity for amenable discrete countable semigroup action are shown by the left Følner sequence. We consider the notion of uniquely ergodic and mean equicontinuous on amenable discrete countable semigroup action and develop the notion of density with respect to the Følner sequence on equicontinuous and sensitivity.
$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus
$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus
Turkish Journal of Mathematics
In the present article, making use of the $(p,q)$-Hurwitz zeta function, we provide and investigate a new integral operator. Also, we define two families ${\mathcal{S}\mathcal{M}}_{p,q}\left(\xi ,\zeta,\delta,u,\tau \right)$ and ${\mathcal{S}\mathcal{C}}_{p,q}\left(\lambda, \zeta,\vartheta,u,\tau \right)$ of biunivalent and holomorphic functions in the unit disc connected with $(p,q)$-Chebyshev Polynomials. Then we find coefficient estimates $\left a_2\right $ and $\left a_3\right .$ Finally, we obtain Fekete-Szeg$\ddot{\mathrm{o}}$ inequalities for these families.
Inverse Nodal Problems For Dirac Type Integro Differential System With A Nonlocal Boundary Condition, Baki̇ Keski̇n
Inverse Nodal Problems For Dirac Type Integro Differential System With A Nonlocal Boundary Condition, Baki̇ Keski̇n
Turkish Journal of Mathematics
In this paper, the Dirac type integro differential system\ with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem.
The Dual Spaces Of Variable Anisotropic Hardy-Lorentz Spaces And Continuity Of A Class Of Linear Operators, Wenhua Wang, Aiting Wang
The Dual Spaces Of Variable Anisotropic Hardy-Lorentz Spaces And Continuity Of A Class Of Linear Operators, Wenhua Wang, Aiting Wang
Turkish Journal of Mathematics
In this paper, the authors obtain the continuity of a class of linear operators on variable anisotropic Hardy--Lorentz spaces. In addition, the authors also obtain that the dual space of variable anisotropic Hardy-Lorentz spaces is the anisotropic BMO-type spaces with variable exponents. This result is still new even when the exponent function $p(\cdot)$ is $p$.
On The Solutions Of Fractional Integro-Differential Equations Involving Ulam-Hyers-Rassias Stability Results Via $\Psi$-Fractional Derivative With Boundary Value Conditions, Kulandhivel Karthikeyan, Gobi Selvaraj Murugapandian, Özgür Ege
On The Solutions Of Fractional Integro-Differential Equations Involving Ulam-Hyers-Rassias Stability Results Via $\Psi$-Fractional Derivative With Boundary Value Conditions, Kulandhivel Karthikeyan, Gobi Selvaraj Murugapandian, Özgür Ege
Turkish Journal of Mathematics
In this paper, we study boundary value problems for the impulsive integro-differential equations via $\psi$-fractional derivative. The contraction mapping concept and Schaefer's fixed point theorem are used to produce the main results. The results reported here are more general than those found in the literature, and some special cases are presented. Furthermore, we discuss the Ulam-Hyers-Rassias stability of the solution to the proposed system.
A Fixed Point Theorem Using Condensing Operators And Its Applications To Erdelyi--Kober Bivariate Fractional Integral Equations, Anupam Das, Mohsen Rabbani, Bipan Hazarika, Sumati Kumari Panda
A Fixed Point Theorem Using Condensing Operators And Its Applications To Erdelyi--Kober Bivariate Fractional Integral Equations, Anupam Das, Mohsen Rabbani, Bipan Hazarika, Sumati Kumari Panda
Turkish Journal of Mathematics
The primary aim of this article is to discuss and prove fixed point results using the operator type condensing map, and to obtain the existence of solution of Erdelyi-Kober bivariate fractional integral equation in a Banach space. An instance is given to explain the results obtained, and we construct an iterative algorithm by sinc interpolation to find an approximate solution of the problem with acceptable accuracy.
Existence Of Fixed Points In Conical Shells Of A Banach Space For Sum Of Two Operators And Application In Odes, Amirouche Mouhous, Karima Mebarki
Existence Of Fixed Points In Conical Shells Of A Banach Space For Sum Of Two Operators And Application In Odes, Amirouche Mouhous, Karima Mebarki
Turkish Journal of Mathematics
In this work a new functional expansion-compression fixed point theorem of Leggett--Williams type is developed for a class of mappings of the form $T+F,$ where $(I-T)$ is Lipschitz invertible map and $F$ is a $k$-set contraction. The arguments are based upon recent fixed point index theory in cones of Banach spaces for this class of mappings. As application, our approach is applied to prove the existence of nontrivial nonnegative solutions for three-point boundary value problem.
Bernstein-Walsh-Type Inequalities For Derivatives Of Algebraic Polynomials On The Regions Of Complex Plane, Naci̇ye Peli̇n Özkartepe, Cevahi̇r Doğanay Gün, Fahreddi̇n Abdullayev
Bernstein-Walsh-Type Inequalities For Derivatives Of Algebraic Polynomials On The Regions Of Complex Plane, Naci̇ye Peli̇n Özkartepe, Cevahi̇r Doğanay Gün, Fahreddi̇n Abdullayev
Turkish Journal of Mathematics
In this paper, we study Bernstein-Walsh-type estimates for the derivatives of an arbitrary algebraic polynomial on some general regions of the complex plane.
Globally Unsolvability Of Integro-Differential Diffusion Equation And System With Exponential Nonlinearities, Meiirkhan Borikhanov
Globally Unsolvability Of Integro-Differential Diffusion Equation And System With Exponential Nonlinearities, Meiirkhan Borikhanov
Turkish Journal of Mathematics
In this paper, the Cauchy problem for an integro-differential diffusion equation and a system with nonlocal nonlinear sources are considered. The results on the existence of local integral solutions and the nonexistence of global weak solutions to the nonlinear integro-differential diffusion equation and system are presented.
On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan
On A Certain Type Of Warped-Twisted Product Submanifolds, Si̇bel Gerdan Aydin, Hakan Mete Taştan
Turkish Journal of Mathematics
We introduce a certain type of warped-twisted product submanifolds which is called warped-twisted product hemislant submanifolds of the form $_{f_2}M^{\bot}\times_{f_1}M^{\theta}$ with warping function $f_2$ on $M^\theta$ and twisting function $f_1$, where $M^\bot$ is a totally real and $M^\theta$ is a slant submanifold of a globally conformal Kaehler manifold. We prove that a warped-twisted product hemislant submanifold of a globally conformal Kaehler manifold is a locally doubly warped product. Then we establish a general inequality for doubly warped product mixed geodesic hemislant submanifolds and get some results for such submanifolds by using the equality sign of the general inequality.
Approximation By Sampling Kantorovich Series In Weighted Spaces Of Functions, Tuncer Acar, Osman Alagöz, Ali̇ Aral, Dani̇lo Costarelli̇, Meti̇n Turgay, Gianluca Vinti
Approximation By Sampling Kantorovich Series In Weighted Spaces Of Functions, Tuncer Acar, Osman Alagöz, Ali̇ Aral, Dani̇lo Costarelli̇, Meti̇n Turgay, Gianluca Vinti
Turkish Journal of Mathematics
This paper studies the convergence of the so-called sampling Kantorovich operators for functions belonging to weighted spaces of continuous functions. This setting allows us to establish uniform convergence results for functions that are not necessarily uniformly continuous and bounded on $\mathbb{R}$. In that context we also prove quantitative estimates for the rate of convergence of the family of the above operators in terms of weighted modulus of continuity. Finally, pointwise convergence results in quantitative form by means of Voronovskaja type theorems have been also established.
A Fredholm Theory On Krein Spaces And Its Application To Weyl-Type Theorems And Homogeneous Equations, Danilo Polo Ojito, Jose Sanabria, Yina Ospino Buelvas
A Fredholm Theory On Krein Spaces And Its Application To Weyl-Type Theorems And Homogeneous Equations, Danilo Polo Ojito, Jose Sanabria, Yina Ospino Buelvas
Turkish Journal of Mathematics
In this paper, we review the approach presented by An and Heo on the study of Weyl-type theorems for self-adjoint operators on Krein spaces and show that this approach is not appropriate due to a fallacy. Motivated by this fact, we define a new modification of the kernel of a bounded linear operator on a Krein space, namely $J$-kernel, which allows us to successfully introduce a Fredholm theory in this context and study some variations of Weyl-type theorems for bounded linear operators defined on these spaces. In addition, we will describe the $J$-index in terms of solution sets of homogeneous …
Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania
Dissipative Mechanism And Global Attractor For Modified Swift-Hohenberg Equation In $R^{N}$, Radoslaw Czaja, Maria Kania
Turkish Journal of Mathematics
A Cauchy problem for a modification of the Swift-Hohenberg equation in $R^{N}$ with a mildly integrable potential is considered. Applying the dissipative mechanism of fourth order parabolic equations in unbounded domains, it is shown that the equation generates a semigroup of global solutions possessing a global attractor in the scale of Bessel potential spaces and in $H^2(R^{N})$ in particular.
On Parabolic And Elliptic Elements Of The Modular Group, Bi̇lal Demi̇r, Özden Koruoğlu
On Parabolic And Elliptic Elements Of The Modular Group, Bi̇lal Demi̇r, Özden Koruoğlu
Turkish Journal of Mathematics
The modular group $\Gamma=PSL(2, \mathbf{Z})$ is isomorphic to the free product of two cyclic groups of orders $2$ and $3$. In this paper, we give a necessary and sufficient condition for the existence of elliptic and parabolic elements in $\Gamma$ with a given cusp point. Then we give an algorithm to obtain such elements in words of generators using continued fractions and paths in the Farey graph.
Initial Value Problem For Elastic System In Transversely Isotropic Inhomogeneous Media, Meltem Altunkaynak
Initial Value Problem For Elastic System In Transversely Isotropic Inhomogeneous Media, Meltem Altunkaynak
Turkish Journal of Mathematics
In this paper, we consider an initial value problem (IVP) for three dimensional elasticity system in a transversely isotropic inhomogeneous media. We will rewrite the problem in the form of Fourier images by means of Fourier transform method. After some arrangements, the problem is reduced to integral equations in the vector form. Using the properties of the vector integral equation and successive approximations method, an explicit formula for the solution of the IVP in transversely isotropic inhomogeneous media is constructed, and existence and uniqueness of the solution is stated. By a computational example, we illustrate the robustness of the method.
A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici
A Note On The Transfinite Diameter Of Bernstein Sets, Özcan Yazici
Turkish Journal of Mathematics
A compact set $K\subset \mathbb C^n$ is called Bernstein set if, for some constant $M>0$, the following inequality $$ D^{\alpha}P _K\leq M^{ \alpha }(\deg P)^{ \alpha } P _K $$ is satisfied for every multiindex $\alpha\in \mathbb N^n$ and for every polynomial $P$. We provide here a lower bound for the transfinite diameter of Bernstein sets by using generalized extremal Leja points.
On Finite Nonsolvable Groups Whose Cyclic $P$-Subgroups Of Equal Order Are Conjugate, Robert Van Der Waall, Sezgi̇n Sezer
On Finite Nonsolvable Groups Whose Cyclic $P$-Subgroups Of Equal Order Are Conjugate, Robert Van Der Waall, Sezgi̇n Sezer
Turkish Journal of Mathematics
The structure of the nonsolvable (P)-groups is completely described in this article. By definition, a finite group $G$ is called a (P)-group if any two cyclic $p$-subgroups of the same order are conjugate in $G$, whenever $p$ is a prime number dividing the order of $G$.
Some Convergence, Stability, And Data Dependence Results For $K^{\Ast }$ Iterative Method Of Quasi-Strictly Contractive Mappings, Ruken Çeli̇k, Neci̇p Şi̇mşek
Some Convergence, Stability, And Data Dependence Results For $K^{\Ast }$ Iterative Method Of Quasi-Strictly Contractive Mappings, Ruken Çeli̇k, Neci̇p Şi̇mşek
Turkish Journal of Mathematics
In a recent paper, Yu et al. obtained convergence and stability results of the $K^{\ast }$ iterative method for quasi-strictly contractive mappings [An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography. AIMS Mathematics 2021; 6 (7): 6699-6714.]. To guarantee these convergence and stability results, the authors imposed some strong conditions on parametric control sequences which are used in the $K^{\ast }$ iterative method. The aim of the presented work is twofold: (a) to recapture the aforementioned results without any restrictions imposed on the mentioned parametric control sequences (b) to complete the work of Yu et …
On The Convergence And Stability Analysis Of Finite-Difference Methods For The Fractional Newell-Whitehead-Segel Equations, İnci̇ Çi̇li̇ngi̇r Süngü, Emre Aydin
On The Convergence And Stability Analysis Of Finite-Difference Methods For The Fractional Newell-Whitehead-Segel Equations, İnci̇ Çi̇li̇ngi̇r Süngü, Emre Aydin
Turkish Journal of Mathematics
In this study, standard and non-standard finite-difference methods are proposed for numerical solutions of the time-spatial fractional generalized Newell-Whitehead-Segel equations describing the dynamical behavior near the bifurcation point of the Rayleigh-Benard convection of binary fluid mixtures. The numerical solutions have been found for high values of $p$ which shows the degree of nonlinear terms in the equations. The stability and convergence conditions of the obtained difference schemes are determined for each value of $p$. Errors of methods for various values of $p$ are given in tables. The compatibility of exact solutions and numerical solutions and the effectiveness of the methods …
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.