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2022

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Articles 1021 - 1050 of 1375

Full-Text Articles in Mathematics

Multiplicative Conformable Fractional Dirac System, Sertaç Göktaş, Hi̇kmet Kemaloğlu, Emrah Yilmaz Jan 2022

Multiplicative Conformable Fractional Dirac System, Sertaç Göktaş, Hi̇kmet Kemaloğlu, Emrah Yilmaz

Turkish Journal of Mathematics

In multiplicative fractional calculus, the well-known Dirac system in fractional calculus is redefined. The aim of this study is to analyze some spectral properties such as self-adjointness of the operator, structure of all eigenvalues, orthogonality of distinct eigenfunctions, etc. for this system. Moreover, Green's function in multiplicative case is reconstructed for this system.

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Berezin Symbol Inequalities Via Grüss Type Inequalities And Related Questions, Rami̇z Tapdigoğlu, Mübari̇z Garayev, Najla Altwaijry Jan 2022

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.

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Compact Matrix Operators On Banach Space Of Absolutely $K$-Summable Series, Fadi̇me Gökçe Jan 2022

Compact Matrix Operators On Banach Space Of Absolutely $K$-Summable Series, Fadi̇me Gökçe

Turkish Journal of Mathematics

In a more recent paper [23], Banach spaces of absolutely $k$-summable series $\left\vert T_{\phi }\right\vert _{k}$ have been introduced and studied by Sarıgöl and Agarwal. In this paper, we characterize matrix and compact operators from the space $\left\vert T_{\phi }\right\vert _{k}$ to the classical spaces $c_{0},c$ and $l_{\infty },$ by determining identities or estimates for operator norms and the Hausdorff measure of noncompactness.

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Clairaut Invariant Riemannian Maps With Kahler Structure, Akhilesh Yadav, Kiran Meena Jan 2022

Clairaut Invariant Riemannian Maps With Kahler Structure, Akhilesh Yadav, Kiran Meena

Turkish Journal of Mathematics

In this paper, we study Clairaut invariant Riemannian maps from Kahler manifolds to Riemannian manifolds, and from Riemannian manifolds to Kahler manifolds. We find necessary and sufficient conditions for the curves on the total spaces and base spaces of invariant Riemannian maps to be geodesic. Further, we obtain necessary and sufficient conditions for invariant Riemannian maps from Kahler manifolds to Riemannian manifolds to be Clairaut invariant Riemannian maps. Moreover, we obtain a necessary and sufficient condition for invariant Riemannian maps from Riemannian manifolds to Kahler manifolds to be Clairaut invariant Riemannian maps. We also give nontrivial examples of Clairaut invariant …

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Metric Connection On Tangent Bundle With Berger-Type Deformed Sasaki Metric, Lokman Bi̇len Jan 2022

Metric Connection On Tangent Bundle With Berger-Type Deformed Sasaki Metric, Lokman Bi̇len

Turkish Journal of Mathematics

Let $TM$ be the tangent bundle over an almost antipara-Hermitian manifold endowed with Berger-type deformed Sasaki metric $% ^{BS}g$. In this paper, we introduce the deformed Sasaki metric which Berger-type and study the metric connection of this metric on the tangent bundle. We give some curvature properties of this metric and characterization of projective vector field which preserving the fiber of $\left( TM, ^{BS}g\right) $. Next, we present some geometric results concerning them.

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Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung Jan 2022

Some Properties Of The Matrix Wiener Transform With Related Topics On Hilbert Space, Hyun Soo Chung

Turkish Journal of Mathematics

Main purpose of this paper is to obtain fundamental relationships for the integrals and the matrix Wiener transforms on Hilbert space. Using some technics and properties of matrices of real numbers, we state some algebraic structure of matrices. We then establish evaluation formulas with examples. Furthermore, we define the matrix Wiener transform, and investigate some properties of the matrix Wiener transform. Finally, we establish relationships for the matrix Wiener transform.

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Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad Jan 2022

Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad

Turkish Journal of Mathematics

We present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients $\left \vert b_{0}\right \vert $ and $% \left \vert b_{1}\right \vert $ for functions belonging to this subclass. Furthermore, the Fekete-Szegö inequality $\left \vert b_{1}-\eta b_{0}^{2}\right \vert $ for this subclass is obtained. We also point out some consequences of results.

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Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie Jan 2022

Oscillation Criteria For Third-Order Neutral Differential Equations With Unbounded Neutral Coefficients And Distributed Deviating Arguments, Yibing Sun, Yige Zhao, Qiangqiang Xie

Turkish Journal of Mathematics

This paper focuses on the oscillation criteria for the third-order neutral differential equations with unbounded neutral coefficients and distributed deviating arguments. Using comparison principles, new sufficient conditions improve some known existing results substantially due to less constraints on the considered equation. At last, two examples are established to illustrate the given theorems.

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On The Paper "Generalized Hyperideals In Locally Associativeleft Almost Semihypergroups", Niovi Kehayopulu Jan 2022

On The Paper "Generalized Hyperideals In Locally Associativeleft Almost Semihypergroups", Niovi Kehayopulu

Turkish Journal of Mathematics

This note is written to show that the definition of the ${\cal L}{\cal A}$-semihypergroup by V. Amjad, K. Hila and F. Yousafzai "Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 2014" should be corrected and that it is not enough to replace the multiplication "$\cdot$" of an ${\cal L}{\cal A}$-semigroup by the hyperoperation "$\circ$" to pass from an ${\cal L}{\cal A}$-semigroup to an ${\cal L}{\cal A}$-semihypergroup. The two examples of the paper based on the definition of the ${\cal L}{\cal A}$-semihypergroup are wrong that is a further indication that this definition needs correction. According to the …

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On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya Jan 2022

On The Inclusion Properties For $\Vartheta $-Spirallike Functions Involving Both Mittag-Leffler And Wright Function, Şahsene Altinkaya

Turkish Journal of Mathematics

By making use of the both Mittag-Leffler and Wright function, we establish a new subfamily of the class $S_{\vartheta }$ of $\vartheta $-spirallike functions. The main object of the paper is to provide sufficient conditions for a function to be in this newly established class and to discuss subordination outcomes.

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Boundedness For Variable Fractional Integral Operators And Their Commutators On Herz-Hardy Spaces With Variable Exponent, Yinping Xin Jan 2022

Boundedness For Variable Fractional Integral Operators And Their Commutators On Herz-Hardy Spaces With Variable Exponent, Yinping Xin

Turkish Journal of Mathematics

Let $E\subset\mathbb{R}^n$ be a bounded open set. In this paper, we establish the boundedness of variable fractional integral operators and their commutators on variable Herz-Hardy spaces $H\dot{K}^{\alpha(\cdot),q(\cdot)}_{p(\cdot)}(E)$ with three variable exponents by using the atomic decomposition.

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On Hom-F-Manifold Algebras And Quantization, Abdelkader Benhassine, Taoufik Chtioui, Mohamed Ali Maalaoui, Sami Mabrouk Jan 2022

On Hom-F-Manifold Algebras And Quantization, Abdelkader Benhassine, Taoufik Chtioui, Mohamed Ali Maalaoui, Sami Mabrouk

Turkish Journal of Mathematics

The notion of a $F$-manifold algebras is an algebraic description of a $F$-manifold. In this paper, we introduce the notion of Hom-$F$-manifold algebras which is generalisation of $F$-manifold algebras and Hom-Poisson algebras. We develop the representation theory of Hom-$F$-manifold algebras and generalize the notion of Hom-pre-Poisson algebras by introducing the Hom-pre-$F$-manifold algebras which give rise to a Hom-$F$-manifold algebra through the subadjacent commutative Hom-associative algebra and the subadjacent Hom-Lie algebra. Using Ο-operators on a Hom-$F$-manifold algebras we construct a Hom-pre-$F$-manifold algebras on a module. Then, we study Hom-pre-Lie formal deformations of commutative Hom-associative algebra and we prove that Hom-$F$-manifold algebras …

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Rough Approximations Based On Different Topologies Via Ideals, Ayşegül Çaksu Güler, Esra Dalan Yildirim, Oya Özbakir Jan 2022

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.

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Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar Jan 2022

Clairaut Semi-Invariant Riemannian Maps From Almost Hermitian Manifolds, Sushil Kumar, Rajendra Prasad, Sumeet Kumar

Turkish Journal of Mathematics

In this article, we define Clairaut semi-invariant Riemannian maps (CSIR Maps, In short) from almost Hermitian manifolds onto Riemannian manifolds and investigate fundamental results on such maps. We also obtain conditions for totally geodesicness on distributions defined in the introduced notion. Moreover, we provide an explicit example of CSIR map.

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Product-Type Operators On Weak Vector Valued $\Alpha$-Besov Spaces, Sepideh Nasresfahani, Ebrahim Abbasi Jan 2022

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.

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On Elastic Graph Spines Associated To Quadratic Thurston Maps, Meli̇ke Yeti̇şer, Ali̇ Berkay Yeti̇şer Jan 2022

On Elastic Graph Spines Associated To Quadratic Thurston Maps, Meli̇ke Yeti̇şer, Ali̇ Berkay Yeti̇şer

Turkish Journal of Mathematics

For a quadratic Thurston map having two distinct critical points and $n$ postcritical points, we count the number of possible dynamical portraits. We associate elastic graph spines to several hyperbolic quadratic Thurston rational functions. These functions have four postcritical points, real coefficients, and invariant real intervals. The elastic graph spines are constructed such that each has embedding energy less than one. These are supporting examples to Dylan Thurston's recent positive characterization of rational maps. Using the same characterization, we prove that with a combinatorial restriction on the branched covering and a cycle condition on the dynamical portrait, a quadratic Thurston …

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Hyperelastic Curves Along Riemannian Maps, Tunahan Turhan, Gözde Özkan Tükel, Bayram Şahi̇n Jan 2022

Hyperelastic Curves Along Riemannian Maps, Tunahan Turhan, Gözde Özkan Tükel, Bayram Şahi̇n

Turkish Journal of Mathematics

The main purpose of this paper is to examine what kind of information the smooth Riemannian map defined between two Riemannian manifolds provides about the character of the Riemannian map when a horizontal hyperelastic curve on the total manifold is carried to a hyperelastic curve on the base manifold. For the solution of the mentioned problem, firstly, the behavior of an arbitrary horizontal curve on the total manifold under a Riemannian map is investigated and the equations related to pullback connection are obtained. The necessary conditions are given for the Riemannian map to be h-isotropic or totally umbilical when a …

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Small Genus-$4$ Lefschetz Fibrations On Simply-Connected $4$-Manifolds, Tüli̇n Altunöz Jan 2022

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.

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A Simple And Constructive Proof To A Generalization Of Lüroth's Theorem, Francois Ollivier, Brahim Sadik Jan 2022

A Simple And Constructive Proof To A Generalization Of Lüroth's Theorem, Francois Ollivier, Brahim Sadik

Turkish Journal of Mathematics

A generalization of Lüroth's theorem expresses that every transcendence degree $1$ subfield of the rational function field is a simple extension. In this note we show that a classical proof of this theorem also holds to prove this generalization.

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Gradient Estimates Of A Nonlinear Elliptic Equation For The $V$-Laplacian On Noncompact Riemannian Manifolds, Deng Yihua Jan 2022

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.

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On The Convergence Of The Abel-Poisson Means Of Multiple Fourier Series, Si̇nem Sezer, Meli̇h Eryi̇ği̇t, Si̇mten Bayrakçi Jan 2022

On The Convergence Of The Abel-Poisson Means Of Multiple Fourier Series, Si̇nem Sezer, Meli̇h Eryi̇ği̇t, Si̇mten Bayrakçi

Turkish Journal of Mathematics

Let $ A_\varepsilon (x,f)$ be the Abel-Poisson means of an integrable function $f(x)$ on $n$-dimensional torus $ \mathbf{T}^n, \; \;\; i= 1,\ldots,n \; (n\geq 2) $ in the Euclidean $n$-space. The famous Bochner's theorem asserts that for any function $ f\in L^1(\mathbf{T}^n)$ the Abel-Poisson means $A_\varepsilon (x,f)$ are pointwise converge to $f(x)$ a.e., that is, $$ \underset{\varepsilon \rightarrow0^+}{\lim}\, A_\varepsilon (x,f)= f(x), \;\; a.e.\; x\in \mathbf{T}^n. $$ In this paper we investigate the rate of convergence of Abel-Poisson means at the so-called $\mu$-smoothness point of $f$ .

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The Integer-Antimagic Spectra Of A Disjoint Union Of Hamiltonian Graphs, Uğur Odabaşi, Dan Roberts, Richard M. Low Jan 2022

The Integer-Antimagic Spectra Of A Disjoint Union Of Hamiltonian Graphs, Uğur Odabaşi, Dan Roberts, Richard M. Low

Turkish Journal of Mathematics

Let $A$ be a nontrivial abelian group. A simple graph $G = (V, E)$ is $A$-antimagic, if there exists an edge labeling $f: E(G) \to A \backslash \{0\}$ such that the induced vertex labeling $f^+(v)=\sum_{uv\in E(G)} f(uv)$ is a one-to-one map. The {integer-antimagic spectrum} of a graph $G$ is the set IAM$(G) = \{k: G {is} \mathbb{Z}_k{-antimagic and } k \geq 2\}$. In this paper, we determine the integer-antimagic spectra for a disjoint union of Hamiltonian graphs.

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Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu Jan 2022

Existence And Multiplicity Of Solutions For P(.)-Kirchhoff-Type Equations, Rabi̇l Ayazoğlu, Sezgi̇n Akbulut, Ebubeki̇r Akkoyunlu

Turkish Journal of Mathematics

his paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for $p(.)$-Kirchhoff-type equation% \begin{equation*} \left\{ \begin{array}{c} M\left( \int_{\Omega }\frac{\left\vert \nabla u\right\vert ^{p(x)}}{p(x)}% dx\right) \left( -\Delta _{p(x)}u\right) =f(x,u),\text{ in }\Omega , \\ u=0,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{on }\partial \Omega .% \end{array}% \right. \end{equation*}% Using the mountain pass theorem, fountain theorem, dual fountain theorem and the theory of …

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Li-Yorke Chaos And Topological Distributional Chaos In A Sequence, Naveenkumar Yadav, Sejal Shah Jan 2022

Li-Yorke Chaos And Topological Distributional Chaos In A Sequence, Naveenkumar Yadav, Sejal Shah

Turkish Journal of Mathematics

We study here the topological notion of Li-Yorke chaos defined for uniformly continuous self-maps defined on uniform Hausdorff spaces, which are not necessarily compact metrizable. We prove that a weakly mixing uniformly continuous self-map defined on a second countable Baire uniform Hausdorff space without isolated points is Li-Yorke chaotic. Further, we define and study the notion of topological distributional chaos in a sequence for uniformly continuous self-maps defined on uniform Hausdorff spaces. We prove that Li-Yorke chaos is equivalent to topological distributional chaos in a sequence for uniformly continuous self-maps defined on second countable Baire uniform Hausdorff space without isolated …

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An Alternative Method For Spp With Full Rank (2,1)-Block Matrix And Nonzero Right-Hand Side Vector, Gül Karaduman, Mei Yang Jan 2022

An Alternative Method For Spp With Full Rank (2,1)-Block Matrix And Nonzero Right-Hand Side Vector, Gül Karaduman, Mei Yang

Turkish Journal of Mathematics

We propose an alternative method to solve large linear saddle point problems arising from computational sciences and engineering such as finite element approximations to Stokes problems, image reconstructions, tomography, genetics, statistics, and model order reductions for dynamical systems. Such problems have large sparse 2-by-2 block structure coefficient matrices with zero (2,2)-block matrix. A new technique is presented to solve saddle point problems with full row rank (2,1)-block matrix and nonzero right-hand side vector. By constructing a projection matrix and transforming the original problem into a least squares problem, a new reduced least squares problem is solved via the well-known iterative …

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Quasilinear Systems With Unpredictable Relay Perturbations, Mehmet Onur Fen, Fatma Fen Jan 2022

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.

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On Nonhomogeneous Geometric Quadratic Stochastic Operators, Siti Nurlaili Karim, Nur Zatul Akmar Hamzah, Nasir Ganikhodjaev Jan 2022

On Nonhomogeneous Geometric Quadratic Stochastic Operators, Siti Nurlaili Karim, Nur Zatul Akmar Hamzah, Nasir Ganikhodjaev

Turkish Journal of Mathematics

n this paper, we construct a nonhomogeneous geometric quadratic stochastic operator generated by 2-partition $\xi$ on countable state space $X=\mathbb{Z}^{*}$. The limiting behavior of such operator is studied. We have proved that such operator possesses the regular property.

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Numerical Simulations Of Traveling Waves In A Counterflow Filtration Combustion Model, Fati̇h Özbağ Jan 2022

Numerical Simulations Of Traveling Waves In A Counterflow Filtration Combustion Model, Fati̇h Özbağ

Turkish Journal of Mathematics

We focused on traveling combustion waves that appear in a simplified, one-dimensional combustion model in porous media. The system we consider is a reaction-convection-diffusion system that can be reduced into two-dimension in order to prove traveling waves by phase plane analysis. In previous studies combustion wave velocity was assumed positive and their existence was proven. Also, all possible wave sequences that solve boundary value problems on infinite intervals with constant boundary data were identified. In this study, we generalize the previous work by including the case of negative combustion wave speed and taking the assumption that oxygen is carried faster …

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Study Of The $\Phi$-Generalized Type $K$-Fractional Integrals Or Derivatives And Some Of Their Properties, Mustafa Aydin, Nazim I. Mahmudov Jan 2022

Study Of The $\Phi$-Generalized Type $K$-Fractional Integrals Or Derivatives And Some Of Their Properties, Mustafa Aydin, Nazim I. Mahmudov

Turkish Journal of Mathematics

A novel fractional integral in the sense of Riemann-Liouville integral and two new fractional derivatives in the sense of Riemann-Liouville derivative and Caputo derivative with respect to another function and two parameters are introduced. Some significant properties of them are presented like semigroup property, inverse property, etc. The solution of the Cauchy-type problem for the nonhomogenous linear differential equation with the $\phi$-generalized Caputo $k$-fractional derivative is given by using the method of successive approximation.

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On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic Jan 2022

On Sharpening And Generalization Of Rivlin's Inequality, Prasanna Kumar, Gradimir Milovanovic

Turkish Journal of Mathematics

n inequality due to T. J. Rivlin from 1960 states that if $P(z)$ is a polynomial of degree $n$ having no zeros in $ z

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