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2019

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Articles 1021 - 1050 of 1389

Full-Text Articles in Mathematics

Riemannian Manifolds Admitting A New Type Of Semisymmetric Nonmetric Connection, Sudhakar K. Chaubey, Ahmet Yildiz Jan 2019

Riemannian Manifolds Admitting A New Type Of Semisymmetric Nonmetric Connection, Sudhakar K. Chaubey, Ahmet Yildiz

Turkish Journal of Mathematics

We define a new type of semisymmetric nonmetric connection on a Riemannian manifold and establish its existence. It is proved that such connection on a Riemannian manifold is projectively invariant under certain conditions. We also find many basic results of the Riemannian manifolds and study the properties of group manifolds and submanifolds of the Riemannian manifolds with respect to the semisymmetric nonmetric connection. To validate our findings, we construct a nontrivial example of a $3$-dimensional Riemannian manifold equipped with a semisymmetric nonmetric connection.

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Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r Jan 2019

Fixed Point Properties For A Degenerate Lorentz-Marcinkiewicz Space, Veysel Nezi̇r

Turkish Journal of Mathematics

We construct an equivalent renorming of $\ell^1$, which turns out to produce a degenerate $\ell^1$-analog Lorentz-Marcinkiewicz space $\ell_{\delta,1}$, where the weight sequence $\delta={(\delta_n)}_{n\in\N}=(2,1,1,1,\cdots)$ is a decreasing positive sequence in $\ell^\infty\backslash c_0$, rather than in $c_0\backslash\ell^1$ (the usual Lorentz situation). Then we obtain its isometrically isomorphic predual $\ell^0_{\delta,\infty}$ and dual $\ell_{\delta,\infty}$, corresponding degenerate $c_0$-analog and $\ell^\infty$-analog Lorentz-Marcinkiewicz spaces, respectively. We prove that both spaces $\ell_{\delta,1}$ and $\ell^0_{\delta,\infty}$ enjoy the weak fixed point property (w-fpp) for nonexpansive mappings yet they fail to have the fixed point property (fpp) for nonexpansive mappings since they contain an asymptotically isometric copy of $\ell^1$ and $c_0$, …

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Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova Jan 2019

Basicity Of A System Of Exponents With A Piecewise Linear Phase In Morrey-Type Spaces, Bilal Bilalov, Fidan Seyidova

Turkish Journal of Mathematics

In this paper a perturbed system of exponents with a piecewise linear phase depending on two real parameters is considered. The sufficient conditions for these parameters are found, under which the considered system of exponents is complete, minimal, or it forms a basis for a Morrey-type space.

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Weak-Stability And Saddle Point Theorems For A Multiobjective Optimization Problem With An Infinite Number Of Constraints, Ta Quang Son, Ching Feng Wen Jan 2019

Weak-Stability And Saddle Point Theorems For A Multiobjective Optimization Problem With An Infinite Number Of Constraints, Ta Quang Son, Ching Feng Wen

Turkish Journal of Mathematics

In this paper, we focus on weak-stability and saddle point theorems of multiobjective optimization problems that have an infinite number of constraints. The obtained results are based on the notion of weak-subdifferentials for vector functions. Some properties of weak stability for the problems are introduced. Relationships between strong duality and saddle points of the augmented Lagrange vector functions associated to the problems are investigated. Connections between weak-stability and saddle point theorems of the problems are established. An example is given.

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On Hypercyclic Fully Zero-Simple Semihypergroups, Mario De Salvo, Domenico Freni, Giovanni Lo Faro Jan 2019

On Hypercyclic Fully Zero-Simple Semihypergroups, Mario De Salvo, Domenico Freni, Giovanni Lo Faro

Turkish Journal of Mathematics

Let $\mfI$ be the class of fully zero-simple semihypergroups generated by a hyperproduct. In this paper we study some properties of residual semihypergroup $(H_+, \star)$ of a semihypergroup $(H,\circ)\in \mfI$. Moreover, we find sufficient conditions for $(H,\circ)$ and $(H_+, \star)$ to be cyclic.

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Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu Jan 2019

Some Results Related To The Berezin Number Inequalities, Ulaş Yamanci, Mübari̇z Tapdigoğlu

Turkish Journal of Mathematics

In this paper, we prove reverse inequalities for the so-called Berezin number of some operators. Also, by using the classical Jensen and Young inequalities, we obtain upper bounds for Berezin number of $A^{\alpha}XB^{\alpha}$ and $A^{\alpha}XB^{1-\alpha}$ for the case when $0\leq\alpha\leq1$.

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An Integral-Boundary Value Problem For A Partial Differential Equation Of Second Order, Anar Assanova Jan 2019

An Integral-Boundary Value Problem For A Partial Differential Equation Of Second Order, Anar Assanova

Turkish Journal of Mathematics

An integral-boundary value problem for a hyperbolic partial differential equation in two independent variables is considered. By introducing additional functional parameters, we investigate the solvability of the problem and develop an algorithm for finding its approximate solutions. The problem is reduced to an equivalent one, consisting of the Goursat problem for a hyperbolic equation with parameters and boundary value problems with an integral condition for ODEs with respect to the parameters entered. We propose an algorithm to find an approximate solution to the original problem, which is based on the algorithm for finding a solution to the equivalent problem. The …

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The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul Jan 2019

The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul

Turkish Journal of Mathematics

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: $$\Delta x(n) = p(n) + b(n)h(x(n)) + \sum^{n}_{k = -\infty}B(n, k)g(x(k)).$$ We employ a Krasnosel'ski\u{i} type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.

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Multiplication Modules With Prime Spectrum, Ortaç Öneş, Mustafa Alkan Jan 2019

Multiplication Modules With Prime Spectrum, Ortaç Öneş, Mustafa Alkan

Turkish Journal of Mathematics

The subject of this paper is the Zariski topology on a multiplication module $M$ over a commutative ring $R$. We find a characterization for the radical submodule $rad_{M}(0)$ and also show that there are proper ideals $I_{1},...,I_{n}$ of $R$ such that $rad_{M}(0)=rad_{M}(\left( I_{1}...I_{n}\right) M)$. Finally, we prove that the spectrum $Spec(M)$ is irreducible if and only if $M$ is the finite sum of its submodules, whose $ \mathcal{T}$-radicals are prime in $M$.

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Studying New Generalizations Of Max-Min Matrices With A Novel Approach, Emrah Kiliç, Talha Arikan Jan 2019

Studying New Generalizations Of Max-Min Matrices With A Novel Approach, Emrah Kiliç, Talha Arikan

Turkish Journal of Mathematics

We consider new kinds of max and min matrices, $\left[ a_{\max(i,j)}\right] _{i,j\geq1}$ and $\left[ a_{\min(i,j)}\right] _{i,j\geq1},$ as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence $\left\{ a_{n}\right\} $ have been studied. We derive their $LU$ and Cholesky decompositions and their inverse matrices as well as the $LU$-decompositions of their inverses. Some interesting corollaries will be presented.

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A Description For The Compactification Of The Orbit Space, Dünya Karapinar, Ali̇ Arslan Özkurt Jan 2019

A Description For The Compactification Of The Orbit Space, Dünya Karapinar, Ali̇ Arslan Özkurt

Turkish Journal of Mathematics

Let$\ X$ be a locally compact and noncompact$\ G-$space with a compact group $G$. In this paper, we give some useful description of a compactification of the orbit space $X/G$ when it is an orbit space of a $G-$compactification of $X$. As an application, we show that the closed bounded interval $[a,b]$ is homeomorphic to the space of maximal ideals with Stone topology of uniformly continuous even functions subring of $\ C^{\ast }(\mathbb{R})$.

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Approximation By Generalized Bernstein-Stancu Operators, Nursel Çeti̇n, Voichita Adriana Radu Jan 2019

Approximation By Generalized Bernstein-Stancu Operators, Nursel Çeti̇n, Voichita Adriana Radu

Turkish Journal of Mathematics

In this paper, we investigate approximation properties of the Stancu type generalization of the $\alpha$-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.

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On Hirano Inverses In Rings, Huanyin Chen, Marjan Sheibani Abdolyousefi Jan 2019

On Hirano Inverses In Rings, Huanyin Chen, Marjan Sheibani Abdolyousefi

Turkish Journal of Mathematics

We completely characterize a subclass of Drazin inverses by means of tripotents and nilpotents. We prove that an element $a$ in a ring $R$ has Hirano inverse if and only if $a^2\in R$ has strongly Drazin inverse, if and only if $a-a^3$ is nilpotent. If $\frac{1}{2}\in R$, we prove that $a\in R$ has Hirano inverse if and only if there exists $p^3=p\in comm^2(a)$ such that $a-p\in N(R)$, if and only if there exist two idempotents $e,f\in comm^2(a)$ such that $a+e-f\in N(R)$. Multiplicative and additive results for this generalized inverse are thereby obtained.

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Categorified Groupoid-Sets And Their Burnside Ring, Laiachi El Kaoutit, Leonardo Spinosa Jan 2019

Categorified Groupoid-Sets And Their Burnside Ring, Laiachi El Kaoutit, Leonardo Spinosa

Turkish Journal of Mathematics

We explore the category of internal categories in the usual category of (right) group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a new Burnside theory, where the equivalence relation between two categorified group-sets is given by a particular equivalence between the underlying categories. We also exhibit some of the differences between the old Burnside theory and the new one. Lastly, we briefly explain how to extend these new techniques and concepts to the context of groupoids, employing the categories of (right) groupoid-sets, aiming by this to give an alternative approach to the classical Burnside ring …

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On Ps-Drazin Inverses In A Ring, Huanyin Chen, Tuğçe Çalci Jan 2019

On Ps-Drazin Inverses In A Ring, Huanyin Chen, Tuğçe Çalci

Turkish Journal of Mathematics

An element $a$ in a ring $R$ has a ps-Drazin inverse if there exists $b\in comm^2(a)$ such that $b=bab, (a-ab)^k\in J(R)$ for some $k\in {\Bbb N}$. Elementary properties of ps-Drazin inverses in a ring are investigated here. We prove that $a\in R$ has a ps-Drazin inverse if and only if $a$ has a generalized Drazin inverse and $(a-a^2)^k\in J(R)$ for some $k\in {\Bbb N}$. We show Cline's formula and Jacobson's lemma for ps-Drazin inverses. The additive properties of ps-Drazin inverses in a Banach algebra are obtained. Moreover, we completely determine when a $2\times 2$ matrix $A\in M_2(R)$ over a local …

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The Boundedness Of $H$-Admissible Fourier Integral Operators On Bessel Potential Spaces, Omar Farouk Aid, Abderrahmane Senoussaoui Jan 2019

The Boundedness Of $H$-Admissible Fourier Integral Operators On Bessel Potential Spaces, Omar Farouk Aid, Abderrahmane Senoussaoui

Turkish Journal of Mathematics

The aim of this work is to study the boundedness of $h$-admissible Fourier integral operators. These operators are bounded on the Bessel potential spaces if the weight of the amplitude is bounded.

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Fibonacci And Lucas Numbers As Products Of Two Repdigits, Fati̇h Erduvan, Refi̇k Keski̇n Jan 2019

Fibonacci And Lucas Numbers As Products Of Two Repdigits, Fati̇h Erduvan, Refi̇k Keski̇n

Turkish Journal of Mathematics

In this study, it is shown that the largest Fibonacci number that is the product of two repdigits is $F_{10}=55=5\cdot 11=55\cdot 1$ and the largest Lucas number that is the product of two repdigits is $L_{6}=18=2\cdot 9=3\cdot 6.$

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Some Permutations And Complete Permutation Polynomials Over Finite Fields, Pinar Ongan, Burcu Gülmez Temür Jan 2019

Some Permutations And Complete Permutation Polynomials Over Finite Fields, Pinar Ongan, Burcu Gülmez Temür

Turkish Journal of Mathematics

In this paper we determine $b\in\F_{q^n}^*$ for which the polynomial $f(x)=x^{s+1}+bx\in\F_{q^n}[x]$ is a permutation polynomial and determine $b\in\F_{q^n}^*$ for which the polynomial $f(x)=x^{s+1}+bx\in\F_{q^n}[x]$ is a complete permutation polynomial where $s=\frac{q^n-1}{t}, t\in \mathbb{Z}^+$ such that $t\mid q^n-1$.

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Positivity Of Continuous Time Irregular Linear Descriptor Systems, Mahmoud Mansouri, Kameleh Nassiri Jan 2019

Positivity Of Continuous Time Irregular Linear Descriptor Systems, Mahmoud Mansouri, Kameleh Nassiri

Turkish Journal of Mathematics

The positivity of continuous-time irregular linear descriptor systems is investigated in this study. The present method is introduced based on Weierstrass decomposition. We obtain necessary and sufficient conditions for the positivity of the linear irregular descriptor systems. The conditions are investigated by two examples with Simulink/MATLAB.

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$(P,Q)$-Lucas Polynomial Coefficient Inequalities Of Thebi-Univalent Function Class, Arzu Akgül Jan 2019

$(P,Q)$-Lucas Polynomial Coefficient Inequalities Of Thebi-Univalent Function Class, Arzu Akgül

Turkish Journal of Mathematics

Recently, Lucas polynomials and other special polynomials gained importance in the field of geometric function theory. In this study, by connecting these polynomials, subordination, and the Al-Oboudi differential operator, we introduce a new class of bi-univalent functions and obtain coefficient estimates and Fekete-SzegÖ inequalities for this new class.

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Extending Self-Orthogonal Codes, Alp Bassa, Nesri̇n Tutaş Jan 2019

Extending Self-Orthogonal Codes, Alp Bassa, Nesri̇n Tutaş

Turkish Journal of Mathematics

In this short note we give an exact count for the number of self-dual codes over a finite field $\mathbb F_q$ of odd characteristic containing a given self-orthogonal code. This generalizes an analogous result of MacWilliams, Sloane, and Thompson over the field $\mathbb F_2$ to arbitrary odd finite fields $\mathbb F_q$.

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Approximation By Generalized Complex Szasz--Mirakyan Operators In Compact Disks, Döne Karahan, Sevi̇lay Kirci Serenbay, Aydin İzgi̇ Jan 2019

Approximation By Generalized Complex Szasz--Mirakyan Operators In Compact Disks, Döne Karahan, Sevi̇lay Kirci Serenbay, Aydin İzgi̇

Turkish Journal of Mathematics

In this study, the generalized complex Szasz-Mirakyan operators are introduced and the approximation properties of these operators are studied. Voronovskaya's theorem with a quantitative estimate for these operators attached to an analytic function is achieved on compact disks.

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Longest Increasing Subsequences In Involutions Avoiding Patterns Of Length Three, Toufi̇k Mansour, Gökhan Yildirim Jan 2019

Longest Increasing Subsequences In Involutions Avoiding Patterns Of Length Three, Toufi̇k Mansour, Gökhan Yildirim

Turkish Journal of Mathematics

We study the longest increasing subsequences in random involutions that avoid the patterns of length three under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes.

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Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz Jan 2019

Asymptotic Behavior Of Solutions Of Second-Order Difference Equations Of Volterra Type, Malgorzata Migda, Aldona Dutkiewicz

Turkish Journal of Mathematics

In this paper we investigate the Volterra difference equation of the form $ \D(r_n\D x_n)=b_n+\sum_{k=1}^{n}K(n,k)f(x_k). $ We establish sufficient conditions for the existence of a solution $x$ of the above equation with the property $ x_n=y_n+\o(n^s), $ where $y$ is a given solution of the equation $\D(r_n\D y_n)=b_n$ and $s$ is nonpositive real number. We also obtain sufficient conditions for the existence of asymptotically periodic solutions.

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A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar Jan 2019

A Certain Subclass Of Bi-Univalent Analytic Functions Introduced Bymeans Of The $Q$-Analogue Of Noor Integral Operator And Horadam Polynomials, Arzu Akgül, Fethi̇ye Müge Sakar

Turkish Journal of Mathematics

In the present study, by using the Horadam Polnomials and $q-$analogue of Noor integral oprerator, we target to construct an interesting connection between the geometric function theory and that of special functions. Also, by defining a new class of bi-univalent analytic functions, we investigate coefficient estimates and famous Fekete-Szegö inequality for functions belonging to this interesting class.

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Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo Jan 2019

Rational Maps From Euclidean Configuration Spaces To Spheres, Urtzi Buijs, Antonio Garvin, Aniceto Murillo

Turkish Journal of Mathematics

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $\map(F(\br^m,k),\bs^n)$ and $\map^*(F(\br^m,k),\bs^n)$. An explicit description of these spaces is given for $k=3$. The general case for $n$ odd is also presented as an immediate consequence of the rational version of a classical result of Thom.

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On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli Jan 2019

On Walker 4-Manifolds With Pseudo Bi-Hermitian Structures, Si̇bel Turanli

Turkish Journal of Mathematics

$\left(M_{2n},g^w,D\right)$ is a 4-dimensional Walker manifold and this triple is also a pseudo-Riemannian manifold $\left(M_{2n},g^w\right)$ of signature $(++--$) (or neutral), which is admitted a field of null 2-plane. In this paper, we consider bi-Hermitian structures $({\varphi }_1,{\ \varphi }_2)$ on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the bi-Kahler forms are symplectic.

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Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al Jan 2019

Spectral Analysis Of Some Classes First-Order Normal Differential Operators, Pembe Ipek Al

Turkish Journal of Mathematics

In this paper, the general form of all normal differential operators generated by first-order linear singular differential expressions in the weighted Hilbert spaces of vector-functions on right semiaxis has been found. Later on, the spectrum set of these type extensions is investigated. Finally, the asymptotical behavior of the singular numbers of any normal extension is studied.

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Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar Jan 2019

Modules In Which Semisimple Fully Invariant Submodules Are Essential In Summands, Ramazan Yaşar

Turkish Journal of Mathematics

One of the useful generalization of extending notion is $FI$-extending property. A module is called $FI$-extending if every fully invariant submodule is essential in a direct summand. In this paper, we explore Weak $FI$-extending concept by considering only semisimple fully invariant submodules rather than all fully invariant submodules. To this end, we call such a module Weak $FI$-extending. We obtain that $FI$-extending modules are properly contained in this new class of modules. Amongst other structural properties, we also deal with direct sums and direct summands of Weak $FI$-extending modules.

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An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek Jan 2019

An Approach To Negative Hypergeometric Distribution By Generatingfunction For Special Numbers And Polynomials, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

The aim of this paper is to not only provide a definition of a new family of special numbers and polynomials of higher-order with their generating functions, but also to investigate their fundamental properties in the spirit of probabilistic distributions. By applying generating functions methods, we derive miscellaneous novel identities and formulas involving the Chu--Vandermonde-type convolution formulas, combinatorial sums, Bernstein basis functions, and the other well-known special numbers and polynomials. Moreover, we provide a computational algorithm which returns special values of these numbers and polynomials. In addition, we show that our new identities and formulas are connected with the interpolation …

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