Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces,
2019
TÜBİTAK
Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar
Turkish Journal of Mathematics
Let $X$ and $Y$ be complex Banach spaces and $\mathbb{D}$ be the open unit disc in the complex plane $\mathbb{C}$. Let $\varphi$ be an analytic self-map of $\mathbb{D}$ and $\psi$ be an analytic operator-valued function from $\mathbb{D}$ into the space of all bounded linear operators from $X$ to $Y.$ The weighted composition operator $W_{\psi,\varphi}:\mathcal{H} \rightarrow\mathcal{H}(\mathbb{D}, Y)$ is defined by $$ W_{\psi,\varphi}( f)(z)=\psi(z)(f(\varphi(z))), \quad \quad (z\in\mathbb{D}, f\in \mathcal{H}),$$ where $\mathcal{H}$ is the space of all analytic $X$-valued functions on $\mathbb{D}$. In this paper we provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators $W_{\psi,\varphi}$ between vector-valued …
Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination,
2019
TÜBİTAK
Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo
Turkish Journal of Mathematics
Let $S_{H}$ be the class of functions $f=h+\bar{g}$ that are harmonic univalent and sense-preserving in the open unit disk $\mathbb{U}=\{z\in \mathbb{C}: z
On Integrability Conditions, Operators, And The Purityconditions Of The Sasakian Metric With Respect To Lifts Of $F_{\Lambda}(7,1)$-Structure On The Cotangent Bundle, Haşi̇m Çayir
Turkish Journal of Mathematics
There are many structures in the cotangent bundle. These include the complete and horizontal lifts of the $F_{\lambda }(7,1)$-structure. The $F_{\lambda }(7,1)$-structure was first extended in $M^{n}$ to $T^{\ast }(M^{n})$ by Das, Nivas, and Pathak. Later, the horizontal and complete lift of the $F_{a}(K,1)$-structure in the tangent bundle was given by Prasad and Chauhan. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete lifts of the $F_{\lambda }(7,1)$-structure. Later, we get the results of the Tachibana operators applied to vector and covector fields according to the …
A Note On Polynomial Expressions For Sums Of Power Of Integers Multiplied By Exponential Terms,
2019
TÜBİTAK
A Note On Polynomial Expressions For Sums Of Power Of Integers Multiplied By Exponential Terms, Altan Erdoğan
Turkish Journal of Mathematics
The possible polynomial expressions for sums of powers of integers multiplied by an exponential term are investigated. We explicitly give factorization of these polynomials in terms of the roots of Apostol-Bernoulli polynomials. As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.
Quartic Trigonometric B-Spline Algorithm Fornumerical Solution Of The Regularized Long Wave Equation,
2019
TÜBİTAK
Quartic Trigonometric B-Spline Algorithm Fornumerical Solution Of The Regularized Long Wave Equation, Dursun Irk, Pinar Keski̇n Yildiz, Meli̇s Zorşahi̇n Görgülü
Turkish Journal of Mathematics
In this paper, an application of the quartic trigonometric B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method based on the quartic trigonometric B-spline function in space discretization together with second and fourth order schemes in time discretization. The accuracy of the proposed methods are demonstrated by test problems and numerical results are compared with the exact solution and some previous results.
On The Starlikeness Of P-Valent Functions,
2019
TÜBİTAK
On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol
Turkish Journal of Mathematics
For an analytic function in open unit disk $\mathbb{D}$, we consider the $p$-valent analogue of the Noshiro-Warschawski univalence condition. We apply the Fejér-Riesz inequality to establish some sufficient conditions for functions to be $p$-valent or to be a Bazilevič function or to be in some other classes.
A Novel 3-Pass Identification Scheme And Signature Scheme Based On Multivariate Quadratic Polynomials,
2019
TÜBİTAK
A Novel 3-Pass Identification Scheme And Signature Scheme Based On Multivariate Quadratic Polynomials, Sedat Akleylek, Meryem Soysaldi
Turkish Journal of Mathematics
Identification schemes are used to verify identities of parties and signatures. Recently, systems based on multivariate polynomials have been preferred in identification schemes due to their resistance against quantum attacks. In this paper, we propose a quantum secure $3$-pass identification scheme based on multivariate quadratic polynomials. We compare the proposed scheme with the previous ones in view of memory requirements, communication length, and computation time. We define an efficiency metric by using impersonation probability and computation time. According to the comparison results, the proposed one has the same computation time as that of Monteiro et al. and reduces impersonation probability …
Notes On Certain Analytic Functions,
2019
TÜBİTAK
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Turkish Journal of Mathematics
Let $\mathcal{A}(n)$ be the class of functions $$f(z)=a_nz^n + a_{n+1}z^{n+1}+\cdots (n\in \mathbb{N}),$$ which are analytic in the open unit disk $\mathbb{U}$, where $a_n \neq 0$. For $f(z)\in \mathcal{A}(n)$, Miller and Mocanu in 1978 showed a very interesting result for $f(z)$. Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial,
2019
TÜBİTAK
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Turkish Journal of Mathematics
In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.
Sectional Curvatures On Weyl Manifolds With A Special Metric Connection,
2019
TÜBİTAK
Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu
Turkish Journal of Mathematics
In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved. We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature. Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
Kernel Operators And Their Boundedness From Weighted Sobolev Space To Weighted Lebesgue Space,
2019
TÜBİTAK
Kernel Operators And Their Boundedness From Weighted Sobolev Space To Weighted Lebesgue Space, Aigerim Kalybay, Ryskul Oinarov
Turkish Journal of Mathematics
In this paper, for a wide class of integral operators, we consider the problem of their boundedness from a weighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.
On A Theorem Of Terzioğlu,
2019
TÜBİTAK
On A Theorem Of Terzioğlu, Asuman Güven Aksoy
Turkish Journal of Mathematics
The theory of compact linear operators acting on a Banach space has a classical core and is familiar to many. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a number of important connections that deserves illumination. In this paper we survey Terzioğlu's characterization theorem for compact maps and some of its consequences. We also prove a similar characterization theorem for $Q$-compact maps.
Univalent Harmonic Mappings And Hardy Spaces,
2019
TÜBİTAK
Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
The main purpose of this paper is to establish a relationship between univalent harmonic mappings and Hardy spaces. The main result obtained in this paper improves previously published results. Moreover, we generalize some nice results in the analytic case to the harmonic case.
A Broken Cycle Theorem For The Restrained Chromatic Function,
2019
TÜBİTAK
A Broken Cycle Theorem For The Restrained Chromatic Function, Aysel Erey
Turkish Journal of Mathematics
A restraint $r$ on a graph $G$ is a function that assigns each vertex of the graph a finite subset of $\mathbb{N}$. For each vertex $v$ of the graph, $r(v)$ is called the set of colors forbidden at $v$. A proper coloring of $G$ is said to be permitted by a given restraint $r$ if each vertex $v$ of the graph receives a color that is not from its set of forbidden colors $r(v)$. The restrained chromatic function, denoted by $\pi_r(G,x)$, is a function whose evaluations at integer $x$ values count the number of proper $x$-colorings of the graph $G$ …
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
Turkish Journal of Mathematics
In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor …
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants,
2019
TÜBİTAK
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Turkish Journal of Mathematics
It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
Hirzebruch-Kummer Covers Of Algebraic Surfaces,
2019
TÜBİTAK
Hirzebruch-Kummer Covers Of Algebraic Surfaces, Piotr Pokora
Turkish Journal of Mathematics
The aim of this paper is to show that using some natural curve arrangements in algebraic surfaces and Hirzebruch-Kummer covers, one cannot construct new examples of ball-quotients, i.e. minimal smooth complex projective surfaces of general type satisfying equality in the Bogomolov-Miyaoka-Yau inequality.
A Discrete Chaotic Dynamical System On The Sierpinski Gasket,
2019
TÜBİTAK
A Discrete Chaotic Dynamical System On The Sierpinski Gasket, Mustafa Saltan, Ni̇sa Aslan, Bünyami̇n Demi̇r
Turkish Journal of Mathematics
The Sierpinski gasket (also known as the Sierpinski triangle) is one of the fundamental models of self-similar sets. There have been many studies on different features of this set in the last decades. In this paper, initially we construct a dynamical system on the Sierpinski gasket by using expanding and folding maps. We then obtain a surprising shift map on the code set of the Sierpinski gasket, which represents the dynamical system, and we show that this dynamical system is chaotic on the code set of the Sierpinski gasket with respect to the intrinsic metric. Finally, we provide an algorithm …
On Essential Cohomology Of Powerful $P$-Groups,
2019
TÜBİTAK
On Essential Cohomology Of Powerful $P$-Groups, Fatma Altunbulak Aksu
Turkish Journal of Mathematics
For an odd prime $p$, we prove that a finite powerful $p$-group having rank two Frattini quotient has nonzero essential cohomology. We also provide some examples and applications.
An Asymptotic-Numerical Hybrid Method For Singularly Perturbed System Of Two-Point Reaction-Diffusion Boundary-Value Problems,
2019
TÜBİTAK
An Asymptotic-Numerical Hybrid Method For Singularly Perturbed System Of Two-Point Reaction-Diffusion Boundary-Value Problems, Süleyman Cengi̇zci̇, Srinivasan Natesan, Mehmet Tarik Atay
Turkish Journal of Mathematics
This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.
