•Journal•ISSN: 2148-1830

# Turkish journal of mathematics & computer science

Turkish Journal of Mathematics and Computer Science, Association of Mathematicians

About: Turkish journal of mathematics & computer science is an academic journal published by Turkish Journal of Mathematics and Computer Science, Association of Mathematicians. The journal publishes majorly in the area(s): Mathematics & Pure mathematics. It has an ISSN identifier of 2148-1830. It is also open access. Over the lifetime, 57 publications have been published receiving 16 citations. The journal is also known as: TJMCS.

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TL;DR: In this article , the Berezin transform and the radius of an operator on the reproducing kernel Hilbert space are defined, and several sharp inequalities are studied. But they do not consider the case where the operator is a sum of two operators.

Abstract: The Berezin transform $\widetilde{T}$ and the Berezin radius of an operator $T$ on the reproducing kernel Hilbert space $\mathcal{H}\left( Q\right) $ over some set $Q$ with the reproducing kernel $K_{\eta}$ are defined, respectively, by
\[
\widetilde{T}(\eta)=\left\langle {T\frac{K_{\eta}}{{\left\Vert K_{\eta
}\right\Vert }},\frac{K_{\eta}}{{\left\Vert K_{\eta}\right\Vert }}%
}\right\rangle ,\ \eta\in Q\text{ and }\mathrm{ber}(T):=\sup_{\eta\in
Q}\left\vert \widetilde{T}{(\eta)}\right\vert .
\]
We study several sharp inequalities by using this bounded function $\widetilde{T},$ involving powers of the Berezin radius and the Berezin norms of reproducing kernel Hilbert space operators. We also give some inequalities regarding the Berezin transforms of sum of two operators.

6 citations

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TL;DR: In this article , a modification of classical Finite Difference Method (FDM) was proposed for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals.

Abstract: In this study, we have proposed a new modification of classical Finite Difference Method (FDM) for the solution of boundary value problems which are defined on two disjoint intervals and involved additional transition conditions at an common end of these intervals. The proposed modification of FDM differs from the classical FDM in calculating the iterative terms of numerical solutions. To illustrate the efficiency and reliability of the proposed modification of FDM some examples are solved. The obtained results are compared with those obtained by the standart FDM and by the analytical method. Corresponding graphical illustration are also presented.

2 citations

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TL;DR: In this paper , the authors studied the geodesics on the tangent bundle with respect to the vertical rescaled Berger deformation metric over an anti-paraK{a}hler manifold.

Abstract: In this paper, we study the geodesics on the tangent bundle $TM$ with respect to the vertical rescaled Berger deformation metric over an anti-paraK\"{a}hler manifold $(M, \varphi, g)$. In this case, we establish the necessary and sufficient conditions under which a curve be geodesic with respect to this. Finally, we also present certain examples of geodesic.

2 citations

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TL;DR: In this article , some properties of hyperbolic numbers are presented and compared with real, dual, and complex matrices, and it is revealed that there are similarities in additive properties and differences in multiplicative properties.

Abstract: In this study, firstly, we will present some properties of hyperbolic numbers. Then, we will introduce hyperbolic matrices, which are matrices with hyperbolic number entries. Additionally, we will examine the algebraic properties of these matrices and reveal its difference from other matrix structures such as real, dual, and complex matrices. As a result of comparing the results found in this work with real, dual, and complex matrices, it will be revealed that there are similarities in additive properties and differences in some multiplicative properties. Finally, we will define some special hyperbolic matrices and give their properties and relations with real matrices.

1 citations

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TL;DR: In this paper , hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as recurrence relations, summation formulas, and generating functions are presented.

Abstract: In this paper, hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as the recurrence relations, summation formulas, and generating functions are presented. In addition, some relationships between the hyper-Fibonacci and hyper-Lucas polynomials are given.

1 citations