Tamkang Journal of Mathematics https://journals.math.tku.edu.tw/index.php/TKJM <p><strong>Welcome to Tamkang Journal of Mathematics </strong><span lang="en"><strong><span lang="en"><span lang="en"><br><br><strong>~Hot News~ </strong><br><strong>Tamkang Journal of Mathematics(TKJM) is included in Emerging Sources Citation Index (ESCI)</strong> <br><br><img src="/public/201709_ESCI_toTKJM.jpg" alt="TKJM in ESCI" width="469" height="220"><br><br><br><strong>Aims and Scope</strong><br></span></span></strong></span></p> <p>&nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p> <p>&nbsp;</p> <div>To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers &nbsp;in pure and applied mathematics. In 1985 it has become a quarterly journal.</div> Tamkang University en-US Tamkang Journal of Mathematics 0049-2930 On the planarity and perfectness of annihilator ideal graphs https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2707 <p>Let $R$ be a commutative ring with unity. The annihilator ideal graph of $R$, denoted by $\Gamma _{\mathrm{Ann}} (R)$, is a graph whose vertices are all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if<br />$I \cap \mathrm{Ann} _{R} (J) \neq \lbrace 0\rbrace$ or $J \cap \mathrm{Ann} _{R} (I) \neq \lbrace 0\rbrace$.<br />In this paper, all rings with planar annihilator ideal graphs are classified.<br />Furthermore, we show that all annihilator ideal graphs are perfect. Among other results, it is proved that if $\Gamma _{\mathrm{Ann}} (R)$ is a tree, then $\Gamma _{\mathrm{Ann}} (R)$ is star.</p> Reza Nikandish M. J Nikmehr S. M Hosseini Copyright (c) 2019 Tamkang Journal of Mathematics https://creativecommons.org/licenses/by-nc-sa/4.0 2019-12-30 2019-12-30 50 4 361 369 10.5556/j.tkjm.50.2019.2707 The reciprocal complementary Wiener number of graphs https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2714 <p>The reciprocal complementary Wiener number (RCW) of a connected graph G is defined as the sum of<br />weights frac{1}{D+1-d_G(x,y)} over all unordered vertex pairs in a graph G, where D is the diameter of G<br />and d_G(x,y) is the distance between vertices x and y. In this paper, we find new bounds for RCW of<br />graphs, and study this invariant of two important types of graphs, named the Bar-Polyhex and the<br />Mycielskian graphs.</p> Ramin Nasiri Copyright (c) 2019 Tamkang Journal of Mathematics https://creativecommons.org/licenses/by-nc-sa/4.0 2019-12-30 2019-12-30 50 4 371 381 10.5556/j.tkjm.50.2019.2714 Chebyshev type inequalities involving generalized Katugampola fractional integral operators https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2791 A number of Chebyshev type inequalities involving various<br /> fractional integral operators have, recently, been presented.<br />Here, motivated essentially by the earlier works and their applications in<br /> diverse research subjects, we aim to establish several Chebyshev type inequalities involving generalized Katugampola fractional integral operator. Relevant connections of the results presented here with those (known and new) involving relatively simpler and familiar fractional integral operators are also pointed out. Erhan Set Junesang Choi \.{I}lker Mumcu Copyright (c) 2019 Tamkang Journal of Mathematics https://creativecommons.org/licenses/by-nc-sa/4.0 2019-12-30 2019-12-30 50 4 381 390 10.5556/j.tkjm.50.2019.2791 A Viscosity Iterative Algorithm Technique for Solving a General Equilibrium Problem System https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2831 In the recent decade, a considerable number of Equilibrium problems have<br />been solved successfully based on the iteration methods. In this paper, we suggest a viscosity iterative algorithm for nonexpansive semigroup in the framework<br /> of Hilbert space. We prove that, the sequence generated by this algorithm under the certain conditions imposed on parameters<br /> strongly convergence to a common solution of general equilibrium problem system. Results presented in this paper extend and unify the previously known<br /> results announced by many other authors. Further, we give some numerical examples to justify our main results. mahdi azhini masoumeh cheraghi hamid reza sahebi Copyright (c) 2019 Tamkang Journal of Mathematics https://creativecommons.org/licenses/by-nc-sa/4.0 2019-12-30 2019-12-30 50 4 391 408 10.5556/j.tkjm.50.2019.2831 An ecological model involving nonlocal operator and reaction diffusion https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2921 <p>Using the method of sub-super solutions, we study the existence of<br />positive solutions for a class of infinite semipositone problems<br />involving nonlocal operator.</p> Saleh Shakeri Armin Hadjian Copyright (c) 2019-12-30 2019-12-30 50 4 409 416 10.5556/j.tkjm.50.2019.2921 Best approximation of conjugate of a function in generalized Zygmund https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3006 <p>In this paper, we, for the very first time, study the error estimates of conjugate of a function ~g of g<br />(2-periodic) in generalized Zygmund class Y w<br />z (z 1); by Matix-Euler (TEq) product operator<br />of conjugate Fourier series. In fact, we establish two theorems on degree of approximation of a<br />function ~g of g (2-periodic) in generalized Zygmund class Y w<br />z (z 1); by Matix-Euler (TEq)<br />product means of its conjugate Fourier series. Our main theorem generalizes three previously<br />known results. Thus the results of ,  and  become the particular cases of our Theorem<br />2.1. Some corollaries are also deduced from our main theorem.</p> Hare Krishna Nigam Copyright (c) 2019 Tamkang Journal of Mathematics https://creativecommons.org/licenses/by-nc-sa/4.0 2019-12-30 2019-12-30 50 4 417 427 10.5556/j.tkjm.50.2019.3006