http://journals.math.tku.edu.tw/index.php/TKJM/issue/feedTamkang Journal of Mathematics2018-11-01T08:01:24+08:00Editorial Officeeo-tkjm@mail2.tku.edu.twOpen Journal Systems<strong>Welcome to Tamkang Journal of Mathematics </strong><br /><br /><strong>~Hot News~ </strong><br /><br /><strong>Tamkang Journal of Mathematics(TKJM) is included in Emerging Sources Citation Index (ESCI)</strong> <br /><br /><img src="/templates/images/201709_ESCI_toTKJM.jpg" alt="TKJM in ESCI" width="469" height="220" /><br /><br /><br /><strong>Aims and Scope</strong><br /><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 in pure and applied mathematics. In 1985 it has become a quarterly journal.</div>http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2605On compact Einstein doubly warped product manifolds2018-11-01T08:01:23+08:00Punam Guptapunam_2101@yahoo.co.inIn this paper, the non-existence of connected, compact Einstein doubly warped product semi-Riemannian manifold with non-positive scalar curvature is proved. It is also shown that there does not exist non-trivial connected Einstein doubly warped product semi-Riemannian manifold with compact base $B$ or fibre $F$.2018-12-25T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2632New Ostrowski and Ostrowski-Gruss type inequalities for double integrals on time scales involving a combination of $\Delta$-integral means2018-11-01T08:01:23+08:00Seth Kermausuorskermausour@alasu.eduEze Raymond Nwaezeenwaeze@tuskegee.eduIn 2014, some Ostrowski type inequalities for functions of a single variable were obtained in [Y. Jiang, H. R\"uzgar, W. J. Liu and A. Tuna: Some new generalizations of Ostrowski type inequalities on time scales involving combination of $\Delta$-integral means, J. Nonlinear Sci. Appl., {\bf{7}} (2014), 311--324]. In this paper, we extend some of the inequalities obtained in the above paper for double integrals. One of our results generalizes a result in the article [W. J. Liu, Q. A. Ng\^o and W. Chen: On new Ostrowski type inequalities for double integrals on time scales, Dyn. Syst. Appl., {\bf 19} (2010), 189--198]. We also apply our results to the continuous, discrete and quantum time scales to obtain some interesting inequalities.2018-12-25T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2653A note on Lamarle formula in Minkowski $3$-space2018-11-01T08:01:23+08:00Ufuk Öztürkozturkufuk06@gmail.comKazım İlarslankilarslan@yahoo.comEsra Betül Koç Öztürke.betul.e@gmail.comEmilija Nesovicnesovickg@sbb.rsThe Lamarle formula is known as a simple relation between the Gaussian curvature and the distribution parameter of a non-developable ruled surface. In this paper, we obtain the Lamarle formula of a non-developable ruled surface with pseudo null base curve and null director vector field in Minkowski $3$-space. We also obtain the corresponding striction line and distribution parameter of such surface. We prove that there is no Lamarle formula when the director vector field is spacelike and its derivative is null, because the ruled surface in that case is a lightlike plane. Finally, we give some examples.2018-12-25T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2718Usage of the homotopy analysis method for solving fractional Volterra-Fredholm integro-differential equation of the second kind2018-11-01T08:01:24+08:00Ahmen Hamouddrahmedselwi985@hotmail.comKirtiwant Ghadledrahmed985@yahoo.comThe reliability of the homotopy analysis method (HAM) and reduction in the size of the computational work give this method a wider applicability. In this paper, HAM has been successfully applied to find the approximate solutions of Caputo fractional Volterra-Fredholm integro-differential equations. Also, the behavior of the solution can be formally determined by analytical approximation. Moreover, the study proves the existence and uniqueness results and the convergence of the solution. This paper concludes with an example to demonstrate the validity and applicability of the proposed technique.2018-12-25T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2772Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings2018-11-01T08:01:24+08:00Artion Kashuriartionkashuri@gmail.comRozana Likorozanaliko86@gmail.comSilvestru Sever Dragomirsever.dragomir@vu.edu.auIn this article, we first introduced a new class of generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings and two interesting lemmas regarding Gauss-Jacobi and\\ Hermite-Hadamard type integral inequalities. By using the notion of generalized\\ $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convexity and the first lemma as an auxiliary result, some new estimates with respect to Gauss-Jacobi type integral inequalities are established. Also, using the second lemma, some new estimates with respect to Hermite-Hadamard type integral inequalities via Caputo $k$-fractional derivatives are obtained. It is pointed out that some new special cases can be deduced from main results of the article.2018-12-25T00:00:00+08:00http://journals.math.tku.edu.tw/index.php/TKJM/article/view/2804A link between harmonicity of 2-distance functions and incompressibility of canonical vector fields2018-11-01T08:01:24+08:00Bang-Yen Chenbychen@math.msu.eduLet $M$ be a Riemannian submanifold of a Riemannian manifold $\tilde M$ equipped with a concurrent vector field $\tilde Z$. Let $Z$ denote the restriction of $\tilde Z$ along $M$ and let $Z^T$ be the tangential component of $Z$ on $M$, called the canonical vector field of $M$. The 2-distance function $\delta^2_Z$ of $M$ (associated with $Z$) is defined by $\delta^2_Z=\$. In this article, we initiate the study of submanifolds $M$ of $\tilde M$ with incompressible canonical vector field $Z^T$ arisen from a concurrent vector field $\tilde Z$ on the ambient space $\tilde M$. First, we derive some necessary and sufficient conditions for such canonical vector fields to be incompressible. In particular, we prove that the 2-distance function $\delta^2_Z$ is harmonic if and only if the canonical vector field $Z^T$ on $M$ is an incompressible vector field. Then we provide some applications of our main results.2018-12-25T00:00:00+08:00