Browsing by Author "Tamar, Mehmet Emin"

Now showing 1 - 2 of 2

Citation - WoS: 1
Citation - Scopus: 1
A New Approaching Method for Linear Neutral Delay Differential Equations by Using Clique Polynomials
(Tubitak Scientific & Technological Research Council Turkey, 2023) Yuzbasi, Suayip; Tamar, Mehmet Emin
This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating y ' (u) using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to several numerical problems. All calculations in this method have been performed using the computer program MATLAB R2021a.
New Proofs of Fejer's and Discrete Hermite-Hadamard Inequalities With Applications
(Ankara Univ, Fac Sci, 2023) Sekin, Cagla; Tamar, Mehmet Emin; Aliyev, Ilham A.
New proofs of the classical Fejer inequality and discrete Hermite-Hadamard inequality (HH) are presented and several applications are given, including (HH)-type inequalities for the functions, whose derivatives have inflection points. Morever, some estimates from below and above for the first moments of functions f : [a, b] -> R about the midpoint c = (a+b)/2 are obtained and the reverse Hardy inequality for convex functions f : (0, infinity) -> (0, infinity) is established.