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3 Journal of Applied Analysis

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Some perturbed inequalities of Ostrowski type for high-order differentiable functions and applications

Erden Samet, Sarikaya Mehmet Zeki

Journal of Applied Analysis

2021

Vol. 27, nr 1

57--64

We firstly establish inequalities for functionswhose high degree derivatives are convex via an equality which was presented previously. Then we derive inequalities for functions whose high-order derivatives are absolutely continuous by using the same equality. In addition,we examine connections between inequalities obtained in earlierworks and our results. Finally, some estimates of composite quadrature rules are given.

Refinements of the Hermite-Hadamard inequality for co-ordinated convex mappings

Budak Huseyin, Usta Fuat, Sarikaya Mehmet Zeki

Journal of Applied Analysis

2019

Vol. 25, nr 1

73--81

This paper is motivated by the recent progress on the Hermite-Hadamard inequality for convex functions defined on the bounded closed interval, obtained by Z. Pavić [Z. Pavić, Improvements of the Hermite-Hadamard inequality, J. Inequal. Appl. 2015 (2015), Article ID 222]. As a generalization, we obtained a new refinement of the Hermite-Hadamard inequality for co-ordinated convex functions defined on the rectangle.

Opial-type inequalities for conformable fractional integrals

Sarikaya Mehmet Zeki, Budak Hüseyin

Journal of Applied Analysis

2019

Vol. 25, nr 2

155--163

In this paper, we establish the Opial-type inequalities for a conformable fractional integral and give some results in special cases of α. The results presented here would provide generalizations of those given in earlier works.