Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings

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Published: Dec 25, 2018
DOI: https://doi.org/10.5556/j.tkjm.49.2018.2772
Keywords:
Hermite-Hadamard inequality Holder's inequality Minkowski inequality power mean inequality Caputo k-fractional derivatives m-invex.

Main Article Content

Artion Kashuri
Rozana Liko
Silvestru Sever Dragomir

Abstract

In 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.

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How to Cite
Kashuri, A., Liko, R., & Dragomir, S. S. (2018). Some new Gauss-Jacobi and Hermite-Hadamard type inequalities concerning $(n+1)$-differentiable generalized $((h_{1},h_{2});(\eta_{1},\eta_{2}))$-convex mappings. Tamkang Journal of Mathematics, 49(4), 317–337. https://doi.org/10.5556/j.tkjm.49.2018.2772
Issue
Vol. 49 No. 4 (2018)
Section
Papers
Author Biographies

Artion Kashuri

Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania.

Rozana Liko

Department ofMathematics, Faculty of Technical Science, University Ismail Qemali, Vlora, Albania.

Silvestru Sever Dragomir

School of Engineering & Science, Victoria University, PO Box 14428, Melbourne City,MC 8001, Australia.

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