Properties and Riemann-Liouville fractional Hermite-Hadamard inequalities for the generalized \alpha,m-preinvex functionsReport as inadecuate




Properties and Riemann-Liouville fractional Hermite-Hadamard inequalities for the generalized \alpha,m-preinvex functions - Download this document for free, or read online. Document in PDF available to download.

Journal of Inequalities and Applications

, 2016:306

First Online: 25 November 2016Received: 31 August 2016Accepted: 17 November 2016

Abstract

The authors first introduce the concepts of generalized \\alpha,m\-preinvex function, generalized quasi m-preinvex function and explicitly \\alpha, m\-preinvex function, and then provide some interesting properties for the newly introduced functions. The more important point is that we give a necessary and sufficient condition respecting the relationship between the generalized \\alpha, m\-preinvex function and the generalized quasi m-preinvex function. Second, a new Riemann-Liouville fractional integral identity involving twice differentiable function on m-invex is found. By using this identity, we establish the right-sided new Hermite-Hadamard-type inequalities via Riemann-Liouville fractional integrals for generalized \\alpha,m\-preinvex mappings. These inequalities can be viewed as generalization of several previously known results.

KeywordsHermite-Hadamard’s inequality \\alpha,m\-preinvex functions Riemann-Liouville fractional integrals MSC26A33 26A51 26D07 26D20 41A55  Download fulltext PDF



Author: TingSong Du - JiaGen Liao - LianZi Chen - Muhammad Uzair Awan

Source: https://link.springer.com/







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