IJPAM: Volume 106, No. 1 (2016)

ON INTEGRAL INEQUALITIES OF HERMITE-HADAMARD
TYPE FOR LOGARITHMICALLY $h$-PREINVEX
FUNCTIONS VIA FRACTIONAL INTEGRALS

Ahmet Çelık$^1$, Bekir Dal$^2$, Mesut Kisa$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science and Arts
University of Kahramanmaraş Sütçü İmam
46000, Kahramanmaraş, TURKEY


Abstract. In this paper, we consider a new class of convex functions which is called logarithmically $h-$preinvex functions. We prove several Hermite-Hadamard type inequalities for differentiable logarithmically$h-$preinvex functions via Fractional Integrals. Some special cases are also discussed. Our results extend and improve the corresponding ones in the literature.

Received: October 29, 2015

AMS Subject Classification: 26D15, 26A51, 26A33, 26A42

Key Words and Phrases: integral inequalities, fractional integrals, hermite-hadamard inequality, logarithmically $h$-preinvex functions

Download paper from here.



DOI: 10.12732/ijpam.v106i1.22 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 279 - 289


$h$-PREINVEX FUNCTIONS VIA FRACTIONAL INTEGRALS%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).