Some generalized Hermite-Hadamard type inequalities involving fractional integral operator for functions whose second derivatives in absolute value are s-convex
1Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey 2Mathematics, College of Engineering and Science, Victoria University, Melbourne City, Australia
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 87-100
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Abdurrahman Gozpinar; Erhan Set; Sever S. Dragomir; Abdurrahman Gozpinar; Erhan Set; Sever S. Dragomir. Some generalized Hermite-Hadamard type inequalities involving fractional integral operator for functions whose second derivatives in absolute value are s-convex. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 87-100. http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a7/
@article{AMUC_2019_88_1_a7,
author = {Abdurrahman Gozpinar and Erhan Set and Sever S. Dragomir and Abdurrahman Gozpinar and Erhan Set and Sever S. Dragomir},
title = { Some generalized {Hermite-Hadamard} type inequalities involving fractional integral operator for functions whose second derivatives in absolute value are s-convex},
journal = {Acta mathematica Universitatis Comenianae},
pages = {87--100},
year = {2019},
volume = {88},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a7/}
}
TY - JOUR
AU - Abdurrahman Gozpinar
AU - Erhan Set
AU - Sever S. Dragomir
AU - Abdurrahman Gozpinar
AU - Erhan Set
AU - Sever S. Dragomir
TI - Some generalized Hermite-Hadamard type inequalities involving fractional integral operator for functions whose second derivatives in absolute value are s-convex
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 87
EP - 100
VL - 88
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a7/
ID - AMUC_2019_88_1_a7
ER -
%0 Journal Article
%A Abdurrahman Gozpinar
%A Erhan Set
%A Sever S. Dragomir
%A Abdurrahman Gozpinar
%A Erhan Set
%A Sever S. Dragomir
%T Some generalized Hermite-Hadamard type inequalities involving fractional integral operator for functions whose second derivatives in absolute value are s-convex
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 87-100
%V 88
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a7/
%F AMUC_2019_88_1_a7
In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral. Also we pointed out, some results in this study in some special cases, such as setting s = 1, λ = α, σ(0) = 1 and w = 0 , more reasonable than those obtained in [8].
