Open AccessCertain exponential type $ m $-convexity inequalities for fractional integrals with exponential kernels
Author(s) -
Hao Wang,
AUTHOR_ID,
Zhijuan Wu,
Xiaohong Zhang,
Shubo Chen
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022351
Subject(s) - mathematics , exponential type , exponential function , type (biology) , convexity , omega , convex function , regular polygon , midpoint , inequality , combinatorics , mathematical analysis , pure mathematics , geometry , physics , finance , ecology , quantum mechanics , economics , biology
By applying exponential type $ m $-convexity, the Hölder inequality and the power mean inequality, this paper is devoted to conclude explicit bounds for the fractional integrals with exponential kernels inequalities, such as right-side Hadamard type, midpoint type, trapezoid type and Dragomir-Agarwal type inequalities. The results of this study are obtained for mappings $ \omega $ where $ \omega $ and $ |\omega'| $ (or $ |\omega'|^q $with $ q\geq 1 $) are exponential type $ m $-convex. Also, the results presented in this article provide generalizations of those given in earlier works.