By Hölder's integral inequality, the authors establish some Hermite-Hadamard type integral inequalities for n-times differentiable and geometrically quasi-convex functions.
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http://dx.doi.org/10.1186/s40064-016-2083-y | DOI Listing |
Heliyon
May 2024
Department of Mathematics, University of Wah, Wah Cantt, 47040, Pakistan.
The main motivation in this article is to prove new integral identities and related results. In this paper, we deal with -convex function, Hermite-Hadamard type inequalities, and Katugampola fractional integrals. Firstly, we established the Hermite-Hadamard type inequalities for -convex function via Katugampola fractional integrals operators.
View Article and Find Full Text PDFMath Biosci Eng
February 2024
Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia.
Convex and preinvex functions are two different concepts. Specifically, preinvex functions are generalizations of convex functions. We created some intriguing examples to demonstrate how these classes differ from one another.
View Article and Find Full Text PDFEntropy (Basel)
June 2023
Department of Mathematics, University of Pannonia, Egyetem u. 10., 8200 Veszprém, Hungary.
In this paper, we present a general framework that provides a comprehensive and uniform treatment of integral majorization inequalities for convex functions and finite signed measures. Along with new results, we present unified and simple proofs of classical statements. To apply our results, we deal with Hermite-Hadamard-Fejér-type inequalities and their refinements.
View Article and Find Full Text PDFEntropy (Basel)
May 2022
Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia.
This article estimates several integral inequalities involving (h-m)-convexity via the quantum calculus, through which Important integral inequalities including Simpson-like, midpoint-like, averaged midpoint-trapezoid-like and trapezoid-like are extended. We generalized some quantum integral inequalities for q-differentiable (h-m)-convexity. Our results could serve as the refinement and the unification of some classical results existing in the literature by taking the limit q→1-.
View Article and Find Full Text PDFMath Biosci Eng
January 2022
Department of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi Arabia.
In this paper, firstly we define the concept of -preinvex fuzzy-interval-valued functions (-preinvex FIVF). Secondly, some new Hermite-Hadamard type inequalities (- type inequalities) for -preinvex FIVFs via fuzzy integrals are established by means of fuzzy order relation. Finally, we obtain Hermite-Hadamard Fejér type inequalities (- Fejér type inequalities) for -preinvex FIVFs by using above relationship.
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