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Article

Refinement Mappings Related to Hermite-Hadamard Type Inequalities for GA-Convex Function

by
Muhammad Amer Latif
1,
Humaira Kalsoom
2,
Zareen A. Khan
3 and
Areej A. Al-moneef
3,*
1
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia
2
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
3
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(9), 1398; https://doi.org/10.3390/math10091398
Submission received: 19 March 2022 / Revised: 14 April 2022 / Accepted: 20 April 2022 / Published: 22 April 2022
Versions Notes

Abstract

In this paper, we present some new refinement mappings associated with the Hermite–Hadamard type inequalities that are constructed for GA-convex mappings. Our investigation of the mappings leads to the discovery of several interesting features as well as the development of some inequalities for the Hermite–Hadamard type inequalities, which have already been established for GA-convex functions, as well as refining the relationship between the middle, rightmost, and leftmost elements of the function. Some applications to special means of positive real numbers are also given.
Keywords: Hermite–Hadamard’s inequality; convex function; GA-convex function; Jensen’s inequality Hermite–Hadamard’s inequality; convex function; GA-convex function; Jensen’s inequality

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MDPI and ACS Style

Latif, M.A.; Kalsoom, H.; Khan, Z.A.; Al-moneef, A.A. Refinement Mappings Related to Hermite-Hadamard Type Inequalities for GA-Convex Function. Mathematics 2022, 10, 1398. https://doi.org/10.3390/math10091398

AMA Style

Latif MA, Kalsoom H, Khan ZA, Al-moneef AA. Refinement Mappings Related to Hermite-Hadamard Type Inequalities for GA-Convex Function. Mathematics. 2022; 10(9):1398. https://doi.org/10.3390/math10091398

Chicago/Turabian Style

Latif, Muhammad Amer, Humaira Kalsoom, Zareen A. Khan, and Areej A. Al-moneef. 2022. "Refinement Mappings Related to Hermite-Hadamard Type Inequalities for GA-Convex Function" Mathematics 10, no. 9: 1398. https://doi.org/10.3390/math10091398

APA Style

Latif, M. A., Kalsoom, H., Khan, Z. A., & Al-moneef, A. A. (2022). Refinement Mappings Related to Hermite-Hadamard Type Inequalities for GA-Convex Function. Mathematics, 10(9), 1398. https://doi.org/10.3390/math10091398

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