# A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions

Volume 26, Issue 4, pp 330--348
Publication Date: December 08, 2021 Submission Date: September 03, 2021 Revision Date: September 23, 2021 Accteptance Date: November 23, 2021
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### Authors

M. Tariq - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. H. Ahmad - Department of Computer Engineering, Biruni University, Istanbul 34025, Turkey. - Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 , Roma, Italy. S. K. Sahoo - Department of Mathematics, Institute of Technical Education and Research, Siksha `O' Anusandhan University, Bhubaneswar 751030, India. L. Sh. Aljoufi - Deanship of Common First Year, Jouf University, P.O.Box 2014 Sakaka, Saudi Arabia. - Basic Sciences Research Unit, Jouf University, P.O.Box 2014 Sakaka, Saudi Arabia. S. K. Awan - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan.

### Abstract

The main objective of this article is to employ the concept of preinvexity to establish some new inequalities. In addition, we discuss some algebraic properties and examples of the generalized preinvex function. With the help of this new relation, we present new version of Hermite-Hadamard inequality and its some of its refinements using fundamental inequalities like Hölder, power-mean, Hölder-Iscan, and improved power-mean inequality. These results are speculations of various recently known outcomes. The immeasurable concepts and tools of this paper may invigorate and revitalize for additional research in this mesmerizing and absorbing field.

### Share and Cite

##### ISRP Style

M. Tariq, H. Ahmad, S. K. Sahoo, L. Sh. Aljoufi, S. K. Awan, A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions, Journal of Mathematics and Computer Science, 26 (2022), no. 4, 330--348

##### AMA Style

Tariq M., Ahmad H., Sahoo S. K., Aljoufi L. Sh., Awan S. K., A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions. J Math Comput SCI-JM. (2022); 26(4):330--348

##### Chicago/Turabian Style

Tariq, M., Ahmad, H., Sahoo, S. K., Aljoufi, L. Sh., Awan, S. K.. "A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions." Journal of Mathematics and Computer Science, 26, no. 4 (2022): 330--348

### Keywords

• $s$-type convex function
• preinvex function
• $m$-preinvex function
• Hölder's inequality
• Hölder-Iscan integral inequality
• power mean inequality
• improved power-mean integral inequality

•  26A51
•  26A33
•  26D07
•  26D10
•  26D15