New class of modified \((m,p,h)\)-convex functions with application to integral inequalities
Volume 38, Issue 3, pp 379--395
https://dx.doi.org/10.22436/jmcs.038.03.07
Publication Date: January 12, 2025
Submission Date: September 30, 2024
Revision Date: November 18, 2024
Accteptance Date: December 04, 2024
Authors
A. Nosheen
- Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
Kh. A. Khan
- Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
M. H. Bukhari
- Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
A. Alburaikan
- Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.
S. El-Morsy
- Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.
- Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt.
Abstract
Modified \((m,p,h)\)-convexity is a new notion that is introduced in this study. It generalizes the classical notion of modified \((p,h)\)-convexity and establishes several important properties for modified \((m,p,h)\)-convex functions. Applications of modified \((m,p,h)\)-convex functions are given in form of extensions of Hermite-Hadamard (H-H), Jensen, and Féjer inequalities. We have shown the validity of results by including several examples of modified \((m,p,h)\)-convex functions and also inspect the viability of proved inequalities by choosing several modified \((m,p,h)\)-convex functions. These results provide powerful tools for analyzing the behavior of modified \((m,p,h)\)-convex functions.
Share and Cite
ISRP Style
A. Nosheen, Kh. A. Khan, M. H. Bukhari, A. Alburaikan, S. El-Morsy, New class of modified \((m,p,h)\)-convex functions with application to integral inequalities, Journal of Mathematics and Computer Science, 38 (2025), no. 3, 379--395
AMA Style
Nosheen A., Khan Kh. A., Bukhari M. H., Alburaikan A., El-Morsy S., New class of modified \((m,p,h)\)-convex functions with application to integral inequalities. J Math Comput SCI-JM. (2025); 38(3):379--395
Chicago/Turabian Style
Nosheen, A., Khan, Kh. A., Bukhari, M. H., Alburaikan, A., El-Morsy, S.. "New class of modified \((m,p,h)\)-convex functions with application to integral inequalities." Journal of Mathematics and Computer Science, 38, no. 3 (2025): 379--395
Keywords
- Convex function
- H-H inequalities
- Jensen inequality
- Féjer inequality
- mathematical operators
- optimization
MSC
- 26D10
- 26D15
- 26B25
- 26A51
- 52A15
- 33B15
- 39B62
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