Integral inequalities involving a new class of generalized strongly modified $ (p, h) $-convex functions

Mudassir Hussain Bukhari; Ammara Nosheen; Khuram Ali Khan; Salwa El-Morsy; Tamador Alihia; Mudassir Hussain Bukhari; Ammara Nosheen; Khuram Ali Khan; Salwa El-Morsy; Tamador Alihia

doi:10.3934/math.2025763

AIMS Mathematics

2025, Volume 10, Issue 7: 16994-17011. doi: 10.3934/math.2025763

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Research article

Integral inequalities involving a new class of generalized strongly modified $ (p, h) $-convex functions

1.
Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
2.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Received: 29 May 2025 Revised: 14 July 2025 Accepted: 21 July 2025 Published: 30 July 2025
MSC : 26D07, 26D15, 26E70

A novel class of generalized strongly modified (GSM) $ (p, h) $-convex functions (CFs) was presented in paper and its fundamental properties were established. Schur, Hermite-Hadamard (H-H), and Fejér inequalities were proved for this new notion of convexity. Several illustrations have been incorporated by selecting several GSM $ (p, h) $-CFs to substantiate the existence and feasibility of Schur, H-H, and Fejér-type inequalities. These inequalities are valuable resources for analyzing the characteristics of newly defined GSM $ (p, h) $-CFs. A comparison was given to show that the results of this study represent a significant improvement over those of earlier publications.
- convex function,
- Schur-type inequalities,
- H-H inequalities,
- Fejér-type inequalities,
- optimization
Citation: Mudassir Hussain Bukhari, Ammara Nosheen, Khuram Ali Khan, Salwa El-Morsy, Tamador Alihia. Integral inequalities involving a new class of generalized strongly modified $ (p, h) $-convex functions[J]. AIMS Mathematics, 2025, 10(7): 16994-17011. doi: 10.3934/math.2025763

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Abstract

A novel class of generalized strongly modified (GSM) $ (p, h) $-convex functions (CFs) was presented in paper and its fundamental properties were established. Schur, Hermite-Hadamard (H-H), and Fejér inequalities were proved for this new notion of convexity. Several illustrations have been incorporated by selecting several GSM $ (p, h) $-CFs to substantiate the existence and feasibility of Schur, H-H, and Fejér-type inequalities. These inequalities are valuable resources for analyzing the characteristics of newly defined GSM $ (p, h) $-CFs. A comparison was given to show that the results of this study represent a significant improvement over those of earlier publications.

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