Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 145-186.

GENERALIZED HERMITE-HADAMARD INEQUALITIES FOR (α, η, γ, δ)-p CONVEX FUNCTIONS

Muhammad Bilal, Silvestru Sever Dragomir and Asif Raza Khan

Mathematics, College of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia
DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
e-mail: sever.dragomir@vu.edu.au

Department of Mathematics, University of Karachi, University Road, Karachi-75270, Pakistan
e-mail: asifrk@uok.edu.pk

Abstract.   In this article, we would like to introduce another generalized class of convex functions which we call as (α, η, γ, δ)-p convex functions. This new class contains another two new classes namely, (α, η)-p convex functions of the 1^st and 2^nd kinds. Further, we also generalize some results related to famous Hermite-Hadamard type inequality stated in [2] for the aforementioned class of functions with distinct techniques. Hence various existed and new results would be captured as special case of our obtained results. Moreover, application to midpoint formula has also been established.

2020 Mathematics Subject Classification.   26A46, 26A51, 26D07, 26D99.

Key words and phrases.   Hermite-Hadamard type inequities, p-convex functions, (α, η)-convex function of the 1^st kind, (α, η)-convex function of the 2^nd kind, (α, η, γ, δ)-convex function.

DOI: https://doi.org/10.21857/mzvkptoj19

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