International Journal of Nonlinear Analysis and Applications

Ostrowski type inequalities via (α,β,γ,δ)-convex function

Articles in Press

Document Type : Research Paper

Authors

1 Shah Abdul Latif University, Department of Mathematics, Khairpur-66020, Pakistan

2 University of Karachi, Faculty of Science, Department of Mathematical Sciences, University Road, Karachi-75270, Pakistan

10.22075/ijnaa.2021.24568.2771

Abstract

In this paper, we are introducing very first time the class of (α,β,γ,δ)− convex (concave) function in mixed kind, which is the generalization of many classes of functions given in   [2, 3, 4, 15, 16, 17].  We would like to state the well-known Ostrowski inequality via generalized Montgomery identity [14] for (α,β,γ,δ)− convex (concave) function in mixed kind. In addition, we establish some Ostrowski-type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α,β,γ,δ)-convex (concave) functions in mixed kind by using different techniques including Holder's inequality [27] and power mean inequality [26]. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 19 January 2025
  • Receive Date: 17 September 2021
  • Revise Date: 24 September 2021
  • Accept Date: 16 December 2021