I.V-CR-γ-Convex Functions and Their Application in Fractional Hermite–Hadamard Inequalities

Miguel Vivas-Cortez, Sofia Ramzan, Muhammad Uzair Awan, Muhammad Zakria Javed, Awais Gul Khan, Muhammad Aslam Noor

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. Interval-valued convex mappings are a special type of set-valued maps. These have a close relationship with symmetry analysis. One of the important aspects of the relationship between convex and symmetric analysis is the ability to work on one field and apply its principles to another. In this paper, we introduce a novel class of interval-valued (I.V.) functions called (Formula presented.) - (Formula presented.) -convex functions based on a non-negative mapping (Formula presented.) and center-radius ordering relation. Due to its generic property, a set of new and known forms of convexity can be obtained. First, we derive new generalized discrete and integral forms of Jensen’s inequalities using (Formula presented.) - (Formula presented.) -convex I.V. functions. We employ this definition and Riemann-Liouville fractional operators to develop new fractional versions of Hermite-Hadamard’s, Hermite-Hadamard-Fejer, and Pachpatte’s type integral inequalities. We examine various key properties of this class of functions by considering them as special cases. Finally, we support our findings with interesting examples and graphical representations.

Original languageEnglish
Article number1405
JournalSymmetry
Volume15
Issue number7
DOIs
StatePublished - 12 Jul 2023

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

Keywords

  • CR-γ-convex interval-valued functions
  • Hermite-Hadamard’s inequality
  • Jensen’s inequality
  • interval-valued functions

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