Fractal and Fractional (Dec 2022)

Some Novel Inequalities for LR-(k,h-m)-p Convex Interval Valued Functions by Means of Pseudo Order Relation

  • Vuk Stojiljković,
  • Rajagopalan Ramaswamy,
  • Ola A. Ashour Abdelnaby,
  • Stojan Radenović

DOI
https://doi.org/10.3390/fractalfract6120726
Journal volume & issue
Vol. 6, no. 12
p. 726

Abstract

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In this paper, a new type of convexity is defined, namely, the left–right-(k,h-m)-p IVM (set-valued function) convexity. Utilizing the definition of this new convexity, we prove the Hadamard inequalities for noninteger Katugampola integrals. These inequalities generalize the noninteger Hadamard inequalities for a convex IVM, (p,h)-convex IVM, p-convex IVM, h-convex, s-convex in the second sense and many other related well-known classes of functions implicitly. An apt number of numerical examples are provided as supplements to the derived results.

Keywords