On Riemann-Liouville integrals and Caputo Fractional derivatives via strongly modified (p, h)-convex functions

PLoS One. 2024 Oct 15;19(10):e0311386. doi: 10.1371/journal.pone.0311386. eCollection 2024.

Abstract

The paper introduces a new class of convexity named strongly modified (p, h)-convex functions and establishes various properties of these functions, providing a comprehensive understanding of their behavior and characteristics. Additionally, the paper investigates Schur inequality and Hermite-Hadamard (H-H) inequalities for this new class of convexity. Also, H-H inequalities are proved within context of Riemann-Liouville integrals and Caputo Fractional derivatives. The efficiency and feasibility of Schur inequality and H-H inequalities are supported by incorporating multiple illustrations, that demonstrate the applicability of strongly modified (p, h)-convex functions. The results contribute to the field of mathematical analysis and provide valuable insights into the properties and applications of strongly modified (p, h)-convex functions.

MeSH terms

  • Algorithms*
  • Models, Theoretical

Grants and funding

The author(s) received no specific funding for this work.