On Riemann-Liouville integrals and Caputo Fractional derivatives via strongly modified (p, h)-convex functions - Nosheen, Ammara; Khan, Khuram Ali; Bukhari, Mudassir Hussain; Kahungu, Michael Kikomba; Aljohani, A. F. (PloS one, 2024)
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.