Department of Mathematics, University of Sargodha, Sargodha, Pakistan.
Higher Institute of Education of Gombe (ISP Gombe), Kinshasa, Congo.
PLoS One. 2024 Oct 15;19(10):e0311386. doi: 10.1371/journal.pone.0311386. eCollection 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.
本文引入了一类新的凸性——强修正（p,h）-凸函数，并建立了这些函数的各种性质，全面了解它们的行为和特征。此外，本文还研究了这一新类凸性的 Schur 不等式和 Hermite-Hadamard（H-H）不等式。此外，H-H 不等式是在 Riemann-Liouville 积分和 Caputo 分数导数的背景下证明的。Schur 不等式和 H-H 不等式的有效性和可行性通过包含多个示例得到支持，这些示例展示了强修正（p,h）-凸函数的适用性。这些结果为数学分析领域做出了贡献，并为强修正（p,h）-凸函数的性质和应用提供了有价值的见解。
