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

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-Had...

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Veröffentlicht in:PloS one Jg. 19; H. 10; S. e0311386
Hauptverfasser: Nosheen, Ammara, Khan, Khuram Ali, Bukhari, Mudassir Hussain, Kahungu, Michael Kikomba, Aljohani, A. F.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States Public Library of Science 15.10.2024
Schlagworte:
Algorithms
Analysis
Applied mathematics
Calculus
Convex analysis
Convex functions
Convexity
Derivatives
Functions (mathematics)
Inequalities
Inequalities (Mathematics)
Integrals
Mathematical analysis
Models, Theoretical
Numerical analysis
Physical Sciences
Research and Analysis Methods
Riemann integral
Validity
Saudi Arabia
ISSN:1932-6203, 1932-6203
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Zusammenfassung: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.
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Competing Interests: The authors have declared that no competing interests exist.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0311386