On Riemann–Liouville Integral via Strongly Modified (<i>h</i>,<i>m</i>)-Convex Functions

On Riemann–Liouville Integral via Strongly Modified (<i>h</i>,<i>m</i>)-Convex Functions

The generalization of strongly convex and strongly <i>m</i>-convex functions is presented in this paper. We began by proving the properties of a strongly modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semanti...

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Bibliographic Details
Main Authors: Ali N. A. Koam, Ammara Nosheen, Khuram Ali Khan, Mudassir Hussain Bukhari, Ali Ahmad, Maryam Salem Alatawi
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Fractal and Fractional
Subjects:
convex function (CF)
schur inequality
Hermite–Hadamard inequalities
Online Access:https://www.mdpi.com/2504-3110/8/12/680
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Summary:The generalization of strongly convex and strongly <i>m</i>-convex functions is presented in this paper. We began by proving the properties of a strongly modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>h</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></semantics></math></inline-formula>-convex function. The Schur inequality and the Hermite–Hadamard (H-H) inequalities are proved for the proposed class. Moreover, H-H inequalities are also proved in the context of Riemann–Liouville (R-L) integrals. Some examples and graphs are also presented in order to show the existence of this newly defined class.
ISSN:2504-3110

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