New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional in...

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Veröffentlicht in:Journal of function spaces Jg. 2021; S. 1 - 11
Hauptverfasser: Butt, Saad Ihsan, Yousaf, Saba, Asghar, Atifa, Khan, Khuram Ali, Moradi, Hamid Reza
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Hindawi 2021
John Wiley & Sons, Inc
Wiley
Schlagworte:
Calculus
Convex analysis
Fractional calculus
Hypergeometric functions
Inequalities
Information theory
Integrals
Random variables
Real numbers
ISSN:2314-8896, 2314-8888
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Zusammenfassung:In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.
Bibliographie:ObjectType-Article-1
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ISSN:2314-8896
2314-8888
DOI:10.1155/2021/5868326