New Modifications of Integral Inequalities via <i>℘</i>-Convexity Pertaining to Fractional Calculus and Their Applications

New Modifications of Integral Inequalities via <i>℘</i>-Convexity Pertaining to Fractional Calculus and Their Applications

Integral inequalities for <i>℘</i>-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for <i>℘</i>-convex functions via generalised fractional integral operator. A novel...

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Bibliographic Details
Main Authors: Saima Rashid, Aasma Khalid, Omar Bazighifan, Georgia Irina Oros
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Mathematics
Subjects:
Hermite–Hadamard inequality
Ostrowski type inequality
℘-convex function
generalised fractional integral
matrices
Fox–Wright function
Online Access:https://www.mdpi.com/2227-7390/9/15/1753
Description
Summary:Integral inequalities for <i>℘</i>-convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for <i>℘</i>-convex functions via generalised fractional integral operator. A novel parameterized auxiliary identity involving generalised fractional integral is proposed for differentiable mappings. By using auxiliary identity, we derive several Ostrowski type inequalities for functions whose absolute values are <i>℘</i>-convex mappings. It is presented that the obtained outcomes exhibit classical convex and harmonically convex functions which have been verified using Riemann–Liouville fractional integral. Several generalisations and special cases are carried out to verify the robustness and efficiency of the suggested scheme in matrices and Fox–Wright generalised hypergeometric functions.
ISSN:2227-7390

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