New Modifications of Integral Inequalities via ? -Convexity Pertaining to Fractional Calculus and Their Applications

Saima Rashid, Aasma Khalid, Omar Bazighifan and Georgia Irina Oros
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Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Aasma Khalid: Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan
Omar Bazighifan: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Georgia Irina Oros: Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania

Mathematics, 2021, vol. 9, issue 15, 1-23

Abstract: Integral inequalities for ? -convex functions are established by using a generalised fractional integral operator based on Raina’s function. Hermite–Hadamard type inequality is presented for ? -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 ? -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.

Keywords: Hermite–Hadamard inequality; Ostrowski type inequality; ?-convex function; generalised fractional integral; matrices; Fox–Wright function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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