REVISITING FEJÉR–HERMITE–HADAMARD TYPE INEQUALITIES IN FRACTAL DOMAIN AND APPLICATIONS

Saima Rashid (), Aasma Khalid (), Yeliz Karaca () and Yu-Ming Chu
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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, Pakistan
Yeliz Karaca: University of Massachusetts Medical School, Worcester, MA 01655, USA
Yu-Ming Chu: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China5Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-26

Abstract: In this paper, some new fractal versions of Fejér–Hermite–Hadamard (FHH) type variants for generalized Raina (Ψ, ℠)-convex mappings are established benefiting from Raina’s function and fractal set ℠φ, 0 < φ < 1. By means of three integral identities coupled with Raina’s function and local differentiation, we established some bounds for the difference between the left and central parts and also the difference between the center and right parts in FHH inequality. Besides that, some illustrative examples and noted special cases are apprehended. Additionally, we developed various generalizations for random variables, cumulative distribution functions, and special function theory as applications of local fractional integrals. The consequences established can provide contribution to inequality theory, fractional calculus and probability theory from the viewpoint of application to establish the other associated classes of functions. With the aid of these methodologies, it is promising to comprise further bounds of other type of variants which involve local fractional techniques.

Keywords: Convex Functions; Fejér–Hermite–Hadamard Inequality; Raina Function; Mittag-Leffler Function; Hypergeometric Function; Local Fractional Integrals (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401338

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