Generalized Hermite–Hadamard type inequalities for generalized F-convex function via local fractional integrals

In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets Rς (0<ς≤1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite–Hadamard type inequalities in the fractals sense. In this...

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Bibliographic Details
Published in:Chaos, solitons and fractals Vol. 168; p. 113172
Main Authors: Razzaq, Arslan, Rasheed, Tahir, Shaokat, Shahid
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.03.2023
Subjects:
Convex functions
Hermite–Hadamard inequality
Hölder’s inequality
Modulus function
Power mean inequality
Power mean inequality
Convex functions
Hermite–Hadamard inequality
Hölder’s inequality
Modulus function
ISSN:0960-0779
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Summary:In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets Rς (0<ς≤1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite–Hadamard type inequalities in the fractals sense. In this work, we present some new results by employing local fractional calculus for twice differentiable functions along with some new definitions. For the development of these new integral inequalities, we will use generalized Hölder-integral inequality and power mean integral inequality by using local fractional calculus. Moreover, we give some new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works.
ISSN:0960-0779
DOI:10.1016/j.chaos.2023.113172