Certain Ostrowski type inequalities for generalized s-convex functions

Tomar, Muharrem; Agarwal, Praveen; Jleli, Mohamed; Samet, Bessem

doi:10.22436/jnsa.010.11.32

Cited by 18 publications

(8 citation statements)

References 10 publications

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“…Taking q-integral for (24) with respect to ı on (0, 1), and substituting u = ℘ 1 + ıF σ ρ,λ (℘ 2 − ℘ 1 ), we deduce the desired inequality (20). The proof of inequality (21) is similar so we omit it.…”

Section: Corollarymentioning

confidence: 96%

Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Vivas-Cortez

Kashuri

Liko

et al. 2020

Axioms

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In this work, a study is conducted on the Hermite–Hadamard inequality using a class of generalized convex functions that involves a generalized and parametrized class of special functions within the framework of quantum calculation. Similar results can be obtained from the results found for functions such as the hypergeometric function and the classical Mittag–Leffler function. The method used to obtain the results is classic in the study of quantum integral inequalities.

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Section: Corollarymentioning

confidence: 96%

Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Vivas-Cortez

Kashuri

Liko

et al. 2020

Axioms

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“…The application of the concept of convexity in modern analysis is a notorious fact [1][2][3]. Due to its importance and applications, this concept has been generalized in different ways.…”

Section: Introductionmentioning

confidence: 99%

Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

Vivas-Cortez

Kashuri

Liko

et al. 2020

Axioms

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In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite–Hadamard inequality for generalized coordinate ϕ-convex functions via an extension of the Riemann–Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina’s special function via generalized coordinate ϕ-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.

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“…In order to describe the denition of the local fractional derivative and local fractional integral, recently, one has introduced the following sets, see [8,21,24,27]. In this paper we are also motivated by, see [3] [5].…”

Section: Introductionmentioning

confidence: 99%

New Inequalities for Local Fractional Integrals Pertaining Generalized Strongly Convex Mappings

Kashuri¹

2020

matbil

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In this paper, we rst obtain a generalized integral identity for twice local fractional dierentiable mappings on fractal sets α (0 < α ≤ 1) of real line numbers. Then, using twice local fractional dierentiable mappings that are in absolute value at certain powers generalized strongly convex, we obtain some new estimates on generalization of trapezium-like inequalities. We also discuss some new special cases which can be deduced from our main results.

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Certain Ostrowski type inequalities for generalized s-convex functions

Abstract: In this paper, we first obtain a generalized integral identity for twice local differentiable functions. Then, using functions whose second derivatives in absolute value at certain powers are generalized s-convex in the second sense, we obtain some new Ostrowski type inequalities.

Cited by 18 publications

References 10 publications

Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions

Trapezium-Type Inequalities for an Extension of Riemann–Liouville Fractional Integrals Using Raina’s Special Function and Generalized Coordinate Convex Functions

New Inequalities for Local Fractional Integrals Pertaining Generalized Strongly Convex Mappings

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