Study of inequalities for unified integral operators of generalized convex functions

In this paper, we give a generalized definition namely strongly α , h ‐ m -convex function that unifies many known definitions. By applying this new definition, we present inequalities for unified integral operators which have connection with many of the well-known results for different kinds of convex functions. Moreover, this paper at once provides refinements and generalizations of a lot of fractional integral inequalities which are identified in remarks.

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“…Adopting the same pattern of simplification as we did for (36) and (38), the following inequality can be observed for (38) and ( 37):…”

Section: Resultsmentioning

confidence: 77%

Inequalities for Unified Integral Operators via Strongly $(α, h ‐ m)$ -Convexity

Zhang

Farid

Mahreen

2021

Journal of Function Spaces

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“…These authors presented Hermite-Hadamard and trapezoidal type inequalities for this kind of fractional integrals in [47]. For the other similar inequalities, we refer to [14,15,25,30,33,45].…”

Section: Introductionmentioning

confidence: 99%

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

2021

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In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane $\mathbb{R} ^{2}$ R 2 . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

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“…Inequality (3), in the literature, is generalized by several fractional integral operators to meet the desired results, see, for instance, [25][26][27][28]. In this paper, we present the Hermite-Hadamard inequality for a strongly convex function in the setting of the Caputo-Fabrizio fractional integral operator.…”

Section: Introductionmentioning

confidence: 99%

On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications

Li¹,

Saleem

Yan³

et al. 2021

Journal of Mathematics

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The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly convex functions involving the Caputo–Fabrizio fractional integral operator are also presented. Moreover, we present some applications of the proposed inequalities to special means.

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Study of inequalities for unified integral operators of generalized convex functions

Cited by 17 publications

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Inequalities for Unified Integral Operators via Strongly $(α, h ‐ m)$ -Convexity

Inequalities for Unified Integral Operators via Strongly $(α, h ‐ m)$ -Convexity

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications

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Study of inequalities for unified integral operators of generalized convex functions

Cited by 17 publications

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Inequalities for Unified Integral Operators via Stronglyα,h‐m-Convexity

Inequalities for Unified Integral Operators via Stronglyα,h‐m-Convexity

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

On Strongly Convex Functions via Caputo–Fabrizio-Type Fractional Integral and Some Applications

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Inequalities for Unified Integral Operators via Strongly $(α, h ‐ m)$ -Convexity

Inequalities for Unified Integral Operators via Strongly $(α, h ‐ m)$ -Convexity