Hermite–Jensen–Mercer type inequalities for conformable integrals and related results

Butt, Saad Ihsan; Nadeem, Mehroz; Qaisar, Shahid; Akdemir, Ahmet Ocak; Abdeljawad, Thabet

doi:10.1186/s13662-020-02968-4

Cited by 22 publications

(13 citation statements)

References 24 publications

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“…assume a critical part in the foundation of the unique solution for fractional differential equations. For some recent articles on fractional inequalities, see References [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications

et al. 2021

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Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.

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Section: Introductionmentioning

confidence: 99%

New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications

et al. 2021

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“…The terms convexity and inequalities have a wide range of applications in the growth of variants branches of pure and applied mathematics as well as in different areas of pure and applied sciences. The initiative works and significant contributions of these two terminologies can be found in the literature, see the references [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. In 1938, Ostrowski [18], developed a significant integral inequality connected with differentiable functions.…”

Section: Introductionmentioning

confidence: 99%