Some New Fractional Inequalities Using n-Polynomials s-Type Convexity

Artion Kashuri, Themistocles M. Rassias () and Rozana Liko
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Artion Kashuri: University “Ismail Qemali”
Themistocles M. Rassias: National Technical University of Athens
Rozana Liko: University “Ismail Qemali”

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 457-476 from Springer

Abstract: Abstract In the present paper, the authors establish a new version of the Hermite–Hadamard and Ostrowski type fractional integral inequalities for a class of n-polynomial s-type convex functions. Using our generalizations we are able to also deduce some already known results. We present two different techniques, for functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex by employing k-fractional integral operators. These techniques have yielded some interesting results. In the form of corollaries, some estimates of k-fractional integrals are obtained which contain bounds of RL-fractional integrals. We also obtain a refined bound of the Midpoint, Trapezoidal, and Simpson type inequalities for twice differentiable n-polynomial s-type convex functions.

Keywords: Hermite–Hadamard inequality; Ostrowski inequality; Convex function; s-type convex functions; Hölder inequality; Power mean inequality; Primary: 26A51; Secondary: 26A33, 26D07, 26D10, 26D15 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_24

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DOI: 10.1007/978-3-030-84122-5_24

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