Abstract
The main objective of this paper is to derive some new generalizations of Ostrowski type inequalities for the functions whose first derivatives absolute value are harmonically convex. We also discuss some special cases of the obtained results. In the last section, we present some applications of the obtained results.
Highlights
Iscan [1] introduced the notion of harmonically convex functions as follows: A function Λ : I ⊂ (0, ∞) → R is said to be harmonically convex, if a1 a2
Iscan [4] obtained some Ostrowski type inequalities using the class of harmonically sconvex functions
Set [12] obtained some generalized fractional refinements of Ostrowski type inequalities using the class of s-convex functions
Summary
Several inequalities constitute direct consequences of applications of convexity In this regard, Hermite–Hadamard’s inequality is one of the most extensively as well as intensively studied result. Hermite–Hadamard’s inequality is one of the most extensively as well as intensively studied result It provides us with an estimate of the (integral) mean value of a continuous convex function. Iscan [4] obtained some Ostrowski type inequalities using the class of harmonically sconvex functions. Obtained new generalizations of Ostrowski type inequalities using harmonically h-convex functions. Set [12] obtained some generalized fractional refinements of Ostrowski type inequalities using the class of s-convex functions. The aim of this paper is to obtain some new generalizations of Ostrowski’s inequality essentially utilising the harmonic convexity property of the functions. We hope that the ideas and techniques presented within this paper will inspire interested readers
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