Abstract
The aim of this paper is to establish the Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integral. We provide Hermite-Hadamard-Fejér inequalities for harmonically convex functions via Katugampola fractional integral in one dimension.
Highlights
A function f : K → R, where K is an interval of real numbers, is called convex if the following inequality holds: f (ru1 + (1 − r)u2) ≤ r f (u1) + (1 − r) f (u2), (1)
We give Hermite-Hadamard-Fejér type inequalities for harmonically convex functions via Katugampola fractional integral in one dimension which will play a key role for the results
The results provided in our paper are the generalizations of some earlier results
Summary
A function f : K → R, where K is an interval of real numbers, is called convex if the following inequality holds:. Dragomir [16] gave the Hadamard’s inequality for convex functions on the co-ordinate which is defined as: Definition 2 ([16]). A function f : ∆ = [u1, u2] × [v1, v2] ⊆ (0, ∞) × (0, ∞) → R is called co-ordinated harmonically convex on ∆ with u1 < u2 and v1 < v2, if f xz , yw ≤ rτ f (x, y) + r(1 − τ) f (x, w) + (1 − r)τ f (z, y) + (1 − r)(1 − τ) f (z, w), rx + (1 − r)z τy + (1 − τ)w for all r, τ ∈ [0, 1] and (x, y), (z, w) ∈ ∆. We give result for harmonically convex functions in one dimension
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