Authors:Adam Najdecki, Jacek Tabor and Józef Tabor
Let X be a real vector space, V a subset of X and δ ≧ 0 a given number. We say that f: V → ℝ is a conditionally δ-convex function if for each convex combination t1υ1 + … + tnυn of elements of V such that t1υ1 + … + tnυn ∈ V the following inequality holds true:
Authors:Muhammad Aslam Noor, Gabriela Cristescu and Muhammad Uzair Awan
The aim of this paper is to obtain some new bounds having Riemann type quantum integrals within the class of strongly convex functions. The results obtained are sharp on limit q → 1. These new results reduce to Tariboon-Ntouyas, Merentes-Nikodem and other previously known results when q → 1, where 0 < q < 1. The sharpness of the results of Tariboon-Ntouyas and Merentes-Nikodem is proved as a consequence.