Abstract
The new outcomes of the present paper are q -analogues ( q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature.
Highlights
Integral inequalities provide a notable role in both pure and applied mathematics in the light of their wide applications in numerous regular and human sociologies, while convexity hypothesis has stayed a significant apparatus in the foundation of the theory of integral inequalities
Many authors proved numerous inequalities associated with the functions of bounded variation, Lipschitzian, monotone, absolutely continuous, convex functions, s-convex, h-convex, and n-times differentiable mappings with error estimates
Let Φ : J ⊂ R+ ⟶ R is a q-differentiable mapping on J∘ and DqΦ ∈ L1⁄2℘,υ, in which ℘, υ ∈ J for ℘
Summary
Integral inequalities provide a notable role in both pure and applied mathematics in the light of their wide applications in numerous regular and human sociologies, while convexity hypothesis has stayed a significant apparatus in the foundation of the theory of integral inequalities. By using Lemma 2, Alomari et al in [26] had proved the Ostrowski type inequality, which holds for s-convex mappings in second sense as follows: Theorem 3. Suppose that Φ : J ⊂ R+ ⟶ R is differentiable on ð℘, υÞ and Φ′ ∈ L1⁄2℘,υ, in which ℘, υ ∈ J for ℘
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