Abstract
In this paper, utilizing an identity given by Yıldız and Sarıkaya in (Yildiz and Sarikaya in Int. J. Anal. Appl. 13(1):64–69, 2017), we establish some weighted Ostrowski type inequalities for co-ordinated convex functions in a rectangle from the plane mathbb{R} ^{2}. Moreover, as special cases of our main results, we give some weighted Hermite–Hadamard type inequalities. The results given in this paper provide generalizations of some result established in earlier works.
Highlights
In the history of calculus development, integral inequalities have been thought of as a key factor in the theory of differential and integral equations
The study of various types of integral inequalities has been in the focus of great attention of a number of scientists interested in both pure and applied mathematics for more than a century
Ostrowski [15] is the following classical integral inequality associated with the differentiable mappings: Let F : [ρ1, ρ2]→ R be a differentiable mapping on (ρ1, ρ2) whose derivative F : (ρ1, ρ2)→ R is bounded on (ρ1, ρ2), i.e., F ∞ = sup |F (ψ)| < ∞
Summary
In the history of calculus development, integral inequalities have been thought of as a key factor in the theory of differential and integral equations. M. Ostrowski [15] is the following classical integral inequality associated with the differentiable mappings: Let F : [ρ1, ρ2]→ R be a differentiable mapping on (ρ1, ρ2) whose derivative F : (ρ1, ρ2)→ R is bounded on (ρ1, ρ2), i.e., F ∞ = sup |F (ψ)| < ∞. These inequalities state that if F : I → R is a convex function
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