Some new generalized 2D Ostrowski-Grüss type inequalities on time scales

AbstractIn this paper, we present some new generalized 2D Ostrowski-Grüss type integral inequalities on time scales, which on one hand extend some known results in the literature, and on the other hand unify corresponding continuous and discrete analysis. New bounds for the 2D Ostrowski-Grüss type inequalities are derived, some of which are sharp

Desigualdades fraccionarias generalizadas de tipo Ostrowski y Grüss que involucran varias funciones valoradas del álgebra de Banach

Usando fórmulas de Taylor vectoriales fraccionarias izquierda y derecha de Caputo generalizadas, establecemos desigualdades fraccionarias mixtas de tipo Ostrowski y Grüss que involucran varias funciones valoradas del álgebra de Banach. Las estimaciones son con respecto a todas las normas ∥·∥p, 1 ≤p ≤∞.Using generalized Caputo fractional left and right vectorial Taylor formulae, we establish mixed fractional Ostrowski and Grüss type inequalities involving several Banach algebra valued functions. The estimates are with respect to all norms ∥·∥p, 1 ≤p ≤∞

Ostrowski type fractional integral operators for generalized (;,,)−preinvex functions

In the present paper, the notion of generalized (;,,)−preinvex function is applied to establish some new generalizations of Ostrowski type inequalities via fractional integral operators. These results not only extend the results appeared in the literature but also provide new estimates on these type

On some Chebyshev type inequalities for the complex integral

Assume that f and g are continuous on γ, γ ⊂ C is a piecewisesmooth path parametrized by z (t) , t ∈ [a, b] from z (a) = u to z (b) = w withw 6= u, and the complex Chebyshev functional is defined bySean f y g funciones continuas sobre γ, siendo γ ⊂ C un caminosuave por partes parametrizado por z (t) , t ∈ [a, b] con z (a) = u y z (b) = w,w 6= u, y el funcional de Chebyshev complejo definido po

Generalized double-integral Ostrowski type inequalities on time scales

AbstractAn Ostrowski type inequality for a double integral is derived via a ΔΔ-integral on time scales; this generalizes an Ostrowski type inequality and some related results from Liu et al. (2010) [1]. Some new applications are also given

Combinatorial extensions of Popoviciu\u27s inequality via Abel-Gontscharoff polynomial with applications in information theory

We establish new refinements and improvements of Popoviciu’s inequality for n-convex functions using Abel-Gontscharoff interpolating polynomial along with the aid of new Green functions. We construct new inequalities for n-convex functions and compute new upper bounds for Ostrowski and Grüss type inequalities. As an application of our work in information theory, we give new estimations for Shannon, Relative and Zipf-Mandelbrot entropies using generalized Popoviciu’s inequality