Explicit bound on a retarded integral inequality

On a Generalized Retarded Integral Inequality with Two Variables

Explicit Bounds on Some Nonlinear Retarded Integral Inequalities

In this paper some new retarded integral inequalities are established and explicit bounds on the unknown functions are derived. The present results extend some existing ones proved by Lipovan in [A retarded integral inequality and its applications, J. Math. Anal. Appl. 285 (2003) 436-443].

A Note on Retarded Ouyang Integral Inequalities

In this note, we generalize two retarded Ouyang integral inequalities. One of these inequalities says: under suitable assumptions of functions w,α, h, f, g and p on [0,∞), if w(t) ≤ h(t) + 2 ∫ α(t) 0 { f(s)w(s) [ w(s) + ∫ s 0 g(r)w(r)dr ] + p(s)w(s) } ds, then w(t) ≤ [ h(t) + ∫ α(t) 0 p(s)ds ] exp {∫ α(t) 0 [ f(s) + (∫ s 0 g(r)dr ) ds ]} , t ≥ 0. AMS Subject Classifications: 26D15.

Generalized retarded integral inequalities

We prove some new retarded integral inequalities. The results generalize those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265–275].

On an Integral Inequality

In this article we give different sufficient conditions for inequality (∫ b a f(x)dx )β ≥ ∫ b a f(x)dx to hold.