Abstract

The aim of this present paper is to establish some new integrodifferential inequalities of Gronwall type involving functions of one independent variable which provide explicit bounds on unknown functions. The inequalities given here can be used in the analysis of a class of differential equations as handy tools.

Highlights

  • The differential and integral inequalities occupy a very privileged position in the theory of differential and integral equations

  • The integrodifferential inequalities recently established by Gronwall and others [1]-[12] have attracted considerable attention in the theory of differential and integral equations. This fact encourages us to find the explicit bounds on some fundamental integrodifferential inequalities which can be applied fairly well to achieve a diversity of desired goals

  • (1977) gave the following useful integrodifferential inequality: Let u (t ), u (t ) and b (t ) be nonnegative continuous functions defined on R+ and a > 0 is constant

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Summary

Introduction

The differential and integral inequalities occupy a very privileged position in the theory of differential and integral equations. The integrodifferential inequalities recently established by Gronwall and others [1]-[12] have attracted considerable attention in the theory of differential and integral equations. This fact encourages us to find the explicit bounds on some fundamental integrodifferential inequalities which can be applied fairly well to achieve a diversity of desired goals.

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