Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

Abstract

This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.

Keywords

• integro-differential equation
• mild solution
• resolvent operator
• global convergence
• uniqueness
• successive approximations
• 45j05
• 47g20
• 34g20
• 65l05
• 34a45