关键词: 锥理论;算子方程;Banach压缩映象原理;微分积分方程.

Abstract:

By using the  cone theory and the Banach contraction mapping principle,  the existence and uniqueness theorem of solutions for a class of nonlinear opera tor equations in ordered Banach spaces are investigated in more general condition. As an application, an existence and uniqueness theorem of solutions for initial  value problems of  nonlinear second order integro differential equations of mixed type in Banach  spaces are given. The results presented here improve and generalize some known results.

Key words: Cone theory, Operator equation, Banach contraction mapping principle, Integro differential equation