ON AN ABSTRACT CONTRACTION MAPPING PRINCIPLE

The existence problems of the theory of differential and integral equations and other functional equatiens leads to fixed point equations considered in various function spaces. There are various methods to deal with the fixed point equations.The classical one is the successive approximations method and Banach's contraction principle. Recently,the classioal contraction principle has been generalized by introducing a much more general form of the comparison function,and both fixed point and common fixed point problems for mappings have been discussed (cf.[1～8]). The purpose of this paper is to extend and unify the results of the authors mentioned above.