A New Common Fixed Point Theorem for Six Self-Mappings in Complete Metric Spaces

Feng Gu, Xiaotang Shi

Abstract

Before, people extend some common fixed point theorems from the commuting mappings to the compatible mappings, so that fixed point theory has been further developed. However, these results are mostly for the two mappings, the three mappings, or four mappings given the circumstances. In this paper, we introduce a new contractive condition for six self-mappings, by using the compatible and sub-compatible conditions of self-mapping pairs, the existence and uniqueness of common fixed point in complete metric spaces is discussed, a new common fixed point theorem is obtained, and we succeed in getting the conclusion that six self-mappings in complete metric space has only one common fixed point. Our result extends, generalized and improves some results of Ciric, Gu, Li, Iseki, Rhoades, etc.