A COMMON FIXED POINT THEOREM OF MEIR AND KEELER TYPE

ABSTRACT. In this paper, we introduce the concept of compatible mappings of type (A) on a metric space, which is equivalent to the concept of compatible mappings under some conditions, and give a common fixed point theorem of Meir and Keeler type. Our result extends, generalized and improves some results of Meir-Keeler, Park-Bae, Park-Rhoades, Pant and Rao-Rao, etc. 1991 AMS SUBJECT CLASSIFICATION CODE. 54H25. KEY WORDS AND PHRASES. Common fixed points, compatible mappings of type (A), generalized (e, 6) {S, T}-contractions, and {S, T}-iterations. 1. INTRODUCTION. In [6], Jungck proved a common fixed point theorem of commuting mappings on a metric space. Since then, he and many authors extended, generalized and unified this theorem in many ways ([2], [4], [5], [7]-[10], [15]-[20], [22], [23]). For example, Sessa ([22])introduced the concept of weakly commuting mappings, which is a generalization of the concept of commuting mappings