Compatible mappings of type (B) and common fixed point theorems of Greguš type

G. Jungck [4] introduced more generalized commuting mappings, called compatible mappings, which are more general than those of weakly commuting mappings [12].Several authors proved common fixed point theorems using this concept ([5]-[6] and [8]-[10]).In general, commuting mappings are weakly commuting and weakly commuting mappings are compatible, but the converses are not necessarily true.Recently, G. Jungck, P. P. Murthy and Y. J. Cho [7] defined the concept of compatible mappings of type (A) which is equivalent to the concept of compatible mappings under some conditions and proved a common fixed point theorem for compatible mappings of type (A) in a metric space.Further, P.P. Murthy, Y. J. Cho and B. Fisher [10] proved some fixed point theorems of Gregus type (see [l]-[3]) for compatible mappings of type (A) in Banach spaces.In this paper we introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in normed spaces.In the sequel, we derive some relations between these mappings.Also, we prove a common fixed point theorem of Gregus type for compatible mappings of type (B) in Banach spaces.* Research partially supported by U.G.C, New Delhi, India.1991 AMS Subject Classification Code: 54H25.Key words and phrases: Compatible mappings, compatible mappings of type (A), compatible mappings of type (B) and common fixed points.