Abstract
The aim of this paper is to introduce the concept of compatible mappings of type (R) in 2-metric spaces and to prove a coincidence point theorem and a fixed point theorem for compatible mappings of type (R) in 2-matric spaces.
Highlights
Rohen Singh, M.R & Shambhu introduced the concept of compatible mappings of type (C) by combinging the definition of compatible mappings and compatible mapping of type (P) and later on it is renamed as compatible mappings of type (R) [9]
Later many authors [1] [5] [8] [16] have studied the aspects of fixed point theory in the setting of 2-metric paces in the last 50 years. They have been motivated by various concepts already known for metric spaces and have introduced analogous of various concepts in the framework of the 2-metric spaces, Murthy-Chang Cho-Sharma [7] introduced the concept of compatible pairs of self-mappings of type (A) in a 2-metric space and proved several common fixed points theorems
Pathak Chang & Cho [8] introduced the mappings of type (P) in 2-metric space and proved fixed point theorem in 2-metric spaces
Summary
Rohen Singh, M.R & Shambhu introduced the concept of compatible mappings of type (C) by combinging the definition of compatible mappings and compatible mapping of type (P) and later on it is renamed as compatible mappings of type (R) [9]. The following proposition show that Definition 2.4 and 2.5 are equivalent under some conditions Proposition (2.9): Let S and T be continuous mappings of a 2-metric space (X, d) into itself. As a direct consequence of Propositions 2.11, 2.12 and 2.13, we have the followings Proposition (2.14): Let S and T be continuous mappings of a 2-metric spaces (X, d) into itself. Proposition (2.15): Let S and T be compatible mappings of type (R) from a 2-metric space (X, d) into itself in
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