Some Fixed Point Theorems in 2-Metric Spaces
نویسندگان
چکیده
The concept of 2-metric space is a natural generalization of the metric space. Initially, it has been investigated by Gähler [3] and has been developed broadly by Gähler [4, 5] and more. After this number of fixed point theorems have been proved for 2-metric spaces by introducing compatible mappings, which are more general than commuting and weakly commuting mappings. Jungck and Rhoades defined the concepts of d-compatible and weakly compatible mappings as extensions of the concept of compatible mapping for single-valued mappings on metric spaces. Several authors used these concepts to prove some common fixed point theorems. Iseki [7,8] is well-known in this literature which also include cho et.al.[1,2], Imdad et.al.[9], Murthy et.al.[11], Naidu and Prasad [12], Pathak et.al. [13]. Vishal Gupta et al [6] also prove some common fixed point theorems for a class of A-contraction on 2metric space. Various authors [14, 15, 16] used the concepts of weakly commuting mappings, compatible mappings of type (A) and (P) and weakly compatible mappings of type(A) to prove fixed point theorems in 2-metric space. Commutability of two mappings was weakened by Sessa [15] with weakly commuting mappings. Jungck [16] extended the class of non-commuting mappings by compatible mappings.
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