Abstract
The aim of this paper is to prove a coincidence point theorem for a class of self mappings satisfying nonexpansive type condition under various conditions and a fixed point theorem is also obtained. Our results extend and generalize the corresponding result of Singh and Chandrashekhar [A fixed point theorem in a 2-metric space and an application, J. Natural and Physical Sci. 15(1-2) (2001), 55-64].
Highlights
The concept of 2-metric space was introduced by Gähler [2, 3, 4] whose abstract properties were suggested by the area function in Euclidean space
Employing various contractive conditions Iséki [5] setout the tradition of proving fixed point theorems in 2-metric spaces
Naidu and Prasad [6] contributed few fixed point theorems in 2-metric spaces introducing the concept of weak commutativity
Summary
Introduction and PreliminariesThe concept of 2-metric space was introduced by Gähler [2, 3, 4] whose abstract properties were suggested by the area function in Euclidean space. Let (X , d ) be a 2-metric space and T : X → X be a self mapping satisfying the following nonexpansive type condition: d (Tx, Ty, u) Let Ψ be a set of all continuous functions ψ : R+ → R+ satisfying the following conditions: ( ψ1 ) ψ is continuous and strictly increasing.
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