Abstract
We prove common fixed point theorem for coincidentally commuting nonself mappings satisfying generalized contraction condition of Ciric type in cone metric space. Our results generalize and extend all the recent results related to non-self mappings in the setting of cone metric space.
Highlights
Huang and Zhang 1 introduced the concept of cone metric space by replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mappings satisfying different contractive conditions
Many authors like Abbas and Jungck 2, Abbas and Rhoades 3, Ilicand Rakocevic 4, Raja and Vaezpour 5 have generalized the results of Huang and Zhang 1 and studied the existence of common fixed points of a pair of self mappings satisfying a contractive type condition in the framework of normal cone metric spaces
The aim of this paper is to prove common fixed point theorems for coincidentally commuting nonself mappings satisfying a generalized contraction condition of Cirictype in the setting of cone metric spaces
Summary
Huang and Zhang 1 introduced the concept of cone metric space by replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mappings satisfying different contractive conditions. Radenovicand Rhoades 10 extended the fixed point theorem of Imdad and Kumar 17 for a pair of nonself mappings to nonnormal cone metric spaces.
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