Abstract
In this paper, we study the existence of coincidence points and common fixed point theorem for three self - mappings in cone metric spaces and relaxing the completeness of the space. This result extends and improves the results of M. Abbas and B. E. Rhoades [M. Abbas and B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22(2009) 511-515] who proved fixed point theorems for two self-mappings without assuming commutativity conditions in cone metric spaces and using the completeness of the space.
Highlights
Ordered Banach spaces, normal cones and topical functions have applications in optimization theory is one of the motivation for research in ordered linear metric spaces
In 2007, cone metric space was introduced by Huang and Zhang [5] which a generalization of metric space into cone metric space replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems in this cone metric space
Rhoades [2] obtained some fixed point theorems in cone metric spaces for two self-maps without using the commutativity conditions
Summary
Let (X, d) be a cone metric space .We say that {xn} is a convergent sequence if for any c>>0, there is an N such that for all n>N, d(xn, x)
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