Some Common Fixed Point Results in Cone Metric Spaces for Rational Contractions

Abstract

A very engrossing technique in theory of contractive mapping fixed point. A number of authors have defined contractive type mappings on a cone metric spaces X which are generalization of the well -known Banach contraction, and have the property that each of such mapping has a unique fixed point. The fixed point can always be found by using Picard Iteration, opening with initial choice x₀∈X. In this manuscript, we generalize, extend and improve the result under the assumption of normality of cone for rational expression type contraction mapping in cone metric spaces. The present article is to provide a new alternative proof for two and three mapping and obtain the entity and exclusiveness of common fixed point. The concernment of the present paper to open a new direction of proof to be extended based on the methods of rational type contraction mapping in cone metric spaces of fixed-point theory. The assistance of this article is organized as follows. In section 2, preliminary notes. In this section we recall some standard notations and definitions which we needed. In section 3, the main results of the author are given. In this section we evidence of new results for two and three maps. In section 4, gives brief concluding note of the paper.