Abstract
ObjectivesIn this paper we present some fixed point theorems for self mappings satisfying generalized (phi , psi )-weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results.ResultWe obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized (phi , psi )-weak contraction mappings in partially ordered complete b-metric space.
Highlights
Fixed points of mappings satisfying contractive conditions in generalized metric spaces are highly useful in large number of mathematical problems of pure and applied mathematics
Ran and Reuings [1] have extended the result in this direction, discussed the existence of fixed points for certain maps in ordered metric space and presented some applications to matrix linear equations
We introduce the class of generalized (φ, ψ)-weak contraction to establish an existence of a fixed point and its uniqueness of a self mapping and common fixed point, coincidence point for two self mappings in ordered complete b metric space
Summary
We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function.
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