Abstract
In this manuscript, using rational type contractive conditions the existence and uniqueness of common $n$-tupled fixed point for a pair of mappings in complete $b$-metric spaces are studied. Using the derived results some fixed theorems can be deduced in $b-$metric spaces.
Highlights
Introduction and preliminariesThe Bananch contraction theorem is the most important technique for solving nonlinear integral equations, differential equations and functional equations etc
To solve the problem of the convergence of measurable functions with respect to a measure, Bakhtin [2] and Czerwik [7] introduced the concept of b-metric spaces called metric type space [18]
Yamaod et al [19] studied the existence of a common solution for a system of nonlinear integral equations via fixed point methods in b-metric space
Summary
The Bananch contraction theorem is the most important technique for solving nonlinear integral equations, differential equations and functional equations etc. Paknazar et al [14] introduced the concept of a new g-monotone mapping and defined the notions of n-fixed point and n-coincidence point and proved some related theorems for nonlinear contractive mappings in partially ordered complete metric spaces. In [22] the authors introduced the notion of compatibility for n-tupled coincidence points and proved n-tupled fixed point for compatible mappings satisfying contractive type conditions in partially ordered metric spaces. Husain et al [23] present some n-tupled coincidence point results for a pair of mappings without mixed monotone property satisfying a rational type contractive condition in metric spaces equipped with a partial ordering as well as present results on the existence and uniqueness of n-tupled common fixed points.
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