Abstract
AbstractIn this paper, we introduce the notion of generalized cyclic contraction pairs in b-metric spaces and establish some fixed point theorems for such pairs. Also, we give some examples to illustrate the main results which properly generalizes some results given by some authors in literature. Further, by using the main results, we prove some common fixed point results for generalized contraction pairs in partially ordered b-metric spaces. Our results generalize and improve the result of Shatanawi and Postolache (Fixed Point Theory Appl. 2013:60, 2013) and several well-known results given by some authors in metric and b-metric spaces.
Highlights
Fixed point theory plays a basic role in applications of many branches of mathematics
Finding fixed points of generalized contraction mappings has become the focus of strong research activity in fixed point theory
We introduce the concept of new generalized cyclic contraction pairs in b-metric spaces and establish some fixed point theorems for such pairs in the setting of b-metric spaces
Summary
Fixed point theory plays a basic role in applications of many branches of mathematics. Since (X, d) is a complete b-metric space and {xn} is a b-Cauchy sequence in X, there exists z ∈ X such that lim n→∞
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