Abstract
We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.
Highlights
Introduction and PreliminariesBanach’s contraction principle [1] has been applied in several branches of mathematics
As a result, researching and generalizing this outcome has proven to be a research area in nonlinear analysis. It is a well-known fact that a map that satisfies the Banach contraction principle is necessarily continuous
The concept of the interpolation Kannan-type contraction appeared with Karapinar [8] in 2018; this concept appealed to many researchers [8,9,10,11,12,13,14], making them invest in various types of contractions: interpolative
Summary
Introduction and PreliminariesBanach’s contraction principle [1] has been applied in several branches of mathematics. Let { xn } be a sequence in a b-metric space ( X, d).
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