Abstract
The concept of symmetry is inherent in the study of metric spaces due to the presence of the symmetric property of the metric. Significant results, such as with the Borsuk–Ulam theorem, make use of fixed-point arguments in their proofs to deal with certain symmetry principles. As such, the study of fixed-point results in metric spaces is highly correlated with the symmetry concept. In the current paper, we first define a new and modified Ćirić-Reich–Rus-type contraction in a b-metric space by incorporating the constant s in its definition and establish the corresponding fixed-point result. Next, we adopt an interpolative approach to establish some more fixed-point theorems. Existence of fixed points for ω -interpolative Ćirić-Reich–Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.
Highlights
IntroductionWe present the literature review in the current context and motivate the present study
In this introductory section, we present the literature review in the current context and motivate the present study.The Banach Contraction principle [1] found its applications in several branches of mathematics, including other branches such as physics, chemistry, economics, computer science, and biology.As a result, investigation and generalization of this result turned out to be a prime area of research in nonlinear analysis
We considered interpolative contractions in bMS
Summary
We present the literature review in the current context and motivate the present study. If a self-map I, defined on a complete metric space ( M, δ) satisfies the inequality: δ( Iμ, Iν) ≤ λ[δ(μ, ν) + δ(μ, Iμ) + δ(ν, Iν)], for all μ, ν ∈ M and for λ ∈ [0, 31 ), I has a unique fixed point. We define a new and modified Ćirić-Reich–Rus type contraction (in short, we call it the MCRR-type contraction) in a bMS by incorporating the constant s in its definition and discuss the corresponding fixed-point theorem. Ćirić-Reich–Rus type contraction (in short, CRR-type contraction) is defined and the existence of its fixed point is established assuming continuity of that self-map. In the third and final result, we show that continuity of the self-map may be dropped if it is replaced by a weaker condition
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