Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

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 modifiedĆirić-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-interpolativeĆirić-Reich-Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.

Unified multivalued interpolative Reich–Rus–Ćirić-type contractions

“…Since the introduction of an interpolative Kannan contraction by Karapınar [8] many of the existing contraction type conditions have been modified utilizing the pattern of interpolative Kannan contraction. Details can be found in [10][11][12][13][14][15][16][17][18]. A few existing interpolative contraction type conditions are as follows:…”

New Extensions of Kannan’s and Reich’s Fixed Point Theorems for Multivalued Maps Using Wardowski’s Technique with Application to Integral Equations

“…Recently, Kannan's and Reich's fixed point theorems have been studied and extended in several directions. Particularly we refer to the research of Aydi et al [10,11], Bojor [12,13], Choudhury and Kundu [14], Debnath and de La Sen [15,16], Debnath et al [17,18], Gornicki [19], Karapinar et al [20], Mohammadi et al [21]. Some important work on the application of multivalued F-contractions were recently carried out by Sgroi and Vetro [22] and Ali and Kamran [23].…”

Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

“…It first knew improvements with Kannan [9] in 1968, and later with other researchers such as Rus,Ćirić, Reich, Hardy, and Rogers. Afterwards, it took another turning with Karapinar [10] in 2018 in a new version, which has made several researchers pursue this field (see [11][12][13][14][15][16][17][18][19]). us, the concept has been applied in various spaces: metric space, b-metric space, rectangular b-metric spaces, and the Branciari distance.…”