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 andmodified 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 w-interpolative Ćirić-Reich-Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.