On the existence of fixed points via condensed Reich-Rus-Ciric-type contractions

Abstract

Many research papers have recently studied the interpolation technique of contractive-type maps to examine the existence of nonlinear operators that do not require unique fixed points. In this article, we introduce a notion of condensed Reich-Rus-Ciric-type (CRRC) contraction to examine the existence of operators that require both unique and non-unique fixed points. By condensing the CRRC map, we establish and prove some fixed point theorems in standard metric spaces. An illustrative example is considered to show that the new CRRC-type map exhibits contracting behaviors when others do not. The study concludes that the new CRRC-type map improves and includes many known Reich-Rus-Ciric-type maps in the literature.