A fixed point approach for tuning circuit problem in dislocated b-metric spaces

Abstract

The content of this article is threefold. First, we enunciate some novel results concerning Reich- (Formula presented.) mappings endowed with a graph (Formula presented.) in the context of dislocated b-metric spaces. By virtue of nontrivial examples, we show our results improve, extend, generalize, and unify several noteworthy results in the existing state-of-art. We adopt computer simulation validating our results. Second, we introduce some new fixed point results having index (Formula presented.) on the underlying mapping, which is entirely a new concept, followed by an illustrative example with various cases. Lastly, we present an application related to electrical engineering, where a problem concerning the transformation of solar energy to electric power is discussed. We also furnish some open problems related to our study that may open up new directions related to our findings.