article · Filomat
This research introduces the concept of a multivalued Geraghty type contraction mapping that incorporates both CG-simulation functions and C-class functions. Using this theoretical framework, the study establishes new fixed point results that extend and generalise various existing theorems within mathematical literature. Furthermore, the findings are applied to derive fixed point results in settings endowed with graphs. The validity and credibility of the theoretical conclusions are demonstrated through an illustrative mathematical example.
Fixed point theorems are fundamental mathematical tools used to establish the existence of solutions for complex systems and equations. By broadening existing mathematical conditions to include graphs and new function types, this theoretical advance expands the analytical foundation available for addressing structured mathematical problems.
The abstract does not indicate an application pathway, as it presents purely theoretical mathematical research.
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The aim of this paper is to introduce the new concept of a multivalued Geraghty type contraction mapping using CG-simulation functions and C-class functions. Additionally, through this type of contraction, we establish fixed point results that generalize several known fixed point results in the literature. As consequences, we arrive at fixed point results endowed with graph. To demonstrate the credibility of our results, we give an example that proves it.
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DOI: 10.2298/fil2328709t
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