Enriched G-Contractions on Banach Spaces with Directed Graphs
DOI:
https://doi.org/10.66147/lnaa.20264390Keywords:
Fixed points, Enriched G-contraction, Averaged OperatorAbstract
This paper introduces enriched G-contraction mappings on Banach spaces endowed with a directed graph, generalizing both enriched contractions and G-contractions. We establish the existence and uniqueness of fixed points under suitable conditions by employing an associated averaged operator. It is shown that such mappings are orbitally G-continuous in symmetric graphs, and their iterates yield anchored contractions.
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