Fixed Points of Almost Geraghty Contraction Type Maps/Generalized Contraction Maps With Rational Expressions in b-Metric Spaces

Document Type: Original Article


Department of Mathematics, Andhra University, Visakhapatnam-530 003, India


In this paper, we introduce almost Geraghty contraction type maps for a single self map and
prove the existence and uniqueness of fixed points. We extend it to a pair of selfmaps by defining
almost Geraghty contraction type pair of maps in which one of the maps is b-continuous in a
complete b-metric space. Further, we prove the existence of common fixed points for a pair of
selfmaps satisfying a generalized contraction condition with rational expression in which one of
the maps is b-continuous. Our results extend and generalize some of the known results that are
available in the literature. We draw some corollaries from our results and provide examples in
support of our results.


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