Document Type : Original Article

**Authors**

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

**Abstract**

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.

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.

**Keywords**

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Summer and Autumn 2019

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