FIXED POINT RESULTS FOR α-ψ-CONTRACTIVE MAPPINGS IN BIPOLAR METRIC SPACES
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Abstract
In this paper, we introduce the notion of alpha-psi contractive type covariant and contravariant mappings in the bipolar metric spaces, which provides a framework to study distances between dissimilar objects. In addition this, we prove some fixed point theorems, which give existence and uniqueness of fixed point, for alpha-psi contractive type covariant and contravariant mappings in complete bipolar metric spaces. On the other hand, we observe that some known fixed point theorems as Banach's and coupled are simple consequences of our obtained results. Once and for all, we state some examples to show usability of our main results.