A New Extension of b-Metric Spaces in BC Frameworks with an Application to Integral Equations

Abstract

In this paper, the term ”Bicomplex valued extended b-metric spaces” or briefly ”BC-valued extended b-metric spaces” refers to a new extension of bicomplex valued b-metric spaces that we introduce in this study. Using this novel class of metric spaces, we extend numerous findings from literature and establish fixed point theorems with the aid of illustrative examples. Moreover, as an application of our results, we show that a unique solution of the Urysohn integral exists.

Keywords: BC numbers; Metric spaces; BC- b-metric spaces; Fixed point.

2010 Mathematics Subject Classification. 54H25, 47H10, 54D99