Extensions of \varphi-Fixed Point Results via w-Distance

In this paper, we obtain a \varphi-fixed point result concerning w-distance. There are three illustrative examples. In a separate section, we compare of the present result with that of the corresponding results prevalent in metric spaces and indicate certain new features obtained using w-distance. One such feature is that under certain circumstances, the fixed point can be a point of discontinuity, which is impossible in the metric case. We give an application to non-linear integral equations. The paper ends with a conclusion.

Keywords:

Fixed point , Metric space , φ-fixed point , w-distance , Integral equation