New dynamic fixed point results in Menger spaces

Abstract

The objective of this paper is to generalize and improve some results in fixed point theorems in both complete metric space and Menger space. These results are generalizations of the analogous ones recently proved by Khojasteh [5], Demma [1], Yildirim [13], where we establish a dynamic information about their other fixed points if there exist i.e the distance between two fixed point in case of metric space and their equivalent in probabilistic metric space. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses. As an application to our main result, we derive a uniqueness fixed point theorem for a self-mapping under strong conditions.

Keywords

• fixed point
• menger space
• picard sequence
• complete metric space