SERENDIPITY FIXED POINT WITH RESPECT TO PGA CONTRACTION

P L Powar and GRK Sahu [14] noticed that the fixed point may not exist for some self maps T defined on a set X. To deal with such cases the idea of Serendipity fixed point had been introduced by P L Powar in 2015. Considering the lighter concept of completeness viz. weak completeness, the existence and uniqueness of Serendipity fixed point had been established under contraction condition. In this paper we established the result for  existence of serendipity fixed point under the PGA contraction [15] defined by  Akhilesh Pathak in 2018. This idea may be useful in solving or simplifying the problems which are totally based on fixed point theory.