Fixed Point Theorems For Probabilistic Densifying Mappings

Abstract

Main objective of this paper is to demonstrate some quirk and common fixed point theorems for probabilistic densifying mappings. The concept of Kuratowski function on a probabilistic metric space as a generalisation of Kuratowski measure of non-compactness were introduced by Bocsan and Constantin[1]. The major role of densifying mappings in the study of fixed point theory in metric and normed linear spaces is well –known. However, the concept of probabilistic densifying mapping was introduced by Bocsan[2] and sometimes Khan and Fisher[3] proved some fixed point theorems for densifying mappings and the results so obtained were generalized by Hadzic[4].Iseki[5] gave a result which is generalisation of the result of Furi and Vignoli[6] in densifying mappings and further Iseki’s results are generalized by Jain and Dixit[7] in same mappings.