Fractal set of generalized countable partial iterated function system with generalized contractions via partial Hausdorff metric

Abstract

The primary interest of this article is to extend the fixed point result proved for a complete partial metric space (simply, pms) with a generalized contraction to a bivariate case. Taking this as a basic note, a generalized countable partial iterated function system (GCPIFS, for short) is introduced with the generalized contractions, using the partial Hausdorff metric. The attractor of this GCPIFS is proved as the fixed point of the generalized Hutchinson operator concentrated on the complete metric space (CBpm⁎(P⁎)×CBpm⁎(P⁎),Hpm⁎). A certain number of examples are given to show the existence of the theoretical results which we proved.