Fixed points on partial metric type spaces

Abstract

In this paper, we give and prove two Chatterjea type fixed point theorems on partial b-metric space. We propose an extension to the Banach contaction principle on partial b-metric space which was already presented by Shukla and also study some related results on the completion of a partial metric type space. In particular, we prove a joint Chatterjea-Kannan fixed point theorem. We verify the T -stability of Picard's iteration and conjecture the P property for such maps. We also give examples to illustrate our results.is a basis for a topology τ (p) on X. The topology τ (p) is T 0 .

Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces

“…For more details on other generalized metric spaces see [8][9][10][11][12][13][14]. The next proposition helps us to construct some more examples of b-metric (respectively partial b-metric, b-metric-like) spaces.…”

Results on Complex Partial b-Metric Space with an Application

“…Many authors have studied related interesting metric such as structures along with some applications. And, in this line, significant results have been obtained and can be read in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In this paper, under new contraction condition, we prove a fixed point theorem in complex partial b-metric space.…”