A Note on Extended Z-Contraction

Abstract

In this article, we aim to evaluate and merge the as-scattered-as-possible results in fixed point theory from a general framework. In particular, we considered a common fixed point theorem via extended Z-contraction with respect to ψ -simulation function over an auxiliary function ξ in the setting of b-metric space. We investigated both the existence and uniqueness of common fixed points of such mappings. We used an example to illustrate the main result observed. Our main results cover several existing results in the corresponding literature.

Generalizations of some contractions in b-metric-like spaces and applications to boundary value problems

“…3 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa. 4 China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan. 5 College of Business Administration-Finance Department, Dar Al Uloom University Saudi Arabia, Riyadh, Saudi Arabia.…”

A new extension to the controlled metric type spaces endowed with a graph

“…That was the starting point for researchers around the globe to start generalize his result whether by changing the contractions or by generalizing the type of metric spaces, so it can cover a larger class of metrics; see . Lately, in [24], an extension of b-metric spaces to extended b-metric spaces was given by Kamran et al For related work, see [25][26][27][28][29][30]. Not much later, Mlaiki et al in [31], introduced another generalization to the b-metric spaces, so called controlled metric type spaces.…”

Proinov type contractions on dislocated b-metric spaces

“…More examples can be given, but here we stop to focus on the main motivation. Two of the new and original generalizations of metric notions are b-metrics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and dislocated metrics [17][18][19][20][21]. Very recently, these two notions have emerged under the name of dislocated b-metric [22,23].…”