Some New Results for Jaggi-W-Contraction-Type Mappings on b-Metric-like Spaces

Abstract

In this article, we generalize, improve, unify and enrich some results for Jaggi-W-contraction-type mappings in the framework of b-metric-like spaces. Our results supplement numerous methods in the existing literature, and we created new approach to prove that a Picard sequence is Cauchy in a b-metric-like space. Among other things, we prove Wardowski’s theorem, but now by using only the property (W1). Our proofs in this article are much shorter than ones in recently published papers.

Some critical remarks on recent results concerning $\digamma-$contractions in $b$-metric spaces

“…For more synthesis on the results based on 𭟋−contractions, we refer the reader to the informative and notable articles [10,11,16,17,18,19,20,21,22,24,26,29,30,31,32,33,34].…”

On F-Contractions: A Survey

“…We recall the following two properties of sequences in metric spaces that have often been used, sometimes implicitly, in proving fixed point results (see, e.g., [6][7][8][9][10][11][12][13] for the first property and [10][11][12][13][14] for the second one).…”

“…Vector-valued spaces and Perov-type problems were treated in [127,128]. F-contractions in metric-like and b-metric-like spaces were under investigation in [9,[129][130][131][132][133][134][135]. Partial metric spaces and F-contractions in them were treated in [136][137][138][139][140][141].…”

Unique Common Fixed Points for Occasionally Weakly Biased Maps of Type A in b -Metric-Like Spaces

“…According to them, their theorems generalize and ameliorate many prominent results in both metric-like and partial metric spaces. Several authors proved the existence and uniqueness of fixed points in b-metric and b-metric-like spaces (see, for instance, [15][16][17][18] and [19]). In addition, fixed points can exist under several different conditions.…”