Notes on Some Recent Papers Concerning $F$-Contractions in $b$-Metric Spaces

Abstract

In several recent papers, attempts have been made to apply Wardowski's method of F-contractions in order to obtain fixed point results for single and multivalued mappings in b-metric spaces. In this article, it is shown that in most cases the conditions imposed on respective mappings are too strong and that the results can be obtained directly, i.e., without using most of the properties of auxiliary function F .

On the Fixed-Circle Problem and Khan Type Contractions

“…In closing, we want to bring to the reader attention the following question, under what conditions we can prove the results in [18][19][20] in fixed circle?…”

Coincidence Point Results for Multivalued Suzuki Type Mappings Using θ-Contraction in b-Metric Spaces

“…For more details, see [23][24][25][26][27][28][29]. Note that, henceforth, X will represent a complete b-metric space instead of (X, d b ), and U 0 and V 0 are nonempty subsets of complete b-metric space X until otherwise stated.…”

Convergence Analysis of an Accelerated Iteration for Monotone Generalizedα-Nonexpansive Mappings with a Partial Order

“…In 1965, Browder [3] proved that every nonexpansive selfmapping of a closed convex and bounded subset has a fixed point in a uniformly convex Banach space. Since then, a number of iteration methods have been developed to approximate fixed point of nonexpansive mappings and some other relevant problems; see [4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. In these algorithms, Mann iteration is a fundamental method 2 Journal of Function Spaces approximating fixed points of nonexpansive mappings, which is defined by…”