Results in wt-Distance over b-Metric Spaces

Abstract

In this manuscript, we introduce Meir-Keeler type contractions and Geraghty type contractions in the setting of the wt-distances over b-metric spaces. We examine the existence of a fixed point for such mappings. Under some additional assumption, we proved the uniqueness of the found fixed point.

Fixed Point Results viaG-Function over the Complete Partialb-Metric Space

“…Of course, since the function Gðτ, υ, ωÞ = τ + υ + ω ∈ F, by Theorem 2, we have that the sequence fx n g defined as x n = Tx n−1 is convergent to a point ς ∈ X, and moreover, ( 22) and ( 23) hold. We claim that this point ς is a fixed point of T. For this purpose, by (31), for x = ς and y = ς, we get Letting n ⟶ ∞, in the above inequality and keeping in mind (19), (22), and (23), we get…”

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].…”

Periodic and Fixed Points for Caristi-Type G -Contractions in Extended b -Gauge Spaces

“…Further, an open (closed) ball is not an open (closed) set. For more details on b-metric and interesting examples, we refer to, e.g., [40][41][42][43][44][45][46][47][48][49].…”