Modified w-distances on quasi-metric spaces and a fixed point theorem on complete quasi-metric spaces

Abstract

ElsevierAlegre Gil, MC.; Marín Molina, J. (2016). Modified w-distances on quasi-metric spaces and a fixed point theorem on complete quasi-metric spaces. AbstractIn this paper we introduce the notion of modified w-distance (mw-distance) on a quasi-metric space which generalizes the concept of quasi-metric. We obtain a fixed point theorem for generalized contractions with respect to mw-distances on complete quasi-metric spaces.

∈φ-contraction and some fixed point results via modified ω-distance mappings in the frame of complete quasi metric spaces and applications

“…Definition 7 [26] if ρ is lower semi-continuous on the first and second coordinates, then ρ is called a strong mω-distance.…”

Nonlinear contractions and fixed point theorems with modified ω-distance mappings in complete quasi metric spaces

“…We say that the sequence (x n ) is Cauchy if for every > 0 there is positive integer N = N( ) such that d(x n , x m ) for all m, n > N; that is (x n ) is a Cauchy sequence if and only if it is left and right Cauchy. A modified ω-distance (shortly mω-distance) mapping on quasi metric space is given by Alegre and Marin [5] as follows.…”

“…For more details on mω-distance, we refer the readers to [5] and references therein. Henceforth, we denote the class of all altering distance functions by Ψ.…”

Fixed Point Theorems through Modified ω-Distance and Application to Nontrivial Equations

“…Definition 7. [10] We call an mω-distance function a p strong mω-distance if p is lower semi-continuous on its second coordinate. Remark 1.…”