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

Abstract

Alegre and Marin [C. Alegre, J. Marin, Topol. Appl., 203 (2016), 32-41] introduced the concept of modified ω-distance mappings on a complete quasi metric space in which they studied some fixed point results. In this manuscript, we prove some fixed point results of nonlinear contraction conditions through modified ω-distance mapping on a complete quasi metric space in sense of Alegre and Marin.

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

“…Remark 2 [33] The above lemma show that if lim s,t→∞ p(e s , e t ) = 0, then (e s ) is Cauchy in (E, q).…”

“…Lemma 1 [33] Let ( s ), (σ s ) be two sequences of nonnegative real numbers that converge to zero. Then we have the following:…”

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

“…Lemma 1. [11] Let (α t ) , (β t ) be two sequences of nonnegative real numbers converging to zero. Assume that p is mω-distance.…”

Common Fixed Point Results for Rational (α,β)φ-mω Contractions in Complete Quasi Metric Spaces

“…The Banach contraction principle [1] is one of the most famous results in the setting of fixed point theory. Subsequently, many generalizations and modifications were studied in many directions by many authors; see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…[19] (i) We call (j k ) left Cauchy if for each γ > 0, there exists a positive integer i such that q(j k , j l ) ≤ γ for all k ≥ l > i. Lemma 1. [7] Let p be an mω-distance on (A, q). Let (j k ) be a sequence in A and (ζ k ) , (ξ k ) be two nonnegative sequences converging to zero.…”