A new concept of (α,Fd )-contraction on quasi metric space

Abstract

In the present paper, we introduce a new concept of (α, F d )-contraction on quasi metric space. Then we provide some new fixed point theorems for such type mappings on left K, left M and left Smyth-complete quasi metric spaces.

Generalization of (α-F_{d})--contraction on quasi--metric space

“…[0; 1) be a function. We will consider the following set (see [1]): T = f(x; y) 2 X X : (x; y) 1 and d(T x; T y) > 0g :…”

“…Various …xed point results for admissible mappings and F contractions on complete metric space can be found in [1,3,4,5] and [1,2,3,7,12], respectively.…”

An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space

“…Samet et al [10] established several universal fixed-point results encompassing several well-known theorems regarding complete metric space by introducing the α-admissibility technique. These discoveries on fixed points offer a framework for investigating the existence and characteristics of fixed points for self-mappings on a complete metric space, employing the α-admissibility method (see [11][12][13][14][15][16][17]).…”

Characterizations of quasi-metric completeness in terms of Kannan-type fixed point theorems

“…), the development of the xed point theory for theses spaces is receiving a signicant boost (see e.g. [1,2,3,5,7,9,12,15,16,17]). In this setting, the problem of characterizing quasi-metric completeness via xed point theorems arises in a natural way.…”