Startpoints and(α,γ)-Contractions in Quasi-Pseudometric Spaces

Abstract

We introduce the concept of startpoint and endpoint for multivalued maps defined on a quasi-pseudometric space. We investigate the relation between these new concepts and the existence of fixed points for these set valued maps. Dedicated to my beloved Clémence on the occasion of her 25th birthday

Some advances in the theory of quasi-pseudometric type spaces

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This paper presents some startpoint (endpoint, fixed point) theorems for mutli-valued maps that generalize recent results proved by Y. U. Gaba [1,2].

Introduction and prelimariesDefinition 1.1 Let X be a non empty set. A function d :Moreover, if d(x, y) = 0 = d(y, x) =⇒ x = y, then d is said to be a T 0 -quasipseudometric.

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“…For the convenience of the reader, we recall the following. We also give here the first result of the theory as they appear in the original paper [1].…”

“…Theorem 1.10 (Gaba [1]) Let (X, d) be a left K-complete quasi-pseudometric space. Let F : X → CB(X) be a set-valued map and f : X → R as f (x) = H({x}, F x).…”

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

“…We can find some recent fixed point results for single valued and multivalued mappings on quasi metric spaces in [1,2,11,18,19,20].…”

New fixed point results in quasi-metric spaces and applications in fractals theory

“…There are two notions for each of them, namely forward and backward ones, since we have two topologies which are the forward topology and the backward topology in quasi-metric spaces (see [7]). In the last decades many authors studied these notions and properties in the settings of quasi-metric spaces (see, e.g., [8][9][10][11][12][13][14][15][16] and the references therein).…”