Abstract
AbstractRecently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space.
Highlights
The condition λ > is important, the function T : R → R defined by Tx = x + ex satisfies the condition |Tx – Ty| ≥ |x – y| for all x, y ∈ R, and T has no fixed point
Let (X, G) be a complete G-metric space, and let T : X → X satisfy one of the following conditions: (a) T is an F-contraction of type I on a G-metric space X, i.e., there exist F ∈ F and t > such that for all x, y ∈ X, G(Tx, Ty, Ty) > ⇒ t + F G(Tx, Ty, Ty) ≤ F G(x, y, y) ; ( )
(b) T is an F-contraction of type II on a G-metric space X, i.e., there exist F ∈ F and t > such that for all x, y, z ∈ X, G(Tx, Ty, Tz) > ⇒ t + F G(Tx, Ty, Tz) ≤ F G(x, y, z)
Summary
Let (X, d) be a complete metric space, and let T : X → X be surjective and expanding. 2 The result we give some fixed point theorem for F-expanding maps. Samet et al [ ] observed that some fixed point theorems in the context of G-metric spaces can be concluded from existence results in the setting of quasi-metric spaces.
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