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Start Over Subject convex metric space

1. On a generalization of a Greguš fixed point theorem

Creator:
Ćirić, Ljubomir
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convex metric space, nonexpansive type mapping, and fixed point
Language:
English
Description:
Let $C$ be a closed convex subset of a complete convex metric space $X$. In this paper a class of selfmappings on $C$, which satisfy the nonexpansive type condition $(2)$ below, is introduced and investigated. The main result is that such mappings have a unique fixed point.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Some fixed point theorems in logarithmic convex structures

Creator:
Moazzen, Alireza, Cho, Yoel-Je, Park, Choonkil, and Eshaghi Gordji, Madjid
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fixed point, logarithmic convex structure, and convex metric space
Language:
English
Description:
In this paper, we introduce the concept of a logarithmic convex structure. Let X be a set and D : X × X → [1, ∞) a function satisfying the following conditions: (i) For all x, y ∈ X, D(x, y) ≥ 1 and D(x, y) = 1 if and only if x = y. (ii) For all x, y ∈ X, D(x, y) = D(y, x). (iii) For all x, y, z ∈ X, D(x, y) ≤ D(x, z)D(z, y). (iv) For all x, y, z ∈ X, z ≠ x, y and λ ∈ (0, 1), D(z, W(x, y, λ)) ≤ D λ (x, z)D 1−λ (y, z), D(x, y) = D(x, W(x, y, λ))D(y, W(x, y, λ)), where W : X ×X ×[0, 1] → X is a continuous mapping. We name this the logarithmic convex structure. In this work we prove some fixed point theorems in the logarithmic convex structure.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public