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Some fixed point theorems in logarithmic convex structures

Title
Some fixed point theorems in logarithmic convex structures
Author
Keywords
fixed point; logarithmic convex structure; convex metric space
Issue Date
2017-02
Publisher
INST MATHEMATICS
Citation
MATHEMATICA BOHEMICA, v. 142, no. 1, page. 1-7
Abstract
In this paper, we introduce the concept of a logarithmic convex structure. Let X be a set and D: X x X -> [1, infinity) a function satisfying the following conditions: (i) For all x,y is an element of X, D(x,y) >= 1 and D(x,y)= 1 if and only if x = y. (ii) For all x,y is an element of X, D(x,y)= D(y,x). (iii) For all x,y,z is an element of X, D(x,y) D(x,z) <= (z,y). (iv) For all x,y,z is an element of X, z not equal x,y and lambda is an element of(0, 1), D(z,W (x,y, lambda)) <= D-lambda (x, z)D1-lambda(y, z), D(x,y)= D(x,W(x,y,lambda))D(y,W(x,y, lambda)), where W: X x 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.
URI
https://articles.math.cas.cz/10.21136/MB.2017.0074-14https://repository.hanyang.ac.kr/handle/20.500.11754/112684
ISSN
0862-7959; 2464-7136
DOI
10.21136/MB.2017.0074-14
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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