Proximity Point Properties for Admitting Center Maps
Authors
Abstract:
In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we show that in some conditions, the set of all best proximity points is nonempty and compact.
similar resources
ADMITTING CENTER MAPS ON MULTIPLICATIVE METRIC SPACE
In this work, we investigate admitting center map on multiplicative metric space and establish some fixed point theorems for such maps. We modify the Banach contraction principle and the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some useful theorems. Our results on multiplicative metric space improve and modify s...
full textBest proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
full textbest proximity pair and coincidence point theorems for nonexpansive set-valued maps in hilbert spaces
this paper is concerned with the best proximity pair problem in hilbert spaces. given two subsets $a$ and $b$ of a hilbert space $h$ and the set-valued maps $f:a o 2^ b$ and $g:a_0 o 2^{a_0}$, where $a_0={xin a: |x-y|=d(a,b)~~~mbox{for some}~~~ yin b}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in a$ such that $$d(g(x_0),f(x_0))=d(a,b).$$
full textOn Best Proximity Point Theorems for New Cyclic Maps
In this paper, we first introduce the concept of MT − K condition. Some best proximity point theorems for mappings satisfying MT − K condition instead of K-cyclic mappings are established in metric spaces. Our results generalize and improve some main results in [5] and references therein. Mathematics Subject Classification: 54H25
full textBest proximity point theorems in Hadamard spaces using relatively asymptotic center
In this article we survey the existence of best proximity points for a class of non-self mappings which satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [A. Abkar, M. Gabeleh, Best proximity points of non-self mappings, Top, 21, (2013), 287-295] which guarantees the existence of best proximity points for nonex...
full textMaps admitting trialities but not dualities
We use group theory to construct infinite families of maps on surfaces which are invariant under Wilson’s map operations of order 3 but not under the operations of order 2, such as duality and Petrie duality. MSC classification: Primary 05C25, secondary 05C10, 20B25.
full textMy Resources
Journal title
volume 15 issue 1
pages 159- 167
publication date 2019-07-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023