BOUNDED ORBITS AND G-CONTRACTIVE FIXED POINTS

T. PHANEENDRA; S. SARAVANAN

Title	BOUNDED ORBITS AND G-CONTRACTIVE FIXED POINTS
Publication Type	Journal Article
Year of Publication	2016
Authors	PHANEENDRA, T, SARAVANAN, S
Secondary Title	Communications in Applied Analysis
Volume	20
Issue	3
Start Page	441
Pagination	18
Date Published	10/2016
Type of Work	scientific: mathematics
ISSN	1083-2564
AMS	54H25
Abstract	Let $f$ be a self-map on a metric space $(X,d)$ and $x_0\in X$. The orbit $O_f(x_0)$ at $x_0$ is the sequence of $f$-iterates $\langle x_0, fx_0,..., f^nx_0,...\rangle$. A fixed point $p$ of $f$ is a contractive fixed point if every $O_f(x_0)$ converges to $p$. The existence of contractive fixed points for self-maps in metric spaces was investigated by Edelstein \cite{edel}, Leader and Hoyle in \cite{lh}, and by Reich \cite{rei}. The notion of $G$-contractive fixed point in a generalized metric space was introduced by the first author and Kumara Swamy in \cite{pk13b} in 2013. This paper devotes to the study of bounded orbits and contractive fixed points for certain self-maps in $G$-metric space, without using the iterations.
URL	http://www.acadsol.eu/en/articles/20/3/12.pdf
DOI	10.12732/caa.v20i3.12
Short Title	BOUNDED ORBITS AND G-CONTRACTIVE FIXED POINTS
Alternate Journal	CAA
Refereed Designation	Refereed
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