IJPAM: Volume 117, No. 3 (2017)




V. Sankar Raj$^1$, S. Jamal Fathima$^2$
$^{1,2}$Department of Mathematics
Manonmaniam Sundaranar University
Tirunelveli 627 012, Tamilnadu, INDIA


Let us consider two nonempty subsets $A$ and $B$ of a metric space $X$ and an upper semicontinuous multivalued non-self mapping $T:A\rightarrow
2^B$, where $2^B$ denotes the set of all nonempty subsets of $B$. It is worth mentioning that the notion of iterated sequence is meaningless since the mapping $T$ is a non-self mapping. In this article, we introduce a new type of Picard's iteration-like sequence for a non-self multivalued mapping and provided sufficient conditions for the existence of a point $x$ in $A$ for which the distance between the point $x$ and the set $T(x)$ is optimum. Using this notion, we obtain a generalized Edelstein's theorem for non-self multivalued contractive mappings.


Received: 2017-01-28
Revised: 2017-08-09
Published: January 11, 2018

AMS Classification, Key Words

AMS Subject Classification: 47H10, 47J25, 54H25
Key Words and Phrases: multivalued contractive, $P-$property, upper semicontinuous, best proximity point, fixed point, Picard's iteration-like sequence, diminishing sequence

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How to Cite?

DOI: 10.12732/ijpam.v117i3.2 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 3
Pages: 375 - 382

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