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Convergence and existence results for best C-proximity points
-
Hemant Kumar Pathak
and
Naseer Shahzad
Published/Copyright:
May 30, 2012
Abstract.
We provide a positive answer to a question raised by Al-Thagafi and Shahzad
[Nonlinear Anal. 70 (2009), 3665–3671] about the existence of a best proximity point
for a cyclic 
-contraction map in a reflexive Banach space
by using appreciable generalized notions. In turn, this also gives
a positive answer to a question raised by Eldred and Veeramani
[J. Math. Anal. Appl. 323 (2006), 1001–1006]. To
this end, we introduce a new concept of C-proximity point
and a new class of maps, called cyclic 
-contractions,
which contains cyclic contraction maps and cyclic
-contraction maps as subclasses. Convergence and
existence results of best
C-proximity points for cyclic -contraction maps are also obtained.
Received: 2011-02-28
Revised: 2011-11-21
Published Online: 2012-05-30
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Best proximity point;
fixed point;
cyclic -contraction map;
metric space;
Banach space
Articles in the same Issue
- Masthead
- Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
- Modules that have a supplement in every cofinite extension
- Boundary value problems of statics of the elastic mixture theory
- On grand Lorentz spaces and the maximal operator
- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
- Continuous Hu cohomology
- Convergence and existence results for best C-proximity points
- Aspects of slice stability in locale theory
- On the irreducibility of Hurwitz spaces of coverings with two special fibers
- Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
