Open AccessBest Proximity Points for Some Classes of Proximal Contractions
Author(s) -
Maryam A Alghamdi,
Naseer Shahzad,
Francesca Vetro
Publication year - 2013
Publication title -
abstract and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.228
H-Index - 56
eISSN - 1687-0409
pISSN - 1085-3375
DOI - 10.1155/2013/713252
Subject(s) - mathematics , contraction principle , contraction mapping , extension (predicate logic) , contraction (grammar) , function (biology) , banach space , point (geometry) , nonlinear system , mathematical optimization , resolution (logic) , iterative method , fixed point , discrete mathematics , mathematical analysis , computer science , geometry , artificial intelligence , medicine , physics , quantum mechanics , evolutionary biology , biology , programming language
Given a self-mapping and a non-self-mapping , theaim of this work is to provide sufficient conditions for the existence of aunique point , called g-best proximity point, which satisfies . In so doing, we provide a useful answer for theresolution of the nonlinear programming problem of globally minimizing thereal valued function , thereby getting an optimalapproximate solution to the equation . An iterative algorithm isalso presented to compute a solution of such problems. Our resultsgeneralize a result due to Rhoades (2001) and hence suchresults provide an extension of Banach's contraction principle to the caseof non-self-mappings
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