Existence of a Unique Fixed Point for Nonlinear Contractive Mappings

Existence of a Unique Fixed Point for Nonlinear Contractive Mappings

In a recent work, we established the existence of a unique fixed point for nonlinear contractive self-mappings of a bounded and closed set in a Banach space. In the present paper we extend this result to the case of unbounded sets.

Bibliographic Details
Main Authors: Simeon Reich, Alexander J. Zaslavski
Format: Article
Language:English
Published: MDPI AG 2020-01-01
Series:Mathematics
Subjects:
banach space
complete metric space
contractive mapping
fixed point
iterate
Online Access:https://www.mdpi.com/2227-7390/8/1/55
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spelling doaj-5b44f27394774391ae0505301aae922e2020-11-25T03:35:56ZengMDPI AGMathematics2227-73902020-01-01815510.3390/math8010055math8010055Existence of a Unique Fixed Point for Nonlinear Contractive MappingsSimeon Reich0Alexander J. Zaslavski1Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, IsraelDepartment of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, IsraelIn a recent work, we established the existence of a unique fixed point for nonlinear contractive self-mappings of a bounded and closed set in a Banach space. In the present paper we extend this result to the case of unbounded sets.https://www.mdpi.com/2227-7390/8/1/55banach spacecomplete metric spacecontractive mappingfixed pointiterate
collection DOAJ
language English
format Article
sources DOAJ
author Simeon Reich
Alexander J. Zaslavski
spellingShingle Simeon Reich
Alexander J. Zaslavski
Existence of a Unique Fixed Point for Nonlinear Contractive Mappings
Mathematics
banach space
complete metric space
contractive mapping
fixed point
iterate
author_facet Simeon Reich
Alexander J. Zaslavski
author_sort Simeon Reich
title Existence of a Unique Fixed Point for Nonlinear Contractive Mappings
title_short Existence of a Unique Fixed Point for Nonlinear Contractive Mappings
title_full Existence of a Unique Fixed Point for Nonlinear Contractive Mappings
title_fullStr Existence of a Unique Fixed Point for Nonlinear Contractive Mappings
title_full_unstemmed Existence of a Unique Fixed Point for Nonlinear Contractive Mappings
title_sort existence of a unique fixed point for nonlinear contractive mappings
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-01-01
description In a recent work, we established the existence of a unique fixed point for nonlinear contractive self-mappings of a bounded and closed set in a Banach space. In the present paper we extend this result to the case of unbounded sets.
topic banach space
complete metric space
contractive mapping
fixed point
iterate
url https://www.mdpi.com/2227-7390/8/1/55
work_keys_str_mv AT simeonreich existenceofauniquefixedpointfornonlinearcontractivemappings
AT alexanderjzaslavski existenceofauniquefixedpointfornonlinearcontractivemappings
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