<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type. Our new results complement and extend recent related results [Berinde, V., Păcurar, M., The contraction principle for nonself mappings on Banach spaces endowed with a graph, J. Nonlinear Convex Anal. 16 (2015), no. 9, 1925-1936; Balog, L., Berinde, V., Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph, Carpathian J. Math. 32 (2016), no. 3 (in press)] and thus provide more general and flexible tools for studying nonlinear functional equations. </p></abstract>

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type. Our new results complement and extend recent related results [Berinde, V., Păcurar, M., The contraction principle for nonself mappings on Banach spaces endowed with a graph, J. Nonlinear Convex Anal. 16 (2015), no. 9, 1925-1936; Balog, L., Berinde, V., Fixed point theorems for nonself Kannan type contractions in Banach spaces endowed with a graph, Carpathian J. Math. 32 (2016), no. 3 (in press)] and thus provide more general and flexible tools for studying nonlinear functional equations.

Approximating Fixed Points of Nonself Contractive Type Mappings in Banach Spaces Endowed with a Graph

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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Let K be a non-empty closed subset of a Banach space X endowed with a graph G. We obtain fixed point theorems for nonself G-contractions of Chatterjea type....

Approximating Fixed Points of Nonself Contractive Type Mappings in Banach Spaces Endowed with a Graph

Published Online: Sep 21, 2017

Page range: 27 - 43

Received: Jan 15, 2016

Accepted: Apr 23, 2016

DOI: https://doi.org/10.1515/auom-2016-0026

Keywords
Banach space, Graph, Fixed point, Property (M), Error estimate

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Approximating Fixed Points of Nonself Contractive Type Mappings in Banach Spaces Endowed with a Graph

Published Online: Sep 21, 2017

Page range: 27 - 43

Received: Jan 15, 2016

Accepted: Apr 23, 2016

DOI: https://doi.org/10.1515/auom-2016-0026

KeywordsBanach space, Graph, Fixed point, Property (M), Error estimate

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Banach space, Graph, Fixed point, Property (M), Error estimate