<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We introduce a new class of contractive mappings: the almost local contractions, starting from the almost contractions presented by V. Berinde in [V. Berinde, <italic>Approximating fixed points of weak contractions using the Picard iteration</italic> Nonlinear Analysis Forum 9 (2004) No.1, 43-53], and also from the concept of local contraction presented by Filipe Martins da Rocha and Vailakis in [V. Filipe Martins-da-Rocha, Y. Vailakis, <italic>Existence and uniqueness of a fixed point for local contractions</italic>, Econometrica, vol.78, No.3 (May, 2010) 1127-1141]. First of all, we present the notion of multivalued self almost contractions with many examples. The main results of this paper are given by the extension to the case of multivalued self almost local contractions.</p></abstract>

We introduce a new class of contractive mappings: the almost local contractions, starting from the almost contractions presented by V. Berinde in [V. Berinde, Approximating fixed points of weak contractions using the Picard iteration Nonlinear Analysis Forum 9 (2004) No.1, 43-53], and also from the concept of local contraction presented by Filipe Martins da Rocha and Vailakis in [V. Filipe Martins-da-Rocha, Y. Vailakis, Existence and uniqueness of a fixed point for local contractions, Econometrica, vol.78, No.3 (May, 2010) 1127-1141]. First of all, we present the notion of multivalued self almost contractions with many examples. The main results of this paper are given by the extension to the case of multivalued self almost local contractions.

Multivalued self almost local contractions

Department of Mathematics and Computer Sciences

North University Center at Baia Mare, Technical University of Cluj-Napoca

Annals of West University of Timisoara - Mathematics and Computer Science

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

{"article-title":"Multivalued self almost local contractions"}

We introduce a new class of contractive mappings: the almost local contractions, starting from the almost contractions presented by V. Berinde in [V. Berinde,...

Multivalued self almost local contractions

Published Online: Dec 08, 2020

Page range: 122 - 138

DOI: https://doi.org/10.2478/awutm-2019-0010

Keywords
almost contractions, local contractions, fixed points, multivalued mappings

© 2019 Monica Zakany, published by Sciendo

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

Multivalued self almost local contractions

Published Online: Dec 08, 2020

Page range: 122 - 138

DOI: https://doi.org/10.2478/awutm-2019-0010

Keywordsalmost contractions, local contractions, fixed points, multivalued mappings

© 2019 Monica Zakany, published by Sciendo

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

Keywords
almost contractions, local contractions, fixed points, multivalued mappings