<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Contractions represents the foundation stone of nonlinear analysis. That is the reason why we propose to unify two different type of contractions: almost contractions, introduced by <xref ref-type="bibr" rid="j_ausm-2018-0030_ref_002_w2aab3b7c13b1b6b1ab1ab2Aa">V. Berinde in [2]</xref> and local contractions (<xref ref-type="bibr" rid="j_ausm-2018-0030_ref_007_w2aab3b7c13b1b6b1ab1ab7Aa">Martins da Rocha and Filipe Vailakis in [7]</xref>). These two types of contractions operate in different space settings: in metric spaces (almost contractions) and semimetric spaces (for local contractions). That new type of contraction was built up in a new space setting, which is the pseudometric space. The main results of this paper represent the extension for various type of operators on pseudometric spaces, such as: generalized ALC, Ćirić-typeALC, quasi ALC, Ćirić-Reich-Rustype ALC. We propose to study the existence and uniqueness of their fixed points, and also the continuity in their fixed points, with a large number of examples for ALC-s.</p></abstract>

Contractions represents the foundation stone of nonlinear analysis. That is the reason why we propose to unify two different type of contractions: almost contractions, introduced by V. Berinde in [2] and local contractions (Martins da Rocha and Filipe Vailakis in [7]). These two types of contractions operate in different space settings: in metric spaces (almost contractions) and semimetric spaces (for local contractions). That new type of contraction was built up in a new space setting, which is the pseudometric space. The main results of this paper represent the extension for various type of operators on pseudometric spaces, such as: generalized ALC, Ćirić-typeALC, quasi ALC, Ćirić-Reich-Rustype ALC. We propose to study the existence and uniqueness of their fixed points, and also the continuity in their fixed points, with a large number of examples for ALC-s.

New classes of local almost contractions

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

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"New classes of local almost contractions"}

Contractions represents the foundation stone of nonlinear analysis. That is the reason why we propose to unify two different type of contractions: almost...

New classes of local almost contractions

Published Online: Mar 04, 2019

Page range: 378 - 394

Received: Jun 13, 2017

DOI: https://doi.org/10.2478/ausm-2018-0030

Keywords
almost local contraction, coefficient of contraction, fixed- point theorem

© 2018 Mónika Zákáany, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

New classes of local almost contractions

Published Online: Mar 04, 2019

Page range: 378 - 394

Received: Jun 13, 2017

DOI: https://doi.org/10.2478/ausm-2018-0030

Keywordsalmost local contraction, coefficient of contraction, fixed- point theorem

© 2018 Mónika Zákáany, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
almost local contraction, coefficient of contraction, fixed- point theorem