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Symmetry 2019, 11(2), 155; https://doi.org/10.3390/sym11020155

Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space

Department of Mathematics and Informatics, Faculty of Sciences, Lucian Blaga University of Sibiu, Sibiu 550012, Romania
Received: 7 December 2018 / Revised: 17 January 2019 / Accepted: 18 January 2019 / Published: 30 January 2019
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Abstract

In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler’s fixed point theorem was generalized by many authors in different ways. Using a method given by Angrisani, Clavelli in 1996 and Mureşan in 2002, we prove in this paper that, for a class of convex multivalued left A-contractions in the sense of Nadler and the right A-contractions with a convex metric, the fixed points set is non-empty and compact. In this paper we present the fixed point theorems for convex multivalued left A-contractions in the sense of Nadler and right A-contractions on the geodesic metric space. Our results are particular cases of some general theorems, to the multivalued left A-contractions in the sense of Nadler and right A-contractions, and particular cases of the results given by Rus (1979, 2008), Nadler (1969), Mureşan (2002, 2004), Bucur, Guran and Petruşel (2009), Petre and Bota (2013), etc., and are applicable in many fields, such as economy, management, society, biology, ecology, etc. View Full-Text
Keywords: fixed point; convex multivalued left A-contraction; right A-contraction; geodesic metric space; regular golbal-inf function; MSC; 47H10; 54H25 fixed point; convex multivalued left A-contraction; right A-contraction; geodesic metric space; regular golbal-inf function; MSC; 47H10; 54H25
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bucur, A. Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space. Symmetry 2019, 11, 155.

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