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Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space

Department of Mathematics and Informatics, Faculty of Sciences, Lucian Blaga University of Sibiu, 550012 Sibiu, Romania
Symmetry 2020, 12(1), 134; https://doi.org/10.3390/sym12010134
Received: 1 December 2019 / Revised: 1 January 2020 / Accepted: 6 January 2020 / Published: 9 January 2020
This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains not only an example of application in science, but also an example of application in real life, in biology, in order to find an equilibrium solution to a prey–predator-type problem. The results of this paper extend theorems for multivalued left-weighted mean contractions in the generalized sense of Nadler, demonstrating that some of the results given by Rus (2008), Mureșan (2002), and Nadler (1969) in metric spaces can also be proved in symmetric generalized metric spaces.
Keywords: fixed points; multivalued left-weighted mean contraction; multivalued right-weighted mean contraction; regular-global-inf function fixed points; multivalued left-weighted mean contraction; multivalued right-weighted mean contraction; regular-global-inf function
MDPI and ACS Style

Bucur, A. Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space. Symmetry 2020, 12, 134.

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