Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph

Ana Savić; Nicola Fabiano; Nikola Mirkov; Aleksandra Sretenović; Stojan Radenović; Ana Savić; Nicola Fabiano; Nikola Mirkov; Aleksandra Sretenović; Stojan Radenović

doi:10.3934/math.2022011

AIMS Mathematics

2022, Volume 7, Issue 1: 187-198. doi: 10.3934/math.2022011

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Research article

Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph

1.
School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, Belgrade, Serbia
2.
University of Belgrade, 'Vinča' Institute of Nuclear Sciences-National Institute of the Republic of Serbia, Mike Petrovića Alasa 12–14, 11351 Belgrade, Serbia
3.
Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade 35, Serbia

Received: 25 June 2021 Accepted: 26 September 2021 Published: 09 October 2021
MSC : 47H10, 54H25, 54E50

Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle.
- common fixed point,
- Perov's type results,
- multivalued mapping,
- directed graph,
- graphic contraction,
- cone metric space,
- c-sequence
Citation: Ana Savić, Nicola Fabiano, Nikola Mirkov, Aleksandra Sretenović, Stojan Radenović. Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph[J]. AIMS Mathematics, 2022, 7(1): 187-198. doi: 10.3934/math.2022011

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Abstract

Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle.

References

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