Open AccessSome significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph
Author(s) -
Ana Savić,
Nicola Fabiano,
Nikola Mirkov,
Aleksandra Sretenović,
Stojan Radenović
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022011
Subject(s) - mathematical proof , mathematics , complement (music) , metric space , contraction (grammar) , type (biology) , fixed point theorem , graph , discrete mathematics , pure mathematics , geometry , medicine , ecology , biochemistry , chemistry , complementation , biology , gene , phenotype
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.