A Novel Fixed Point Theorem of Reich-Perov Type α−Contractive Mapping in Vector-Valued Metric Spaces

Sunarsini ⁽¹⁾, Mahmud Yunus ⁽²⁾ and Subiono ⁽³⁾

(1) Department of Mathematics, Institut Teknologi Sepuluh Nopember, ITS
Campus, Building F, 2nd Floor, Keputih, Sukolilo, Surabaya 60111, Indonesia

Email address: sunarsini@matematika.its.ac.id

(2) Department of Mathematics, Institut Teknologi Sepuluh Nopember, ITS
Campus, Building F, 2nd Floor, Keputih, Sukolilo, Surabaya 60111, Indonesia

Email address: yunusm@matematika.its.ac.id

(3) Department of Mathematics, Institut Teknologi Sepuluh Nopember, ITS
Campus, Building F, 2nd Floor, Keputih, Sukolilo, Surabaya 60111, Indonesia

Email address: subiono2008@matematika.its.ac.id

Doi : https://doi.org/10.47013/16.4.1

Cited by : Jordan J. Math & Stat., 16 (4) (2023), 599 - 616

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 Abstract. This article discusses a novel concept of Reich-Perov type α-contractive mappings in vector-valued metric spaces. First, we define Reich-Perov-type contractive mappings using a novel concept in vector-valued metric spaces. Later, we investigate the sufficient conditions for a Reich-Perov type contractive mapping to have a unique fixed point in the spaces. By defining an α-contractive mapping, we next show the sufficient conditions of the existence and uniqueness of a fixed point of the Reich-Perov type α-contractive mappings in vector-valued metric spaces. 

Keywords: Reich-Perov contractive mapping; Reich-Perov α-contractive mapping; α-admissible; fixed point.