Application of Reich-Perov -Contractive Mapping in Vector Valued Metric Space

Sunarsini Sunarsini (Institut Teknologi Sepuluh Nopember)
Mahmud Yunus (Institut Teknologi Sepuluh Nopember)
Subiono Subiono (Institut Teknologi Sepuluh Nopember)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

This paper presents two new applications of a fixed point theorem for Reich–Perov α-contractive mappings in vector-valued metric spaces. As a new application, we first demon-strate the existence and uniqueness of a solution to the vector valued Volterra-Fredholm integral equation system. By constructing suitable integral operators, we show that they satisfy the α-contractive Reich-Perov condition. The second application concerns the determination of the fixed point for discrete recursive systems with coupled components, for which the existence of a unique solution is established.