A coincidence-point problem of Perov type on rectangular cone metric spaces

Abstract

We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using α-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.

Application of Perov type fixed point results to complex partial differential equations

“…In this context, in 1964, Perov 2 generalized this principle for vector‐valued metric space. Later on, several contributions have been made (see in previous studies 3‐14 ). In order to talk about Perov's fixed point theorem, we need to recall some fundamental notations: Throughout this paper, we denote by the set of m × 1 real matrices, by the set of m × 1 real matrices with nonnegative elements, by the set of m × 1 real matrices in which every elements are greater than j , by θ the zero m × 1 matrix, by the set of all m × m matrices with nonnegative elements, by Θ the zero m × m matrix, and by I the identity m × m matrix.…”