On monotonic solutions of the Schröder equation in Banach spaces

Abstract

We prove the existence and uniqueness of solutions of the Schröder equation (1) in the class of monotonic functions on cones in Banach spaces. (2000). Primary 39B12, 39B52. Mathematics Subject Classification

Applications of Banach Limit in Ulam Stability

“…On the other hand, monotonic solutions of Equation ( 8) were studied in Banach spaces in [27], whereas continuous and smooth solutions of this equation in the case of normed spaces were investigated in [28]. The Schröder equation in several variables was considered in [29][30][31][32][33][34], and its regularly varying solutions, among others, in [35].…”

Theorems of Thron's type for random-valued vector functions and the Krein–Rutman theorem

“…also [11]. In the deterministic case some versions of Thron's theorem for more general spaces were obtained in [13], [15] and [16].…”

“…We follow the general idea of J. Walorski to apply the theorem of Krein-Rutman. We use part of his reasoning presented in [15] and [16] (cf. also [6]).…”

On the convergence of sequences of iterates of random-valued vector functions

“…also [13], [14]). The present paper is intended as an attempt to get results on the speed of convergence of iterates of a random-valued vector function f :…”