Abstract
This paper is motivated by the nonlinear ergodic theory developed by T. Fujimoto and Krause [6], and Nussbaum [11]. Their works depend heavily on projective metrics. This motivates us to consider the convergence problems of inhomogeneous iterates in metric spaces, and to apply them to study the nonlinear ergodic problems in ordered Banach spaces, which are related to certain problems from population biology and economics [3, 5]. Throughout this paper, X will be a complete metric space. Let T :X →X be a mapping. We say T is a generalized contraction [7] if any for 0iaibi∞, there exists L(a; b)∈ (0; 1) such that d(Tx; Ty)≤L(a; b)d(x; y); (1)
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