Abstract
In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
Highlights
The study of fixed points of functions satisfying certain contractive conditions has been at the center of vigorous research activity, for example see 1–5 and it has a wide range of applications in different areas such as nonlinear and adaptive control systems, parameterize estimation problems, fractal image decoding, computing magnetostatic fields in a nonlinear medium, and convergence of recurrent networks, see 6–10
Huang and Zhang generalized the concept of a metric space, replacing the set of real numbers by an ordered Banach space and obtained some fixed point theorems for mapping satisfying different contractive conditions 11
Let X, d be a cone metric space, P be a normal cone with normal constant K
Summary
The study of fixed points of functions satisfying certain contractive conditions has been at the center of vigorous research activity, for example see 1–5 and it has a wide range of applications in different areas such as nonlinear and adaptive control systems, parameterize estimation problems, fractal image decoding, computing magnetostatic fields in a nonlinear medium, and convergence of recurrent networks, see 6–10. As it has been defined in 11 , a function d : X × X → E is called a cone metric on X if it satisfies the following conditions: i d x, y ii d x, y iii d x, y
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