A unified theory of cone metric spaces and its applications to the fixed point theory

Abstract

In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a solid vector space.

51 pages

References in corpus (5)

• Sequential convergence in topological spaces
• On Some Topological Concepts of TVS-Cone Metric Spaces and Fixed Point Theory Remarks
• Metrizability of Topological Vector Space Valued Cone Metric Spaces
• Metrizability of Cone Metric spaces
• Some Notes on the paper "The Equivalence of Cone Metric Spaces and Metric Spaces"

Cited by in corpus (3)

• A new survey: Cone metric spaces
• General convergence theorems for iterative processes and applications to the Weierstrass root-finding method
• On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously