Abstract
The purpose of this paper is to present some topological properties in E-metric spaces such as the properties of e-sequences, the decision conditions of e-Cauchy sequences, the characteristics of non-normal cones, and so on. Moreover, the theorem of nested closed-balls in such spaces is displayed. In addition, some principal applications to fixed point theory are also given.
Highlights
Over the past several decades, nonlinear functional analysis, especially fixed point theory in ordered normed spaces had covered a large number of applications in optimization theory, game theory, variational inequalities, dynamical systems, fractals, graph theory, models in economy, computer science, and many other fields
Certain elements may be compared better than crude estimates via a norm
By substituting an ordered Banach space instead of the real line, in 2007, Huang and Zhang [1] introduced the concept of cone metric space with a new point of view
Summary
Over the past several decades, nonlinear functional analysis, especially fixed point theory in ordered normed spaces had covered a large number of applications in optimization theory, game theory, variational inequalities, dynamical systems, fractals, graph theory, models in economy, computer science, and many other fields. They considered convergent and Cauchy sequences in terms of interior points with regard to the underlying cone partial ordering. They dealt with convergent and Cauchy sequences via interior points regarding the same cone partial ordering as the mentioned above.
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