GENERALIZED CONE METRIC SPACES

Fixed point theorems on generalized $c$-distance in ordered cone $b$-metric spaces

In this paper, we introduce a concept of a generalized $c$-distance in ordered cone $b$-metric spaces and, by using the concept, we prove some fixed point theorems in ordered cone $b$-metric spaces. Our results generalize the corresponding results obtained by Y. J. Cho, R. Saadati, Shenghua Wang (Y. J. Cho, R. Saadati, Shenghua Wang, Common fixed point  heorems on generalized distance in ordere...

Common Fixed Points of Generalized Contractive Maps in Cone Metric Spaces

Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

Completion of Cone Metric Spaces

In this paper a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space E.

Complete Generalized Metric Spaces

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...