Common Fixed Points for Maps on Topological Vector Space ValuedCone Metric Spaces

Abstract

We introduced a notion of topological vector space valued cone metric space and obtained some common fixed point results. Our results generalize some recent results in the literature.

Common Fixed Points for Two Mappings With Expansive Properties on Complex Valued Metric Spaces

“…For example, cone metric spaces ( [7]) and topological vector space-valued cone metric spaces( [3]). A number of authors discussed and obtained some fixed point and common fixed point theorems in these spaces, greatly generalized and improved some corresponding results.…”

“…A number of authors discussed and obtained some fixed point and common fixed point theorems in these spaces, greatly generalized and improved some corresponding results. Recently, Azam et al ([1]) introduced a partial order ≤ on the set C of complex numbers, used the idea in ( [3,7]) to define a complex metric d on a nonempty set X and a complex metric space (X, d), and gave coincidence point theorems and common fixed point theorems for two mappings satisfying a contractive type condition. The authors in ( [11,14,15]) further generalized and improved the corresponding results in ( [1]).…”

Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces

“…Du in [13] introduced the concept of topological vector space (tvs)-cone metric and tvs-cone metric space to improve and extend the concept of cone metric space in the sense of Huang and Zhang [1]. In [7,9,13,14] the authors tried to generalize this approach using cones in tvs instead of Banach spaces. However, it should be noted that an old result shows that if the underlying cone of an ordered tvs is solid and normal, then such tvs must be an ordered normed space.…”

Two Fixed Point Theorems in Topological vector space Valued Cone Metric Spaces with Complete Topological Algebra Cones

“…In 2009 I.Beg et al [3] and in 2010 Du [5] generalized cone metric spaces to topological vector space valued cone metric spaces (TVS-CMS). In this approach ordered topological vector spaces are used as the codomain of the metric, instead of Banach spaces.…”

“…See [2], [3] and [5]. One of the tools used to prove such equivalences is the so called nonlinear scalarization function.…”