In this paper, several fixed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.

Wardowski (2011) in this paper for a normal cone metric space (X, d) and for the family A of subsets of X established a new cone metric H : A × A → E and obtained fixed point of set-valued contraction of Nadler type. Further, it is noticed in the work of Janković et al., 2011 that the fixed-point problem in the setting of cone metric spaces is appropriate only in the case when the underlying co...

In this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. Weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In 2007, Long-Guang and Xian[3] replaced introduced cone metric spaces. They replaced the set of real numbers by an ordered Banach space in the definition of metric and generalized the notion of metric space. Recently, Ayse Sönemaz [5] proved a cone metric space with a normal cone, of course it has to be strongly minihedral, is paracompact. In this paper we omit the strongly minihedral of cone....

This paper discusses balls in partial b-metric spaces and cone metric spaces, respectively. Let (X ,pb) be a partial b-metric space in the sense of Mustafa et al. For the family of all pb-open balls in (X ,pb), this paper proves that there are x, y ∈ B ∈ such that B′ B for all B′ ∈ , where B and B′ are with centers x and y, respectively. This result shows that is not a base of any topology on X...

In 2011, Gabeleh and Akhar [3] introduced semi-cyclic-contraction and considered the existence and convergence results of best proximity points in Banach spaces. In this paper, the author introduces a cone semicyclic φ-contraction pair in cone metric spaces and considers best proximity points for the pair in cone metric spaces. His results generalize the corresponding results in [1–5]..

Huang and Zhang 1 reintroduced the notion of cone metric spaces and established fixed point theorems for mappings on this space. After that, many fixed point theorems have been proved in normal or nonnormal cone metric spaces by some authors see e.g. 1–26 and references contained therein . We need to recall some basic notations, definitions, and necessary results from literature. Let R be the s...