In this paper, we introduce the notion of an extended metric space ($p$-metric space) as a new generalization of the concept of $b$-metric space. Also, we present the concept of $(psi ,varphi )_{Omega}$-contractive mappings and we establish some fixed point results for this class of mappings in ordered complete $p$-metric spaces. Our results generalize several well...

In this paper, we introduce the concepts of an inferior idempotent cone and a BID-cone b-metric space over Banach algebra. We establish some new existence theorems fixed point in setting complete spaces Some fundamental questions examples are also given.

Huang and Zhang 1 generalized the notion of metric space by replacing the set of real numbers by ordered Banach space, deffined a cone metric space, and established some fixed point theorems for contractive type mappings in a normal cone metric space. Subsequently, several other authors 2–5 studied the existence of common fixed point of mappings satisfying a contractive type condition in normal...

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

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....

Abstract: Replacing the set of real numbers by an ordered Banach space in the definition of a metric, Guang and Xian [5] introduced the concept of a cone metric and obtained some fixed point Theorems for contractive mappings on cone metric spaces. It has been shown that every cone metric space is metrizable [2-4]. In this paper we review and simplify some results of [6] and as a consequence of ...

Every TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.

A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in [1].