This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theor...

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space and Gromov hyperbolic. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

*Correspondence: [email protected] Faculty of Mathematics and Informatics, University of Plovdiv, Plovdiv, 4000, Bulgaria Abstract In this paper, we establish a full statement of Ćirić’s fixed point theorem in the setting of cone metric spaces. More exactly, we obtain a priori and a posteriori error estimates for approximating fixed points of quasi-contractions in a cone metric space. Our ...

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in cone metric space. Our results extends the result of A.Bhatt, et al.[A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal., 73(2010) 176-182]. Mathematics Subject Classification: Primary: 47H10, 54H25

The purpose of this paper is to obtain some common fixed point theorems under weaker conditions such as sub compatible mappings and weakly commuting with respect g in the setting of non normal cone metric space.

In this short note, we prove that the square root of quantum Jensen-Shannon divergence is a true metric on cone positive matrices, and hence in particular state space.