GENERALIZED CONE METRIC SPACES

We prove in this paper several fixed point results for mappings that satisfy certain contractive conditions in generalized cone metric spaces. Our results generalize, extend, and unify some other results in the literature in the sense that they are analogous to those for cone metric spaces, but in a more general setting, where we have here G-cone metric spaces, or in the sense that they are extension or generalization of some other results proved previously in G-metric spaces.

International Journal of Applied Mathematical Research, 2013

Cone metric space was introduced by Huang Long-Guang et al. (2007) wh ich generalized the concept of metric space. Several fixed point results have been proved in such spaces which generalized and extended the analogous results in metric spaces by different authors. In the present paper two co mmon fixed point results for a sequence of self maps of a complete cone metric space, using altering distance function between the points under a certain continuous control function, are obtained, which generalize the results of Sastry et al. (2001) and Pandhare et al. (1998). Two examples are given in support of our results.

Nonlinear Analysis: Theory, Methods & Applications, 2011

Using an old M. Krein's result and a result concerning symmetric spaces from [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (1) (2011), 38-50], we show in a very short way that all fixed point results in cone metric spaces obtained recently, in which the assumption that the underlying cone is normal and solid is present, can be reduced to the corresponding results in metric spaces. On the other hand, when we deal with non-normal solid cones, this is not possible. In the recent paper [M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, 7 pages, Article ID 315398, doi:10.1115/2010/315398] the author claims that most of the cone fixed point results are merely copies of the classical ones and that any extension of known fixed point results to cone metric spaces is redundant; also that underlying Banach space and the associated cone subset are not necessary. In fact, Khamsi's approach includes a small class of results and is very limited since it requires only normal cones, so that all results with non-normal cones (which are proper extensions of the corresponding results for metric spaces) cannot be dealt with by his approach.

In this paper we introduce cone D-metric spaces, we prove some fixed point theorems on the D-cone metric spaces.

Journal of Mathematical Analysis and …, 2008

Huang and Zhang reviewed cone metric spaces in 2007 [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476]. We shall prove that there are no normal cones with normal constant M < 1 and for each k > 1 there are cones with normal constant M > k. Also, by providing non-normal cones and omitting the assumption of normality in some results of [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476], we obtain generalizations of the results.

Kyungpook mathematical journal, 2015

The aim of this paper is to prove a fixed point theorem on a generalised cone metric spaces for maps satisfying general contractive type conditions.

In the present paper, we have proved some convergence properties of a sequence of elements in a partial cone metric space and thereby we have established some fixed point theorems on it.

Matematicki Vesnik

The concept of generalized cone b-metric space is introduced as a generalization of cone metric space, cone b-metric space and cone rectangular metric space. An analogue of Banach contraction principle and Kannan&#39;s fixed point theorem is proved in this space. Our result generalizes many known results in fixed point theory.

Fixed Point Theory and Applications, 2009

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

Journal of Scientific Research, 2011

We prove coincidence and common fixed point theorems of four self mappings satisfying a generalized contractive type condition in complete cone metric spaces. Our results generalize some well-known recent results.