Fixed Point Results in Generalized Cone Metric Spaces

Various types of cones in topological vector spaces are discussed. In particular, the usage of (non)-solid and (non)-normal cones in fixed point results is presented. A recent result about normable cones is shown to be wrong. Finally, a Geraghty-type fixed point result in spaces with cones which are either solid or normal is obtained.

The purpose of this paper is to translate a set of generalized contractive conditions for a couple of self-mappings to have a unique common fixed point in the language of cone 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.

Cornell University - arXiv, 2022

The main aim of this paper is to study of fixed point theory in partial cone metric spaces. Infact, some common fixed point theorems for two mappings in partial cone metric spaces are obtained.

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.

Applied Mathematics Letters, 2011

In the present work, using Minkowski functionals in topological vector spaces, we establish the equivalence between some fixed point results in metric and in (topological vector space) cone metric spaces. Thus, a lot of results in the cone metric setting can be directly obtained from their metric counterparts. In particular, a common fixed point theorem for f -quasicontractions is obtained. Our approach is even easier than that of Du [Wei-Shih Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (2010) 2259-2261] where similar conclusions were obtained using scalarization functions.

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.

In this paper we establish some Fixed Point theorems by altering distances in a complete cone metric space with assumption that the cone is normal, also we introduce MS-Altering function. All the results in this paper are new.

2009

We obtain sufficient conditions for existence of points of coincidence and common fixed points of three self mappings satisfying a contractive type conditions in cone metric spaces. Our results generalize several well-known recent results. * Corresponding author. 2000 Mathematics Subject Classification. 47H10; 54H25.

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.