Ordered cone metric spaces and fixed point results

Fixed Point Theory and Applications, 2010

We prove some fixed point theorems for multivalued maps in cone metric spaces. We improve and extend a number of known fixed point results including the corresponding recent fixed point results of Feng and Liu 1996 and Chifu and Petrusel 1997. The remarks and example provide improvement in the mentioned results.

Fixed Point Theory and Applications, 2012

Recently, Chen et al. (Appl. Math. Lett. 25:692-697, 2012) introduced the concept of the cone ball-metric and studied the common fixed-point theorems for the stronger Meir-Keeler cone-type function in cone ball-metric spaces. The purpose of this paper is to establish the coupled fixed-point theorems for nonlinear contraction mappings, which have a mixed monotone property by using the cone ball-metric. Also, we give some examples to validate our main results. At the end of this paper, we give an open problem for further investigation. MSC: 47H10; 54H25

Applied Mathematics and Computation, 2012

We establish coupled coincidence point results for mixed g-monotone mappings under general contractive conditions in partially ordered cone metric spaces over solid cones. We also present results on existence and uniqueness of coupled common fixed points. Our results generalize, extend and unify several well known comparable results in the literature. To illustrate our results and to distinguish them from the earlier ones, we equip the paper with examples.

Topology and its Applications, 2015

In this paper we extend main fixed point results of Kikkawa and Suzuki (2008) [19] and Mot and Petruşel (2009) [21] for the case of cone metric spaces without assumption of normality on cone. We also support our results by a nontrivial example and establish a homotopy theorem as an application.

Arxiv preprint arXiv:1102.4019, 2011

The aim of this paper is to present some fixed point theorems for generalized contractions by altering distance functions in a complete cone metric spaces endowed with a partial order. We also general-ize fixed point theorems of J. Harjani, K. Sadarangani [J. Harjani, K. ...

Fixed Point Theory and Applications, 2009

In this paper at first we introduce a new order on the subsets of cone metric spaces then, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.

Computers & Mathematics With Applications, 2011

In this paper, we introduce a concept of the c-distance in a cone metric space and, by using the concept of the c-distance, prove some fixed point theorems in ordered cone metric spaces.

Computers & Mathematics with Applications, 2010

In the first part of this paper we generalize results on common fixed points in ordered cone metric spaces obtained by I. Altun and G. Durmaz [I. Altun, G. Durmaz, Some fixed point theorems on ordered cone metric spaces, Rend. Circ. Mat. Palermo, 58 319-325] and I. Altun, B. Damnjanović and D. Djorić [I. Altun, B. Damnjanović, D. Djorić, Fixed point and common fixed point theorems on ordered cone metric spaces, ] by weakening the respective contractive condition. Then, the notions of quasicontraction and g-quasicontraction are introduced in the setting of ordered cone metric spaces and respective (common) fixed point theorems are proved. In such a way, known results on quasicontractions and g-quasicontractions in metric spaces and cone metric spaces are extended to the setting of ordered cone metric spaces. Examples show that there are cases when new results can be applied, while old ones cannot.

Recently, Cho et al. [Y. J. Cho, R. Saadati, S. H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] defined the concept of the c-distance in a cone metric space and proved some fixed point theorems on c-distance. In this paper, we prove some new fixed point and common fixed point theorems by using the distance in ordered cone metric spaces.

In this paper, the existence and uniqueness of coupled fixed point for mapping having the mixed monotone property in partially ordered metric spaces which endowed with vector-valued metrics are given.

2010

In this paper we prove common xed point theorems for two multivalued maps in complete cone metric spaces withnormal constant M = 1. Our results generalize and extend the results of Rezapour[12] and others.

Journal of Function Spaces, 2022

In this paper, we provide a short, comprehensive, and brief proof for Caristi-Kirk fixed point result for single and set-valued mappings in cone metric spaces. In addition, we partially addressed an open problem in which Caristi-Kirk fixed point result in cone metric spaces reduces to a classical result in metric spaces and provided a brief justification for a partial positive answer to this open problem using Caristi-Kirk fixed point theorem on uniform space. The proofs given to Caristi-Kirk’s result vary and use different techniques.

Computers & Mathematics with Applications, 2011

a b s t r a c t Recently, Cho et al. [Y.J. Cho, R. Saadati, S.H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011) 1254-1260] introduced the concept of the c-distance in a cone metric space and established some fixed point theorems on c-distance. The aim of this paper is to extend and generalize the main results of Cho et al. [20] and also show some examples to validate our main results.

In this paper we obtain some results on fixed point theorem in cone metric space which extends some known results that are already proved in .

Journal of Information Engineering and Applications, 2014

In the Present paper we prove some fixed point theorems in cone metric space our result generalizes the previous result of mathematicians.