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In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f-MK-pair mappings and f-CJM-pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfies
2009
Several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps satisfying generalized contractive conditions are established in a symmetric space.
Rendiconti Del Circolo Matematico Di Palermo, 2008
We prove the existence of points of coincidence and common fixed points of a pair of self-mappings satisfying a generalized contractive condition in cone metric spaces. Our results generalize several well-known recent and classical results.
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.
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.
International Journal of Pure and Apllied Mathematics, 2013
The purpose of this paper is to establish some common fixed point results for two Banach pairs of mappings which satisfy T-Reich and T-Rhoades contraction conditions in cone metric spaces without the assumption of normality condition of the cone.
This paper is devoted to prove the S. L. Singh's common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of generalized Kannan contraction, generalized Zamfirescu contraction and generalized Weak contraction for a pair of mappings, proving afterward fixed point results.
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.
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.
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.
The object of this paper is to establish some common Fixed Point Theorems for weakly compatible pair of self maps in cone metric spaces which is not necessarily normal. It turns out the generalization of results of Huang and Zhang [3], also we prove the existence of unique common fixed point of sequence of mappings satisfying contractive condition in cone metric space.
Journal of Mathematical Analysis and Applications, 2008
The purpose of this paper is to generalize and to unify fixed point theorems of Das and Naik,Ćirić, Jungck, Huang and Zhang on complete cone metric space.
Journal of Nonlinear Analysis and Application, 2012
The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results.
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.
Bulletin of The Iranian Mathematical Society, 2011
We prove a coincidence and common fixed point theorems of three self mappings satisfying a generalized contractive type condition in cone metric spaces. Our results generalize some well-known recent results.
Fixed Point Theory and Applications, 2009
A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assumption that the cone interior is nonempty. We modify the definition of property E.A , introduced recently in the work by Aamri and Moutawakil 2002 , and use it instead of usual assumptions about commutativity or compatibility of the given pair. Examples show that the obtained results are proper extensions of the existing ones.
2018
In this paper, we establish the common fixed point theorems of weakly compatible mappings in cone metric space. Our results extend, modify and improve various well known results in the literature.
Fixed Point Theory and Applications, 2011
In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. We prove some common fixed point theorems for four mappings in those spaces. Obtained results extend and generalize well-known comparable results in the literature. All results are proved in the settings of a solid cone, without the assumption of continuity of mappings.
Fixed Point Theory and Applications, 2011
In this paper, we introduce the concepts of w-compatible mappings, b-coupled coincidence point and b-common coupled fixed point for mappings F, G : X × X X, where (X, d) is a cone metric space. We establish b-coupled coincidence and bcommon coupled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in the literature, in particular the recent results of Abbas et al. [Appl. Math. Comput. 217, 195-202 (2010)]. Some examples are given to illustrate our obtained results. An application to the study of existence of solutions for a system of non-linear integral equations is also considered.
Abstract and Applied Analysis, 2012
The existence and uniqueness of the common coupled fixed point in cone metric spaces have been studied by considering different types of contractive conditions. A new concept of the cdistance in cone metric space has been recently introduced in 2011. Then, coupled fixed point results for contraction-type mappings in ordered cone metric spaces and cone metric spaces have been considered. In this paper, some common coupled fixed point results on c-distance in cone metric spaces are obtained. Some supporting examples are given.
We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS valued cone metric spaces. Our results generalize some well-known recent results in the literature.
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