Common Fixed Point Theorems for Weakly Compatible Mappings on Cone Banach Space (original) (raw)

Common fixed point results in cone metric spaces for a family of weakly compatible maps

Cone metric space was introduced by Huang Long- 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. and . Two examples are given in support of our results.

Common Fixed Point Point Theorem for a Pair of Weakly Compatible Mappings on Banach Spaces

East Asian mathematical journal, 2011

Abstract. In this paper, we prove a common xed point theorem fornoncompatible, discontinuous mappings on a Banach space. Our maintheorem extends, improves, generalizes some known results on Banachspaces. 1. Introduction and PreliminariesHusain and Sehgal [1] proved common xed point theorems for a familyof mappings. Khan and Imdad [5] extended result of Husain and Sehgal [1].Imdad, Khan and Sessa [2] extended above results and proved common xedpoints for three mappings de ned on a closed subset of a uniformly convexBanach space.Rashwan [9] extended result of Imdad, Khan and Sessa [2] by employingfour compatible mappings of type (A) instead of weakly commuting mappingsand by using one continuous mapping as opposed to two.Sharma and Bamboria [12] improved results of Rashwan [9] by removingthe condition of continuity and replacing the compatibility of mappings of type(A) by weak compatibility. Sharma and Tilwankar [13] proved a common xedpoint theorem for four mappings under the conditi...

Compatible and weakly compatible mappings in cone metric spaces

Mathematical and Computer Modelling, 2010

In this paper we extend and generalize common fixed point theorems for six self-maps of Singh and Jain [B. Singh, S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 from Menger and metric spaces to cone metric spaces. We also extend the notions of compatible and weakly compatible mappings from the setting of Menger and metric spaces to the setting of cone metric spaces. We do not impose the normality property on the cone, but suppose only that the cone P, in the ordered Banach space E, has a nonempty interior. Examples are given to illustrate the results.

Common Fixed Point Theorems in Cone Banach Spaces ABSTRACT| FULL TEXT

Recently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.

COMMON FIXED POINT THEOREMS IN CONE BANACH SPACES

Recently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.

Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces

Fixed Point Theory and Applications, 2013

In this paper, we establish common fixed point theorems for two weakly compatible self-mappings satisfying the contractive condition or the quasi-contractive condition in the case of a quasi-contractive constant λ ∈ (0, 1/s) in cone b-metric spaces without the normal cone, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

Coupled fixed point results in cone metric spaces for -compatible 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.

Some common fixed point results for weakly compatible mappings in cone metric type space

In this paper we consider cone metric type spaces which are introduced as a generalization of symmetric and metric spaces by Khamsi and Hussain in 2010. Then we prove several common fixed point for weakly compatible mappings in cone metric type spaces. All results are proved in the settings of a solid cone, without the assumption of continuity of the mappings.