Stojan Radenović

Common coupled fixed point theorems in cone metric spaces for w-compatible mappings

In this paper we introduce the concept of a w-compatible mappings to obtain coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in cone metric space with a cone having non-empty interior. Coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend and unify several well known comparable results in the literature. Results are supported by three examples.

Common Fixed Point Theorems for Weakly Compatible Pairs on Cone Metric Spaces

We prove several fixed point theorems on cone metric spaces in which the cone does not need to be normal. These theorems generalize the recent results of Huang and Zhang (2007), Abbas and Jungck (2008), and Vetro (2007). Furthermore as corollaries, we obtain recent results of Rezapour and Hamlborani (2008).

Generalized weak contractions in partially ordered metric spaces

Recent results of Doric [D. Doric, Common fixed point for generalized (@j,@f)-weak contractions, Appl. Math. Lett. 22 (2009) 1896-1900] on generalized weakly contractive mappings are extended to the setting of partially ordered metric spaces. Thus, generalization of fixed point results of Harjani and Sadarangani [J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71 (2009) 3403-3410] is obtained. Some applications are presented. Examples are given to show that our results are proper generalizations of the existing ones.

Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces

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 (2009) 319-325] and I. Altun, B. Damnjanovic and D. Djoric [I. Altun, B. Damnjanovic, D. Djoric, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett. (2009) doi:10.1016/j.aml.2009.09.016] 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.

Suzuki-type fixed point results in metric type spaces

Suzuki’s fixed point results from (Suzuki, Proc. Am. Math. Soc. 136:1861-1869, 2008) and (Suzuki, Nonlinear Anal. 71:5313-5317, 2009) are extended to the case of metric type spaces and cone metric type spaces. Examples are given to distinguish our results from the known ones.MSC:47H10, 54H25.

A note on the equivalence of some metric and cone metric fixed point results

Abstract 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.

Remarks on “Quasi-contraction on a cone metric space”

Abstract Recently, D. Ilic and V. Rakocevic [D. Ilic, V. Rakocevic, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011 ] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.

COMMON FIXED POINTS OF FOUR MAPS IN PARTIALLY ORDERED METRIC SPACES

In this paper, common fixed points of four mappings satisfying a generalized weak contractive condition in the framework of partially ordered metric space are obtained. We also provide examples of new concepts introduced herein.

Some periodic point results in generalized metric spaces

Abstract We prove some fixed point and periodic point theorems for a map in generalized metric spaces. An example is provided to support our result. The results presented in this paper generalize several well known comparable results in the literature.

Common fixed point results in metric-type spaces.

Several fixed point and common fixed point theorems are obtained in the setting of metric-type spaces introduced by M. A. Khamsi in 2010.