Common fixed points of nonlinear hybrid mappings under strict contractions in semi-metric spaces

In this paper, we extend the notion of common property (E.A) to pairs of hybrid mappings defined on an arbitrary set with values in a semi-metric space and use it to prove some coincidence and common fixed point theorems in semi-metric (potent semi-metric) spaces under strict contractions. Our results generalize several previously known fixed point theorems of the existing literature.     

Common fixed point theorems under strict contractive conditions in Menger spaces

The main purpose of this paper is to establish some common fixed point theorems under strict contractive conditions for mappings satisfying the property (E.A) in Menger probabilistic metric spaces. As applications, we obtain the corresponding common fixed point theorems under strict contractive in metric spaces.     

Coincidence and fixed points in symmetric spaces under strict contractions

Some common fixed point theorems due to Aamri and El Moutawakil [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188] and Pant and Pant [R.P. Pant, V. Pant, Common fixed points under strict contractive conditions, J. Math. Anal. Appl. 248 (2000) 327-332] proved for strict contractive mappings in metric spaces are extended to symmetric (semi-metric) spaces under tight conditions. Some related results are derived besides discussing illustrative examples which establish the utility of results proved in this note.     

Coincidence and fixed points for hybrid strict contractions

We define the property (E.A) for single-valued and multivalued mappings and introduce the notion of T-weak commutativity for a hybrid pair (f,T) of single-valued and multivalued maps. We obtain some coincidence and fixed point theorems for this class of maps and derive, as application, an approximation theorem.     

Common fixed points of generalized contractions on partial metric spaces and an application

In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved. Presented theorems extend the very recent results of I. Altun, F. Sola and H. Simsek [Generalized contractions on partial metric spaces, Topology and its applications 157 (18) (2010) 2778-2785]. As application, some homotopy results for operators on a set endowed with a partial metric are given.     

Common fixed points in cone metric spaces

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces. Supported by Universitá degli Studi di Palermo, R. S. ex 60%.     

Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces

In this paper, we prove some existence results on coincidence and common fixed points of two pairs of self mappings without continuity under relatively weaker commutativity requirement in Menger PM spaces. Our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides furnishing illustrative examples.     

Connected extensions of metric spaces and fixed points of Banach contractions

Two theorems announced by the author are proved. The first theorem concerns the existence of connected metrizable extensions of metric spaces. The second theorem is a slightly paradoxical assertion about the validity of the fixed-point principle. Bibliography: 4 titles. Translated fromProblemy Matematicheskogo Analiza, No. 17, 1997, pp. 227–237.     

Common fixed points of two maps in cone metric spaces

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.      

Common fixed points for four maps in cone metric spaces

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.     

Common fixed points for R-weakly commuting in fuzzy metric spaces

In this paper, we study the concept of R-weakly commuting of type (A _g ) of Pathak et?al. (Bull Korean Math Soc 34:247?C257, 1997) in fuzzy metric spaces. We also establish the existence of common fixed point theorems by using the common limit in the range property and give an example to validate our the main results.     

Common fixed points for discontinuous mappings in fuzzy metric spaces

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition

In this work, we establish new coincidence and common fixed point theorems for hybrid strict contraction maps by dropping the assumption “f is T-weakly commuting” for a hybrid pair (f,T) of multivalued maps in Theorem 3.10 of T. Kamran (2004) [8]. As an application, an invariant approximation result is derived.     

Dynamic processes and fixed points of set-valued nonlinear contractions in cone metric spaces

Investigations concerning the existence of dynamic processes convergent to fixed points of set-valued nonlinear contractions in cone metric spaces are initiated. The conditions guaranteeing the existence and uniqueness of fixed points of such contractions are established. Our theorems generalize recent results obtained by Huang and Zhang [L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive maps, J. Math. Anal. Appl. 332 (2007) 1467–1475] for cone metric spaces and by Klim and Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (1) (2007) 132–139] for metric spaces. The examples and remarks provided show an essential difference between our results and those mentioned above.     

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.     

Set-valued contractions and fixed points

A common fixed point theorem is proved for a family of set-valued contraction mappings in gauge spaces. This result is related to a recent result of Frigon for ‘generalized contractions’ and it includes a method for approximating the fixed point. The remainder of the paper is devoted to results for families of set-valued contraction mappings in hyperconvex spaces. It is proved, for example, that if M is a hyperconvex metric space and f_α is a family of set-valued contractions indexed over a directed set Λ and taking values in the space of all nonempty admissible subsets of M endowed with the Hausdorff metric, then the condition f_β(x)⊆f_α(x) for all x∈M and β⩾α implies that the set of points x∈M for which x∈⋂_α∈Λf_β(x) is nonempty and hyperconvex.     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

Common fixed points for generalized contractive multivalued operators in complete metric spaces

In this paper,we discuss some new fixed point theorems for a pair of multivalued operators which satisfy generalized contractive condition. Our results are the extension and improvement of corresponding results of single-valued operators. Finally, some examples are given to illustrate the usability of our results.     

Common coupled fixed points of generalized contractive mappings in partially ordered metric spaces

In this paper, we introduce the concept of a $w^{*}$ -compatible mappings to obtain coupled coincidence point and coupled common fixed points of nonlinear contractive mappings in partially ordered metric spaces. Our results generalize, extend, unify, enrich and complement various comparable results in the existing literature.     

A fixed point result in Menger spaces using a real function

The main result of this paper is a fixed point theorem of self-mappings in Menger spaces which satisfy certain inequality. This inequality involves a class of real functions which we call Φ-functions. As a corollary we obtain a result in the corresponding metric spaces. The result is supported by an example. The class of real functions we have used is the conceptual extension of altering distance functions used in metric fixed point theory.