http://www.fixedpointtheoryandapplications.com The latest research articles published by Fixed Point Theory and Applications 2013-05-20T00:00:00Z In the present paper, an extension of Edelstein contraction theorem for cyclic contractions in a fuzzy metric space is established, which also can be considered as a generalization of fuzzy Edelstein contraction theorem introduced by Grabiec. Additionally, we extend afixed point theorem in G-complete fuzzy metric spaces given by Shen et al. to M-complete fuzzy metric spaces. Meantime, two examples are constructed to illustrate the corresponding results, respectively. http://www.fixedpointtheoryandapplications.com/content/2013/1/133 Yonghong Shen Fixed Point Theory and Applications 2013, null:133 2013-05-20T00:00:00Z doi:10.1186/1687-1812-2013-133 /content/figures/1687-1812-2013-133-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 133 2013-05-20T00:00:00Z PDF An iterative sequence for total quasi-$\phi$-asymptotically nonexpansive multi-valued mapping for modifying Halpern-Mann's iterations is introduced. Under suitable limit conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results in \cite{Cha2}. http://www.fixedpointtheoryandapplications.com/content/2013/1/132 Li Yi Liu Hong Bo Fixed Point Theory and Applications 2013, null:132 2013-05-17T00:00:00Z doi:10.1186/1687-1812-2013-132 /content/figures/1687-1812-2013-132-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 132 2013-05-17T00:00:00Z PDF We establish some common fixed point theorems for mappings satisfying a (psi, alpha, beta)-weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing results in the literature http://www.fixedpointtheoryandapplications.com/content/2013/1/131 Huseyin ISIK Duran TURKOGLU Fixed Point Theory and Applications 2013, null:131 2013-05-16T00:00:00Z doi:10.1186/1687-1812-2013-131 /content/figures/1687-1812-2013-131-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 131 2013-05-16T00:00:00Z PDF In this paper, tripled coincidence points of mappings satisfying some nonlinear contractive conditions in the framework of partially ordered b-metric spaces are obtained. Our results extend the results of Berinde and Borcut [V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partiallyordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897] and Borcut [M. Borcut, Tripled coincidence theorems for contractive type mappings in partially orderedmetric spaces, Appl. Math. Comput., 218 (2012), 7339-7346] from the context of ordered metric spaces to the setting of ordered b-metric spaces. Moreover, some examples of the main result are given. Finally, some tripled coincidence point results for mappings satisfying some contractive conditions of integral type in complete partiallyordered b-metric spaces are deduced. Also, an application is given to support our results. http://www.fixedpointtheoryandapplications.com/content/2013/1/130 Vahid Parvaneh Jamal Rezaei Roshan Stojan Radenovic Fixed Point Theory and Applications 2013, null:130 2013-05-16T00:00:00Z doi:10.1186/1687-1812-2013-130 /content/figures/1687-1812-2013-130-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 130 2013-05-16T00:00:00Z PDF A `generalized metric space' is a semimetric space which does not satisfythe triangle inequality, but which satisfies a weaker assumption called thequadrilateral inequality. After reviewing various related axioms, it isshown that Caristi's Theorem holds in complete generalized metric spaceswithout further assumptions. This is noteworthy because Banach's fixed pointtheorem seems to require more than the quadrilateral inequality, and becausestandard proofs of Caristi's theorem require the triangle inequality. http://www.fixedpointtheoryandapplications.com/content/2013/1/129 William Kirk Naseer Shahzad Fixed Point Theory and Applications 2013, null:129 2013-05-15T00:00:00Z doi:10.1186/1687-1812-2013-129 /content/figures/1687-1812-2013-129-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 129 2013-05-15T00:00:00Z PDF In quasi-pseudometric spaces (X,p) (not necessarily Hausdorff), the concepts of the left quasi-closed maps (generalizing continuous maps) and generalized quasi-pseudodistances J:XxX->[0,infinity) (generalizing in metric spaces: metrics, Tataru distances, w-distances of Kada et al., tau-distances of Suzuki and tau-functions of Lin and Du) are introduced, the asymmetric structures on X determined by J (generalizing the asymmetric structure on X determined by quasi-pseudometric p) are described and the contractions T:X->X with respect to J (generalizing Banach and Rus contractions) are defined. Moreover, if (X,p) are left sequentially complete (in the sense of Reilly, Subrahmanyam and Vamanamurthy), then, for these contractions T:X->X such that T^{[q]} is left quasi closed for some q[element of]N, the global minimum of the map x->J(x,T^{[q]}(x)) is studied and theorems concerning the existence of global optimal approximate solutions of the equation T^{[q]}(x)=x are established. The results are new in quasi-pseudometric and quasi-metric spaces and even in metric spaces. Examples showing the difference between our results and the well-known ones are provided. In the literature the fixed and periodic points in not Hausdorff spaces were not studied. http://www.fixedpointtheoryandapplications.com/content/2013/1/128 Kazimierz Wlodarczyk Robert Plebaniak Fixed Point Theory and Applications 2013, null:128 2013-05-15T00:00:00Z doi:10.1186/1687-1812-2013-128 /content/figures/1687-1812-2013-128-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 128 2013-05-15T00:00:00Z PDF In this note we present some corrections on our previous paper [Fixed PointTheory Appl. 2012, 2012:228.].In the paper [1], the following corrections are required on Page 3 and 6:Inequality (3.1) in Theorem 3.4 on Page 3 and the same inequality in Theorem 3.5on Page 6, should read as follows:(x; y);(u; v))d(F(x; y); F(u; v)) + d(F(y; x); F(v; u))2d(x; u) + d(y; v)2The corresponding changes in the proofs of these theorems shall lead to the con-clusions easily. Moreover, we can easily choose suitable F(x; y) in Examples 3.7 and3.8 to meet our requirements. http://www.fixedpointtheoryandapplications.com/content/2013/1/127 M. Mursaleen S. Mohiuddine R. Agarwal Fixed Point Theory and Applications 2013, null:127 2013-05-15T00:00:00Z doi:10.1186/1687-1812-2013-127 /content/figures/1687-1812-2013-127-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 127 2013-05-15T00:00:00Z PDF In this paper, we introduce a new iterative algorithm by relaxed extragradient-like method for finding a common element of the set of solutions of the generalized mixed equilibriumproblems, the set of solutions of a more general system ofvariational inequalities for finite inverse strongly monotonemappings and the set of solutions of a fixed point problem ofa strictly pseudocontractive mapping in a Hilbert space. Then we prove strong convergence of the scheme to a common element of the three above described sets. http://www.fixedpointtheoryandapplications.com/content/2013/1/126 Yifen Ke Changfeng Ma Fixed Point Theory and Applications 2013, null:126 2013-05-15T00:00:00Z doi:10.1186/1687-1812-2013-126 /content/figures/1687-1812-2013-126-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 126 2013-05-15T00:00:00Z PDF We give new criteria for the existence of nontrivial fixed points on cones assuming some monotonicity of the operator on a suitable conical shell. Moreover we give an application to the existence of multiple solutions for a nonlocal boundary value problem that models the displacement of a beam subject to some feedback controllers. http://www.fixedpointtheoryandapplications.com/content/2013/1/125 Alberto Cabada Jose Angel Cid Gennaro Infante Fixed Point Theory and Applications 2013, null:125 2013-05-13T00:00:00Z doi:10.1186/1687-1812-2013-125 /content/figures/1687-1812-2013-125-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 125 2013-05-13T00:00:00Z PDF In this paper, we consider an iterative method for finding a fixed point of continuous mappings on an arbitrary interval. Then, we give the necessary and sufficient conditions for the convergence of the proposed iterative methods for continuous mappings on an arbitrary interval. We also compare the rate of convergence between iteration methods. Finally, we provide a numerical example which supports our theoretical results. http://www.fixedpointtheoryandapplications.com/content/2013/1/124 Nazli KADIOGLU Isa YILDIRIM Fixed Point Theory and Applications 2013, null:124 2013-05-13T00:00:00Z doi:10.1186/1687-1812-2013-124 /content/figures/1687-1812-2013-124-toc.gif Fixed Point Theory and Applications 1687-1812 ${item.volume} 124 2013-05-13T00:00:00Z PDF