http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2011/297360/We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.D. Gopal, M. Imdad, and C. VetroCopyright © 2011 D. Gopal et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/257034/Piri and Vaezi (2010) introduced an iterative scheme for finding a common fixed point of a semigroup of nonexpansive mappings in a Hilbert space. Here, we present that their conclusions are not original and most parts of their paper are picked up from Saeidi and Naseri (2010), though it has not been cited.Farman Golkarmanesh and Saber NaseriCopyright © 2011 Farman Golkarmanesh and Saber Naseri. All rights reserved.http://www.hindawi.com/journals/fpta/2011/706206/We prove several strong convergence theorems for the Ishikawa iterative sequence with errors to a fixed point of strictly pseudocontractive mapping of Browder-Petryshyn type in Banach spaces and give sufficient and necessary conditions for the convergence of the scheme to a fixed point of the mapping. The results presented in this work give an affirmative answer to the open question raised by Zeng et al. 2006, and generalize the corresponding result of Zeng et al. 2006, Osilike and Udomene 2001, and others.Yu-Chao Tang, Yong Cai, and Li-Wei LiuCopyright © 2011 Yu-Chao Tang et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/496417/We prove the existence of solutions for an elliptic partial differential equation having more general flux term than either p-Laplacian or flux term of the Leray-Lions type conditions: -∑j=1n(∂/∂xj)(α(|uxj|)/uxj)=f. Brouwer's fixed point theorem is one of the fundamental tools of the proof.Hee Chul PakCopyright © 2011 Hee Chul Pak. All rights reserved.http://www.hindawi.com/journals/fpta/2011/216146/We generalize and modify Lefschetz sets defined in 1976 by L. Górniewicz, which leads to more general results in fixed point theory.Mirosław ŚlosarskiCopyright © 2011 Mirosław Ślosarski. All rights reserved.http://www.hindawi.com/journals/fpta/2011/847170/We study common fixed point theorems for a finite family of discontinuous and noncommutative single-valued functions defined in complete metric spaces. We also study a common fixed point theorem for two multivalued self-mappings and a stationary point theorem in complete metric spaces. Throughout this paper, we establish common fixed point theorems without commuting and continuity assumptions. In contrast, commuting or continuity assumptions are often assumed in common fixed point theorems. We also give examples to show our results. Results in this paper except those that generalized Banach contraction principle and those improve and generalize recent results in fixed point theorem are original and different from any existence result in the literature. The results in this paper will have some applications in nonlinear analysis and fixed point theory.Lai-Jiu Lin and Sung-Yu WangCopyright © 2011 Lai-Jiu Lin and Sung-Yu Wang. All rights reserved.http://www.hindawi.com/journals/fpta/2011/971479/We introduce new iterative algorithms by hybrid method for finding a common element of the set of solutions of fixed points of infinite family of nonexpansive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational inequality with inverse-strongly monotone mappings in a real Hilbert space. We prove the strong convergence of the proposed iterative method under some suitable conditions. Finally, we apply our results to complementarity problems and optimization problems. Our results improve and extend the results announced by many others.Thanyarat Jitpeera, Uamporn Witthayarat, and Poom KumamCopyright © 2011 Thanyarat Jitpeera et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/484717/In the paper by Olaleru and Akewe (2007), the authors tried to generalize Gregus fixed point theorem. In this paper we give a counterexample on their main statement.Sirous MoradiCopyright © 2011 Sirous Moradi. All rights reserved.http://www.hindawi.com/journals/fpta/2011/180534/We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality: finding a point x* with the property x*∈Fix(T) such that 〈(I-S)x*,x-x*〉≥0, x∈Fix(T) where S, T are two pseudocontractive self-mappings of a closed convex subset C of a Hilbert space with the set of fixed points Fix(T)≠∅. Assume the solution set Ω of (VI) is nonempty. In this paper, we introduce one implicit scheme which can be used to find an element x*∈Ω. Our results improve and extend a recent result of (Lu et al. 2009).Yonghong Yao, Giuseppe Marino, and Yeong-Cheng LiouCopyright © 2011 Yonghong Yao et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/867932/This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or contractive self-mappings from initial conditions to points of the state-trajectory solution. The existence of a unique fixed point leading to a globally asymptotically stable equilibrium point is investigated, in particular, under easily testable sufficiency-type stability conditions. The study is performed for both the uncontrolled case and the controlled case under a wide class of state feedback laws.M. De la SenCopyright © 2011 M. De la Sen. All rights reserved.http://www.hindawi.com/journals/fpta/2011/589725/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.Aleksandar S. Cvetković, Marija P. Stanić, Sladjana Dimitrijević, and Suzana SimićCopyright © 2011 Aleksandar S. Cvetković et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/976192/We define and study a new iterative algorithm inspired by Matsushita and Takahashi (2008). We establish a strong convergence theorem of the proposed algorithm for asymptotically nonexpansive in the intermediate sense mappings in uniformly convex and smooth Banach spaces by using metric projections. This theorem generalizes and refines Matsushita and Takahashi's strong convergence theorem which was established for nonexpansive mappings.Hossein Dehghan, Amir Gharajelo, and Davood AfkhamitabaCopyright © 2011 Hossein Dehghan et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/979261/We define the concept of the generalized u0-concave operators, which generalize the definition of the u0-concave operators. By using the iterative method and the partial ordering method, we prove the existence and uniqueness of fixed points of this class of the operators. As an example of the application of our results, we show the existence and uniqueness of solutions to a class of the Hammerstein integral equations.Yanqiu Zhou, Jingxian Sun, and Jie SunCopyright © 2011 Yanqiu Zhou et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/363716/We prove a common fixed point theorem for mappings under ϕ-contractive conditions in fuzzy metric spaces. We also give an example to illustrate the theorem. The result is a genuine generalization of the corresponding result of S.Sedghi et al. (2010)Xin-Qi HuCopyright © 2011 Xin-Qi Hu. All rights reserved.http://www.hindawi.com/journals/fpta/2011/572156/We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate setting, we obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.Weerayuth NilsrakooCopyright © 2011 Weerayuth Nilsrakoo. All rights reserved.http://www.hindawi.com/journals/fpta/2011/857520/Some relationships between the second-order contingent derivative of a set-valued map and its profile map are obtained. By virtue of the second-order contingent derivatives of set-valued maps, some results concerning sensitivity analysis are obtained in multiobjective optimization. Several examples are provided to show the results obtained.Q. L. Wang and S. J. LiCopyright © 2011 Q. L. Wang and S. J. Li. All rights reserved.http://www.hindawi.com/journals/fpta/2011/208434/We introduce a viscosity approximation method for finding a common element of the set of solutions for an equilibrium problem involving a bifunction defined on a closed, convex subset and the set of fixed points for a nonexpansive semigroup on another one in Hilbert's spaces.Nguyen Buong and Nguyen Dinh DuongCopyright © 2011 Nguyen Buong and Nguyen Dinh Duong. All rights reserved.http://www.hindawi.com/journals/fpta/2011/840978/The purpose of this paper is (1) a general nonlinear mixed set-valued inclusion framework for the over-relaxed A-proximal point algorithm based on the (A, η)-accretive mapping is introduced, and (2) it is applied to the approximation solvability of a general class of inclusions problems using the generalized resolvent operator technique due to Lan-Cho-Verma, and the convergence of iterative sequences generated by the algorithm is discussed in q-uniformly smooth Banach spaces. The results presented in the paper improve and extend some known results in the literature.Xian Bing Pan, Hong Gang Li, and An Jian XuCopyright © 2011 Xian Bing Pan et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/381218/A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results extend and unify some recent results for implicit vector equilibrium problems, multivalued vector variational inequality problems, and vector variational inequality problems.Sanhua Wang and Qiuying LiCopyright © 2011 Sanhua Wang and Qiuying Li. All rights reserved.http://www.hindawi.com/journals/fpta/2010/547828/Let H be a Hilbert space and C a nonempty closed convex subset of H. Let A:C→H be a maximal monotone mapping and f:C→C a bounded demicontinuous strong pseudocontraction. Let {xt} be the unique solution to the equation f(x)=x+tAx. Then{xt} is bounded if and only if {xt} converges strongly to a zero point of A as t→∞ which is the unique solution in A−1(0), where A−1(0) denotes the zero set of A, to the following variational inequality 〈f(p)−p,y−p〉≤0, for all y∈A−1(0).Yuan Qing, Xiaolong Qin, Haiyun Zhou, and Shin Min KangCopyright © 2010 Yuan Qing et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/604046/By using the Krasnoselskii's fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter u(4)(t)+B(t)u′′(t)=λf(t, u(t), u′′(t)), 0<t<1, u(0)=u(1)=∫01p(s)u(s)ds, u′′(0)=u′′(1)=∫01q(s)u′′(s)ds is considered, where p, q∈L1[0,1],  λ>0 is a parameter, and B∈C[0,1], f∈C([0,1]×[0, ∞)×(-∞, 0], [0, ∞)).Xiaoling Han, Hongliang Gao, and Jia XuCopyright © 2011 Xiaoling Han et al. All rights reserved.http://www.hindawi.com/journals/fpta/2011/563136/We obtain some new existence and uniqueness theorems of positive fixed point of mixed monotone operators in Banach spaces partially ordered by a cone. Some results are new even for increasing or decreasing operators.Xinsheng Du and Zengqin ZhaoCopyright © 2011 Xinsheng Du and Zengqin Zhao. All rights reserved.http://www.hindawi.com/journals/fpta/2010/107182/We consider the intuitionistic fuzzy stability of the quadratic functional equation f(kx+y)+f(kx−y)=2k2f(x)+2f(y) by using the fixed point alternative, where k is a positive integer.Liguang WangCopyright © 2010 Liguang Wang. All rights reserved.http://www.hindawi.com/journals/fpta/2010/458086/Using the setting of generalized metric space, the so-called G-metric space, fixed point theorems for mappings with a contractive and a generalized contractive iterate at a point are proved. These results generalize some comparable results in the literature. A common fixed point result is also proved.Ljiljana Gajić and Zagorka Lozanov-CrvenkovićCopyright © 2010 Ljiljana Gajić and Zagorka Lozanov-Crvenković. All rights reserved.http://www.hindawi.com/journals/fpta/2010/169062/We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.B. E. Rhoades and Zhiqun XueCopyright © 2010 B. E. Rhoades and Zhiqun Xue. All rights reserved.http://www.hindawi.com/journals/fpta/2010/246808/We introduce a new system of general variational inequalities in Banach spaces. The equivalence between this system of variational inequalities and fixed point problems concerning the nonexpansive mapping is established. By using this equivalent formulation, we introduce an iterative scheme for finding a solution of the system of variational inequalities in Banach spaces. Our main result extends a recent result acheived by Yao, Noor, Noor, Liou, and Yaqoob.S. Imnang and S. SuantaiCopyright © 2010 S. Imnang and S. Suantai. All rights reserved.http://www.hindawi.com/journals/fpta/2011/346059/Farshid Khojasteh, Zahra Goodarzi, and Abdolrahman RazaniCopyright © 2011 Farshid Khojasteh et al. All rights reserved.http://www.hindawi.com/journals/fpta/2010/268450/Let X be a compact Hausdorff topological space and let C(X) and Cℝ(X) denote the complex and real Banach algebras of all continuous complex-valued and continuous real-valued functions on X under the uniform norm on X, respectively. Recently, Fupinwong and Dhompongsa (2010) obtained a general condition for infinite dimensional unital commutative real and complex Banach algebras to fail the fixed-point property and showed that Cℝ(X) and C(X) are examples of such algebras. At the same time Dhompongsa et al. (2011) showed that a complex C∗-algebra A has the fixed-point property if and only if A is finite dimensional. In this paper we show that some complex and real unital uniformly closed subalgebras of C(X) do not have the fixed-point property by using the results given by them and by applying the concept of peak points for those subalgebras.Davood Alimohammadi and Sirous MoradiCopyright © 2010 Davood Alimohammadi and Sirous Moradi . All rights reserved.http://www.hindawi.com/journals/fpta/2010/210340/Let C be a nonempty closed convex subset of a real Hilbert space H, and let T:C→H be a boundedly Lipschitzian strong pseudo-contraction with a nonempty fixed point set. Three iterative algorithms are proposed for approximating the unique fixed point of T; one of them is for the self-mapping case, and the others are for the nonself-mapping case. Not only the strong convergence, but also the degree of convergence of the three iterative algorithms is obtained. Some numerical results corresponding to the self-mapping case are given which show advantages of our methods. As an application of our results, adopting the regularization idea, we also propose implicit and explicit algorithms for approximating a fixed point of a boundedly Lipschitzian pseudocontractive self-mapping from C into itself, respectively.Songnian He, Yongfu Su, and Ronghua LiCopyright © 2010 Songnian He et al. All rights reserved.http://www.hindawi.com/journals/fpta/2010/723216/The measurability of order continuous random mappings in ordered Polish spaces is studied. Using order continuity, some random fixed point theorems and random periodic point theorems for increasing, decreasing, and mixed monotone random mappings are presented.Xing-Hua Zhu and Jian-Zhong XiaoCopyright © 2010 Xing-Hua Zhu and Jian-Zhong Xiao. All rights reserved.