http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/491583.htmlThe viscosity approximation methods are employed to establish strong convergence of the modified Mann iteration scheme to a common zero of a finite family of accretive operators on a strictly convex Banach space with uniformly Gâteaux differentiable norm. Our work improves and extends various results existing in the current literature.Liang-Gen Hu and Jin-Ping Wang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/791514.htmlWe use a concept of abstract convexity to define the almost S-KKM𝒞 property, al-S-KKM𝒞(X,Y) family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors.Tong-Huei Chang, Chi-Ming Chen, and Yueh-Hung Huang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/917175.htmlWe prove some fixed point results for mappings satisfying various contractive conditions on Complete G-metric Spaces. Also the Uniqueness of such fixed point are proved, as well as we showed these mappings are G-continuous on such fixed points.Zead Mustafa and Brailey Sims© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/891965.htmlWe consider a new Noor-type iterative procedure with errors for approximating the common fixed point of a finite family of uniformly quasi-Lipschitzian mappings in convex metric spaces. Under appropriate conditions, some convergence theorems are proved for such iterative sequences involving a finite family of uniformly quasi-Lipschitzian mappings. The results presented in this paper extend, improve and unify some main results in previous work.Tian You-xian and Yang Chun-de© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/824374.htmlWe discuss the following viscosity approximations with the weak contraction A for a non-expansive mapping sequence {Tn}, yn=αnAyn+(1−αn)Tnyn, xn+1=αnAxn+(1−αn)Tnxn. We prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern's type iteration and Mouda's viscosity approximations with the weak contraction.Yisheng Song and Xiao Liu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/192872.htmlIn order to observe the condition of Kannan mappings, we prove a generalization of Kannan's fixed point theorem. Our theorem involves constants and we obtain the best constants to ensure a fixed point.Yusuke Enjouji, Masato Nakanishi, and Tomonari Suzuki© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/207503.htmlCommon fixed point results for some new classes of nonlinear noncommuting maps on a locally convex space are proved. As applications, related invariant approximation results are obtained. Our work includes improvements and extension of several recent developments of the existing literature on common fixed points. We also provide illustrative examples to demonstrate the generality of our results over the known ones.F. Akbar and A. R. Khan© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/546273.htmlWe consider complete Menger probabilistic quasimetric space and prove common fixed point theorems for weakly compatible maps in this space.Shaban Sedghi, Tatjana Žikić-Došenović, and Nabi Shobe© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/194671.htmlSome generalized Ky Fan minimax inequalities for vector-valued mappings are established by applying the classical Browder fixed point theorem and the Kakutani-Fan-Glicksberg fixed point theorem.Xianqiang Luo© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/609353.htmlWe introduce and study a new system of nonlinear variational-like inclusions involving s-(G,η)-maximal monotone operators, strongly monotone operators, η-strongly monotone operators, relaxed monotone operators, cocoercive operators, (λ,ξ)-relaxed cocoercive operators, (ζ,φ,ϱ)-g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique associated with s-(G,η)-maximal monotone operators and Banach contraction principle, we demonstrate the existence and uniqueness of solution for the system of nonlinear variational-like inclusions. The results presented in the paper improve and extend some known results in the literature.Zeqing Liu, Min Liu, Jeong Sheok Ume, and Shin Min Kang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/362191.htmlWe introduce an iterative method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for the minimization problem.HongYu Li and HongZhi Li© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/786357.htmlThe purpose of this paper is to study the existence of fixed points for contractive-type and nonexpansive-type multivalued maps in the setting of modular function spaces. We also discuss the concept of w-modular function and prove fixed point results for weakly-modular contractive maps in modular function spaces. These results extend several similar results proved in metric and Banach spaces settings.Marwan A. Kutbi and Abdul Latif© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/719360.htmlThe purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.Prasit Cholamjiak© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/571546.htmlWe present a new and interesting extension theorem for concave operators as follows. Let X be a real linear space, and let (Y,K) be a real order complete PL space. Let the set A⊂X×Y be convex. Let X0 be a real linear proper subspace of X, with θ∈(AX−X0)ri, where AX={x∣(x,y)∈A for some y∈Y}. Let g0:X0→Y be a concave operator such that g0(x)≤z whenever (x,z)∈A and x∈X0. Then there exists a concave operator g:X→Y such that (i) g is an extension of g0, that is, g(x)=g0(x) for all x∈X0, and (ii) g(x)≤z whenever (x,z)∈A.Jian-wen Peng, Wei-dong Rong, and Jen-Chih Yao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/643840.htmlWe 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).G. Jungck, S. Radenović, S. Radojević, and V. Rakočević© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/493965.htmlWe prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.Muhammad Arshad, Akbar Azam, and Pasquale Vetro© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/809232.htmlUsing the fixed point method, we prove the generalized Hyers-Ulam stability of homomorphisms in C∗-algebras and Lie C∗-algebras and of derivations on C∗-algebras and Lie C∗-algebras for the Cauchy functional equation.Choonkil Park© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/892691.htmlBy means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation 𝒫(f)∘f=F. Moreover, we get that the solution f depends continuously on F. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation ∑n=1∞anfn(x)=F(x),  x∈𝔹 with a general boundary restriction, where F:𝔹→𝔸 is a given Lipschitz function, and 𝔹,𝔸 are compact convex subsets of ℝN with nonempty interior.Wei Song, Guo-qiu Yang, and Feng-chun Lei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/462489.htmlThe purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings. Further, we apply our results to solve the equilibrium and optimization problems. The results of this paper improved and extended the results of W. Nilsrakoo and S. Saejung (2008) and some others in some respects.Liping Yang and Yongfu Su© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/762478.htmlWe prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation zn+1=F(zn,zn−1), n=2,3,…, where F satisfies mixed-monotone conditions with respect to the given ordering.Dž. Burgić, S. Kalabušić, and M. R. S. Kulenović© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/170140.htmlWe present generalized versions of Caristi's fixed point theorem for multivalued maps. Our results either improve or generalize the corresponding generalized Caristi's fixed point theorems due to Bae (2003), Suzuki (2005), Khamsi (2008), and others.Abdul Latif© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/612491.htmlWe obtain strong convergence theorems of two modifications of Mann iteration processes with errors in the doubly sequence setting. Furthermore, we establish some weakly convergence theorems for doubly sequence Mann's iteration scheme with errors in a uniformly convex Banach space by a Frechét differentiable norm.A. El-Sayed Ahmed and A. Kamal© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/369215.htmlWe introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of k-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho (2008).Rabian Wangkeeree and Uthai Kamraksa© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/804734.htmlWe establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988). Also, an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces.M. A. Ahmed© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/531037.htmlLet X be a finite polyhedron that has the homotopy type of the wedge of the projective plane and the circle. With the aid of techniques from combinatorial group theory, we obtain formulas for the Nielsen numbers of the selfmaps of X.Seung Won Kim, Robert F. Brown, Adam Ericksen, Nirattaya Khamsemanan, and Keith Merrill© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/794178.htmlWe introduce a new approximation scheme combining the viscosity method with parallel method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a family of finitely strict pseudocontractions. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also get some new and interesting results. The results in this paper extend and improve some well-known results in the literature.Jian-Wen Peng, Yeong-Cheng Liou, and Jen-Chih Yao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2008/583082.htmlThe convex feasibility problem (CFP) of finding a point in the nonempty intersection ⋂i=1NCi is considered, where N⩾1 is an integer and the Ci's are assumed to be convex closed subsets of a Banach space E. By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.Somyot Plubtieng and Kasamsuk Ungchittrakool© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2009/487161.htmlWe prove some results on the existence of fixed points for multivalued generalized w-contractive maps not involving the extended Hausdorff metric. Consequently, several known fixed point results are either generalized or improved.Abdul Latif and Afrah A. N. Abdou© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2008/131294.htmlA concept of g-monotone mapping is introduced, and some fixed and common fixed point theorems for g-non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. (2008).Ljubomir Ćirić, Nenad Cakić, Miloje Rajović, and Jeong Sheok Ume© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/fpta/2008/363257.htmlLet S be a left amenable semigroup, let 𝒮={T(s):s∈S} be a representation of S as Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition, let {μn} be a strongly left regular sequence of means defined on an 𝒮-stable subspace of l∞(S), let f be a contraction on C, and let {αn}, {βn}, and {γn} be sequences in (0, 1) such that αn+βn+γn=1, for all n. Let xn+1=αnf(xn)+βnxn+γnT(μn)xn, for all n≥1. Then, under suitable hypotheses on the constants, we show that {xn} converges strongly to some z in F(𝒮), the set of common fixed points of 𝒮, which is the unique solution of the variational inequality 〈(f−I)z,J(y−z)〉≤0, for all y∈F(𝒮).Shahram Saeidi© 2009, Hindawi Publishing Corporation. All rights reserved.