http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/645419The purpose of this paper is to present existence, uniqueness, and data dependence results for the strict fixed points of a multivalued operator of Reich type, as well as, some sufficient conditions for the well-posedness of a fixed point problem for the multivalued operator.Cristian Chifu and Gabriela Petruşel© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/274793M. Abbas and B. E. Rhoades© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/484050Let C be nonempty closed convex subset of real Hilbert space H. Consider C a nonexpansive semigroup ℑ={T(s):s≥0} with a common fixed point, a contraction f with coefficient 0<α<1, and a strongly positive linear bounded operator A with coefficient γ¯>0. Let 0<γ<γ¯/α. It is proved that the sequence {xn} generated iteratively by xn=(I−αnA)(1/tn)∫0tnT(s)ynds+αnγf(xn),yn=(I−βnA)xn+βnγf(xn) converges strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality 〈(γf−A)x∗,z−x∗〉≤0 for all z∈F(ℑ).Lihua Li, Suhong Li, and Yongfu Su© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/902985We consider an implicit iterative process with mixed errors for a finite family of pseudocontractive mappings in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others.Yan Hao© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/607926A best proximity pair for a set-valued map F:A⊸B with respect to a set-valued map G:A⊸A is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application, we derive a coincidence point theorem.A. Amini-Harandi, A. P. Farajzadeh, D. O'Regan, and R. P. Agarwal© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/648591We introduce the notion of middle point linear operators. We prove a fixed point result for middle point linear operators in L1. We then present some examples and, as an application, we derive a Markov-Kakutani type fixed point result for commuting family of α-nonexpansive and middle point linear operators in L1.Milena Chermisi and Anna Martellotti© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/230101We introduce the new concepts of e-distance, e-type mapping with respect to some e-distance and S-complete quasimetric space, and prove minimization theorems, fixed point theorems, and variational principles on an S-complete quasimetric space. We also give some examples of quasimetrics, e-distances, and e-type mapping with respect to some e-distance. Our results extend, improve, and unify many known results due to Caristi, Ekeland, Ćirić, Kada-Suzuki-Takahashi, Ume, and others.Jeong Sheok Ume© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/324575In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007), Liu (1996), Osilike (2004), Su and Li (2006), Gu (2007), Xu and Ori (2001).You Xian Tian, Shih-sen Chang, Jialin Huang, Xiongrui Wang, and J. K. Kim© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/350483Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let {Ti}i=1∞ be an infinite countable family of asymptotically nonexpansive mappings with the sequence {kin} satisfying kin≥1 for each i=1,2,…, n=1,2,…, and limn→∞kin=1 for each i=1,2,…. In this paper, we introduce a new implicit iterative scheme generated by {Ti}i=1∞ and prove that the scheme converges strongly to a common fixed point of {Ti}i=1∞, which solves some certain variational inequality.Shenghua Wang, Lanxiang Yu, and Baohua Guo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/401947A class of semilinear impulsive periodic system on Banach spaces is considered. First, we introduce the T0-periodic PC-mild solution of semilinear impulsive periodic system. By virtue of Gronwall lemma with impulse, the estimate on the PC-mild solutions is derived. The continuity and compactness of the new constructed Poincaré operator determined by impulsive evolution operator corresponding to homogenous linear impulsive periodic system are shown. This allows us to apply Horn's fixed-point theorem to prove the existence of T0-periodic PC-mild solutions when PC-mild solutions are ultimate bounded. This extends the study on periodic solutions of periodic system without impulse to periodic system with impulse on general Banach spaces. At last, an example is given for demonstration.JinRong Wang, X. Xiang, W. Wei, and Qian Chen© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/189870We prove some fixed point results for mapping satisfying sufficient conditions on complete G-metric space, also we showed that if the G-metric space (X,G) is symmetric, then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space (X,dG), where (X,dG) is the usual metric space which defined from the G-metric space (X,G).Zead Mustafa, Hamed Obiedat, and Fadi Awawdeh© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/752657We prove a global bifurcation result for an equation of the type Lx+λ(h(x)+k(x))=0, where L:E  →  F is a linear Fredholm operator of index zero between Banach spaces, and, given an open subset Ω of E, h,k:Ω×[0,+∞)  →  F are C1 and continuous, respectively. Under suitable conditions, we prove the existence of an unbounded connected set of nontrivial solutions of the above equation, that is, solutions (x,λ) with λ≠0, whose closure contains a trivial solution (x¯,0). The proof is based on a degree theory for a special class of noncompact perturbations of Fredholm maps of index zero, called α-Fredholm maps, which has been recently developed by the authors in collaboration with M. Furi.Pierluigi Benevieri and Alessandro Calamai© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/562130We give an axiom (C.C) in symmetric spaces and investigate the relationships between (C.C) and axioms (W3), (W4), and (H.E). We give some results on coinsidence and fixed-point theorems in symmetric spaces, and also, we give some examples for the results of Imdad et al. (2006).Seong-Hoon Cho, Gwang-Yeon Lee, and Jong-Sook Bae© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/302617Based on previous notions of expansive mapping, n times reasonable expansive mapping is defined. The existence of fixed point for n times reasonable expansive mapping is discussed and some new results are obtained.Chunfang Chen and Chuanxi Zhu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/768294In this paper we consider complete cone metric spaces. We generalize some definitions such as c-nonexpansive and (c,λ)-uniformly locally contractive functions f-closure, c-isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.P. Raja and S. M. Vaezpour© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/916187As a generalization to Banach contraction principle, Ćirić introduced the concept of quasi-contraction mappings. In this paper, we investigate these kinds of mappings in modular function spaces without the Δ2-condition. In particular, we prove the existence of fixed points and discuss their uniqueness.M. A. Khamsi© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/134148We introduce a new iterative scheme for finding the common element of the set of common fixed points of nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings, and the problem of finding a zero of a monotone operator. This main theorem extends a recent result of Yao et al. (2007) and many others.Rabian Wangkeeree© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/945010Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the stability of a functional equation of the spiral of Theodorus, f(x+1)=(1+i/x+1)f(x).Soon-Mo Jung and John Michael Rassias© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/407352We consider the mean square asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are also given to illustrate our results.Meng Wu, Nan-jing Huang, and Chang-Wen Zhao© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/242916We prove a convergence result and a data dependence for Ishikawa iteration when applied to contraction-like operators. An example is given, in which instead of computing the fixed point of an operator, we approximate the operator with a contractive-like one. For which it is possible to compute the fixed point, and therefore to approximate the fixed point of the initial operator.Ş. M. Şoltuz and Teodor Grosan© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/312876We introduce the notion of a generalized iterated function system (GIFS), which is a finite family of functions fk:Xm → X, where (X,d) is a metric space and m∈ℕ. In case that (X,d) is a compact metric space and the functions fk are contractions, using some fixed point theorems for contractions from Xm to X, we prove the existence of the attractor of such a GIFS and its continuous dependence in the fk's.Alexandru Mihail and Radu Miculescu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/732086Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we will adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation with involution.Soon-Mo Jung and Zoon-Hee Lee© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/824607This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.Liang-Gen Hu, Ti-Jun Xiao, and Jin Liang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/872190we prove the Hyers-Ulam-Rassias stability of C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following Cauchy-Jensen functional equation 2f((x+y)/2+z)=f(x)+f(y)+2f(z), which was introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from the stability theorem of Th. M. Rassias that appeared in (1978).Choonkil Park and Jong Su An© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/167535Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f:C  →  C a contractive mapping (or a weakly contractive mapping), and T:C  →  C nonexpansive mapping with the fixed point set F(T)  ≠  ∅. Let {xn} be generated by a new composite iterative scheme: yn=λnf(xn)+(1−λn)Txn, xn+1=(1−βn)yn+βnTyn, (n≥0). It is proved that {xn} converges strongly to a point in F(T), which is a solution of certain variational inequality provided that the sequence {λn}⊂(0,1) satisfies limn→∞λn=0 and ∑n=1∞λn=∞, {βn}⊂[0,a) for some 0<a<1 and the sequence {xn} is asymptotically regular.Jong Soo Jung© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/387504In the work of Babu and Vara Prasad (2006), the claim is made that Mann iteration converges faster than Ishikawa iteration when applied to Zamfirescu operators. We provide an example to demonstrate that this claim is false.Yuan Qing and B. E. Rhoades© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/164537In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.Man Kam Kwong© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/634921We introduce and study a new class of general nonlinear implicit variational inequalities, which includes several classes of variational inequalities and variational inclusions as special cases. By applying the resolvent operator technique and fixed point theorem, we suggest a new perturbed three-step iterative algorithm with errors for solving the class of variational inequalities. Several existence and uniqueness results of solutions for the general nonlinear implicit variational inequalities, and convergence and stability results of the sequence generated by the algorithm are obtained. The results presented in this paper extend, improve, and unify a host of results in recent literatures.Zeqing Liu, Shin Min Kang, and Jeong Sheok Ume© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/672301Let E be a real q-uniformly smooth Banach space which is also uniformly convex (e.g., Lp or lp spaces (1<p<∞)), and K a nonempty closed convex subset of E. By constructing nonexpansive mappings, we elicit the weak convergence of Mann's algorithm for a κ-strictly pseudocontractive mapping of Browder-Petryshyn type on K in condition thet the control sequence {αn} is chosen so that (i) μ≤αn<1,n≥0; (ii) ∑n=0∞(1−αn)[qκ−Cq(1−αn)q−1]=∞, where μ∈[max⁡{0,1−(qκ/Cq)1/(q−1)},1). Moreover, we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms.Ying Zhang and Yan Guo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/417089We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium problem. This study, proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point problems, variational inequality problems, and mixed equilibrium problems.Yonghong Yao, Yeong-Cheng Liou, and Jen-Chih Yao© 2008, Hindawi Publishing Corporation. All rights reserved.