[PDF] Top 20 Synchronal and cyclic algorithms for fixed point problems and variational inequality problems in Banach spaces

... The variational inequality problem was initially introduced and studied by Stampacchia [] in ...years, variational inequality problems have been extended to study a large variety of ... See full document

... thematical problems as particular cases, for example, mathematical programming problems, complementary problems, variational inequality problems, Nash equi- librium ... See full document

... algorithm converges weakly to a fixed point of T . Reich 33 showed that the conclusion also holds good in the setting of uniformly convex Banach spaces with a Fr´ehet differentiable norm. It is ... See full document

... classical variational inequality (1.2) and fixed point problem of nonexpansive mappings have received rapid development, see, for example, [1-17] and the references ...for variational ... See full document

... In 1997, Fl˚am and Antipin 9 introduced an iterative scheme of finding the best approximation to initial data when EPΦ is nonempty and proved a strong convergence theorem. In 2003, Iusem and Sosa 10 presented some ... See full document

... Corollary 3.3. Let C be a nonempty closed and convex subset of a uniformly smooth and strictly convex Banach space E which has the Kadec-Klee property. Let S : C → C be a closed quasi-φ- nonexpansive mapping, f : ... See full document

... fixed point problem of an infinite family of nonexpansive mappings in a uniformly convex and -uniformly smooth Banach ...following inequality in a -uniformly smooth Banach space ... See full document

... (Fixed Point Theory and Applications 2012:46, ...for variational inequality problems in q-uniformly smooth Banach spaces under very mild ... See full document

... 28 Ya. I. Alber, “Metric and generalized projection operators in Banach spaces: properties and applications,” in Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. ... See full document

... design synchronal algorithm and cyclic algorithm based on the general iterative algorithm proposed by Tian in 2010 for finding the common fixed point x * of finite family of strict ... See full document

... of variational inequalities has been used as a tool to study the Nash equilibrium problem for a finite or infinite number of players; see, for ex- ample, [–] and the references ...using variational ... See full document

... fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert ... See full document

... split variational inequality problem [], split common null point problem and Moudafi’s split feasibility problem, and derived the algorithm for these prob- lems from the main algorithm for ...these ... See full document

... Ceng et al. 29 studied the problem 1.3 by transforming it into a fixed-point problem. Precisely and for easy reference, we state their results in the following lemma and theorem. Lemma CWY see 29. For given ... See full document

... split variational inequality problem defined over the solution set of monotone variational inclusion problem, the split variational inequality problem defined over the solution set of ... See full document

... Yang, L, Zhao, F, Kim, JK: Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-φ -nonexpansive mappings in[r] ... See full document

... inverse problems []. In addition, various problems reduced to find the common element of the fixed point set of a family of nonlin- ear mappings such as image restoration (see for example ...fixed ... See full document

... This alternative formula enables us to suggest and analyze a two-step explicit projection method for solving system (.), and this is the main motivation of our next result. Theorem . Let C be a nonempty closed convex ... See full document

... inclusion problems, which include many important problems in nonlinear func- tional analysis and optimization such as the Nash equilibrium problem, complementarity prob- lems, vector optimization ... See full document

... A1–A4: A1 fx, x 0, ∀x ∈ C; A2 f is monotone, that is, fx, y fy, x ≤ 0, ∀x, y ∈ C; A3 limsup t↓0 fx tz − x, y ≤ fx, y, ∀x, y, z ∈ C; A4 the function y → fx, y is convex and lower semicontinuous. The purpose of this paper ... See full document