[PDF] Top 20 General Iterative Method for Convex Feasibility Problem via the Hierarchical Generalized Variational Inequality Problems

... the variational inequality (3). It is well known that the variational inequality theory has emerged as an important tool in studying a wide class of obstacle, unilateral, and equilibrium ... See full document

... the hierarchical fixed point problem ...and convex programming problems; see ...the hierarchical fixed point problem; see ...convergence iterative algorithm to solve prob- ... See full document

... very general in the sense that it includes, as special cases, optimization problems, variational inequalities, minimax problems, and Nash equilibrium problems; see, for example, ...a ... See full document

... This iterative method is based on the extragradient ...equilibrium problem, the constrained convex minimization problem, and the split feasibility ... See full document

... closed convex subset of a real Hilbert space H with inner product 〈 ·, · 〉 , and T, g: H ® H be ...value problems arising in pure and applied can be studied in the unified framework of general ... See full document

... an iterative process for finding a common element of the set of common fixed points of infinitely many nonexpansive mappings, the set of solutions of ...the variational inequality problem for ... See full document

... complementarity problems and variational inequalities,” in Handbook of Generalized Convexity and Generalized Monotonicity, ...for generalized set-valued ... See full document

... Sol(GEP(.)). Problem (.) includes fixed point problems, optimization problems, variational inequality problems, Nash equilib- rium problems, ...many iterative ... See full document

... Find x ∗ ∈ F (T) such that h(I − S)x ∗ , x − x ∗ i ≥ 0, ∀x ∈ F (T ), (1.2) where T and S are nonexpansive mappings such that F (T ) is nonempty. It is easy to see that x ∗ is a solution of the variational ... See full document

... Lemma 2.3 (Browder and Petryshyn [12]). Let H be a Hilbert space, C be a closed convex subset of H, and T : C ® H be a k-strictly pseudo-contractive mapping. Define a mapping J : C ® H by Jx = a x +(1-a)Tx for all ... See full document

... an iterative method for finding the approxi- mate element of the common set of solutions of ...this method. The presented method improves and generalizes many known re- sults for solving ... See full document

... of generalized proximity operators and propose an iterative method of approximating so- lutions for the following generalized variational inequality problem: find x ¯ ∈ dom ... See full document

... descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive ...in Feasibility and Optimization and Their Applications (Haifa, ... See full document

... of problems arising in various branches of pure and applied ...years, variational inequalities have been generalized and extended novel and new tech- niques in several ...various iterative ... See full document

... the problem (1.3) coupled with the fixed point problem, many authors have introduced some iterative schemes for finding a common element of the set of the solutions of the problem ... See full document

... the hierarchical fixed point problem ...monotone variational inequalities and convex programming problems; see ...the hierarchical fixed point problem; see Yao and Liou in ... See full document

... optimization problems. The advantage of a regularization method is its possible strong convergence to the minimum-norm solution of the optimization ... See full document

... of variational inequalities defined over the intersection of the set of solutions of an equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings, and the solution set of ... See full document

... solution problems have been extensively studied by many schol- ars; see, for example, [–] and the references ...solution problem of a monotone variational inequality, a system of ... See full document

... to variational inclusion, equilibrium and fixed point problems have been recently extensively investigated based on iterative methods; see [–] and the ref- erences ...complex problems, which ... See full document