[PDF] Top 20 Affine algorithms for the split variational inequality and equilibrium problems

... 5. Yang, Q: The relaxed CQ algorithm for solving the split feasibility problem. Inverse Probl. 20, 1261-1266 (2004) 6. Qu, B, Xiu, N: A note on the CQ algorithm for the split feasibility problem. Inverse ... See full document

... this variational inequality admits a unique solution e R , (since F r is strictly monotone), which is the norma ed Rosen ui- librium corresponding to the given ...the variational in- equality ... See full document

... It is known that the hierarchical fixed point problem () links with some monotone varia- tional inequalities and convex programming problems; see [, ]. Various methods have been proposed to solve the ... See full document

... 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 ... See full document

... The set of solutions of the equilibrium problem for the bifunction F is denoted by EP(F). Let B : C → H be a nonlinear mapping. Then Blum and Oettli [], Moudafi and Thera [] and Takahashi and Takahashi [] ... See full document

... The split feasibility problem when C or Q are fixed points of mappings or common fixed points of mappings and solutions of variational inequality problems was considered in some recent research ... See full document

... considered 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 ... See full document

... iterative algorithms for solving equi- librium problems in finite-dimensional ...the equilibrium problem and proved the strong convergence theorem for approximating the solutions of the ... See full document

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

... economics equilibrium, and so on. Moreover, it contains fixed point problems, optimiza- tion problems, complementarity problems, and systems of nonlinear equations as special cases (see [3, 12, ... See full document

... the problems (.) and (.) are nothing but hierarchical Minty variational inequality ...the split fixed point problem ...existing split-type problems, which we will discuss in ... See full document

... the split generalized equilibrium problem reduces to the gener- alized equilibrium problem considered by Cianciaruso et ...the split generalized equilibrium problem reduces to the ... See full document

... Then the set C and the mapping F satisfy the assumptions of Theorem . and (, , ) is a solution of the multi-valued variational inequality. Example . is tested in [, ]. We choose σ = ., γ = . ... See full document

... We denote by Ξ the set of minimizers of problem (.), and we assume that Ξ = ∅ . The gradient-projection algorithm (GPA) is one of the most elegant methods to solve the min- imization problem (.). The convergence of ... See full document

... generalized equilibrium problem, a variational inequality, and fixed point problems of an asymptotically strict pseudocontraction based on a hybrid ... See full document

... [26] G. Marino, V. Colao, L. Muglia, and Y. Yao, “Krasnoselski-Mann iteration for hierarchical fixed points and equilibrium problem,” Bulletin of the Australian Mathematical Society, vol. 79, no. 2, pp. 187200, ... See full document

... J  be the normalized duality mappings. Let F i , f i , G i , g i : C i  E i be nonlinear mappings, and let A : E 1  E 2 be a bounded linear operator. We introduced the following system of split general ... See full document

... mixed equilibrium problems, a variational inequality problem for an inverse strongly monotone mapping and common fixed points of a finite family of strictly pseudo contractive ... See full document

... of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) ...invex equilibrium problems includes equilib- rium problems, variational ... See full document

... Proof We first show the uniqueness of a solution of the variational inequality (.), which is indeed a consequence of the strong monotonicity of A – I. In fact, since A is a strongly positive bounded linear ... See full document