Regularization methods for a class of variational inequalities in banach spaces

Regularization Methods and Iterative Methods for Variational Inequality with Accretive Operator

“…We have Remark 1 The sequences α n = (1 + n) −p , 0 < p < 1/2 and β n = γ 0 α n with 0 < γ 0 < 1/(c 1/(q−1) q (2 + α 0 ) q/(q−1) ) satisfy all the necessary conditions in Theorem 3.3 for the case q = 2. For the case 1 < q < 2, α n = (1 + n) −p with p < (q − 1)/(2q) and β n = γ 0 α 1/(q−1) n also satisfy all the conditions (see [5]). …”

“…Liskovets [17,18] introduced the method of regularization on the base of solving the perturbative variational inequality with monotone operator. Buong and Phuong [5] studied the VI * (A, C) by regularizing the mapping F n + α n A where F n = (I − V n ) and V n is defined by…”

Steepest‐descent proximal point algorithms for a class of variational inequalities in Banach spaces

“…proposed a strongly convergent implicit iteration method, when C is the set of common fixed points for an infinite family of asymptotically nonexpansive mappings on E , that admits a weakly sequential continuous duality mapping. Without this weak continuity, recently, in and , the author and Phuong suggested several implicit iterative and regularization methods when C is the set of common fixed points for an infinite family of nonexpansive mappings on E . Explicit iterative methods for the class of variational inequalities were considered in and .…”