Self-adaptive algorithms for the split problem of the demicontractive operators

Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions

“…(iii) Letting ϕ = 0 and A = 0, GMEP (7) reduces to find x † ∈ C verifying (EP) : Θ(x † , y) ≥ 0, ∀y ∈ C, which was discussed in [18,19]. GMEP (7) has been discussed extensively in the literature; see e.g., [6,7,[20][21][22][23][24][25][26][27][28][29][30][31][32]. Now, we consider the minimization problem (CMP):…”

Approximating fixed points of $$\left( \lambda ,\rho \right) $$ λ , ρ -firmly nonexpansive mappings in modular function spaces

“…Nowadays, a vigorous research activity is developed in the area of numerical reckoning fixed points for suitable classes of nonlinear operators, see, for example, [9,10], and applications to image recovery and variational inequalities, see for example, [11][12][13][14]. Existence of fixed points in modular function spaces has been studied by many researchers, for example, see Khamsi and Kozlowski [3] and the references therein.…”

Split Systems of Nonconvex Variational Inequalities and Fixed Point Problems on Uniformly Prox-Regular Sets

“…By applying Lemma 1 to relation (27), we achieve lim n→∞ x n = x * and lim n→∞ y n = y * . Thus, we conclude that the sequence {(x n , y n )} computed by (12) converges strongly to an element of Ξ Fix(S).…”

“…There is a substantial number of methods, including the linear approximation method [19,20], the auxiliary principle [21,22], the projection technique [9,11], and the descent framework [23]. For applications, numerical techniques and other aspects of variational inequalities and split problems, please see [19,20,[24][25][26][27][28].…”