Variational convergence of a new proximal algorithm for nonlinear general -monotone operator equation systems in Banach spaces

Graphical approximation of common solutions to generalized nonlinear relaxed cocoercive operator equation systems with (A, η)-accretive mappings

“…Several classes of relaxed cocoercive variational inequalities and variational inclusions have been studied in [2,5,[7][8][9][10]12,[16][17][18].…”

“…This class of nonlinear Yosida approximations have been applied to approximation solvability of nonlinear inhomogeneous evolution inclusions of the form f (t) ∈ u (t) + Mu(t) − ωu(t), u(0) = u 0 for almost all t [0, T], where T (0,1) is fixed, ω R (see [1]). For more general details on approximation solvability of general nonlinear inclusion problems, we refer the reader to [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein.…”

“…Among these methods, the resolvent operator technique is very important. For some literature, we recommend to the following example, and the reader [2][3][4][5][6][7][8][9][10][11][12][13][14][15]17,18] and the references therein. where ∂V(x*) denotes the subdifferential of V at x* and N K (x * ) the normal cone of K at x*.…”

“…Furthermore, by using the resolvent operator technique, Petrot [14] studied the common solutions for a generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces, and Agarwal and Verma [2] introduced and studied a new system of nonlinear (set-valued) variational inclusions involving (A, h )-maximal relaxed monotone and relative (A, h)-maximal monotone mappings in Hilbert spaces and proved its approximation solvability based on the variational graphical convergence of operator sequences. For more literature, we recommend to the reader [9,20] and the references therein.…”