Nonlinear relaxed cocoercive variational inclusions involving (A, η)-accretive mappings in banach spaces

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

“…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*.…”

“…In 2006, Lan et al [7] introduced a new concept of (A, h)-accretive mappings, which provides a unifying framework for maximal monotone operators, m-accretive operators, h-subdifferential operators, maximal h-monotone operators, H-monotone operators, generalized m-accretive mappings, H-accretive operators, (H, h)-monotone operators, and A-monotone mappings. Recently, by using the concept of (A, h)-accretive mappings and the resolvent operator technique associated with (A, h)-accretive mappings, Jin [5] introduced and studied a new class of nonlinear variational inclusion systems with (A, h)-accretive mappings in q-uniformly smooth Banach spaces and developed some new iterative algorithms to approximate the solutions of the mentioned nonlinear variational inclusion systems.…”

GENERALIZED FUZZY RANDOM SET-VALUED MIXED VARIATIONAL INCLUSIONS INVOLVING RANDOM NONLINEAR (Aω,ηω )-ACCRETIVE MAPPINGS IN BANACH SPACES

“…In a paper [14], Fang and Huang et al further introduced a new class of generalized monotone operators, (H, η)-monotone operators, which provide a unifying framework for classes of maximal monotone operators, maximal η-monotone operators, and H-monotone operators. Recently, Lan et al [27] introduced a new concept of (A, η)-accretive mappings, which generalizes the existing monotone or accretive operators, and studied some properties of (A, η)-accretive mappings and defined resolvent operators associated with (A, η)-accretive mappings. They also studied a class of variational inclusions using the resolvent operator associated with (A, η)-accretive mappings.…”

“…For these reasons, various variational inclusions have been intensively studied in recent years. For details, we refer the reader to [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] and the references therein.…”