A new system of variational inclusions with (H, η)-monotone operators in hilbert spaces

On multivalued nonlinear variational inclusion problems with (A,η)-accretive mappings in Banach spaces

“…Very recently, Fang et al [7], studied the (H,η)-monotone operators in Hilbert spaces, which are a special case of (H,η)-accretive operator [2]. Some works are motivated by this work and some related works.…”

A system of generalized variational inclusion problems involving (A, η): Monotone mappings

“…Recently, as an extension of H-monotone operator, Fang and Huang introduced and studied a new class of monotone operators so-called (H, η)-monotone operators and then they studied a new system of variational inclusions involving (H, η)-monotone operators in Hilbert spaces. Further, in [7] by the resolvent operator method associated with (H, η)-monotone operators due to Fang and Huang, the existence and uniqueness of solutions for a new system of variational inclusions is proved and also a new algorithm for approximating the solution of this system of variational inclusions is constructed and the convergence of iterative sequence generated by this algorithm is discussed. Verma announced the notion of the Amonotone mapping and its applications to the solvability of nonlinear variational inclusions and systems of nonlinear variational inclusions [13,14,16] and [17].…”

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

“…They also established the Lipschitz continuity of the resolvent operator and studied a class of variational inclusions in Hilbert spaces using the resolvent operator associated with H-monotone operators. 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.…”