--monotone operators in Banach spaces with an application to variational inclusions

Existence of solution and iterative approximation of a system of generalized variational-like inclusion problems in semi-inner product spaces

“…Here the constant of smoothness is p − 1. [19], Sahu et al [23]) Let X be a real 2-uniformly smooth Banach space, η : X × X → X and T : X → X be single-valued mappings. Then T is said to be…”

“…Definition 2.9. (Luo and Huang [19], Sahu et al [23]) Let X be a real 2-uniformly smooth Banach space. The mapping M : X → 2 X is said to be…”

“…Let H : X → X, ϕ : X → X, η : X × X → X be single-valued mappings and M : X → 2 X be a multi-valued mapping. The mapping M is said to be (H [19]) Let X be a real 2-uniformly smooth Banach space. Let H : X → X, ϕ : X → X, η : X × X → X be single-valued mappings and M : X → 2 X be a multi-valued mapping.…”

“…It is remarked that they discussed the existence and convergence analysis by relaxing the condition of monotonicity on the set-valued map considered. Very recently Luo and Huang [19], introduced and studied a class of (H, φ)-η-monotone operators in Banach spaces which provides a unifying framework for classes of maximal monotone operators, maximal η-monotone operators, m-η-accretive operators, H-monotone operators and (H, η)-monotone operators. Using proximal-point operator technique, they studied the convergence analysis of the iterative algorithms for some classes of variational inclusions.…”

“…Using proximal-point operator technique, they studied the convergence analysis of the iterative algorithms for some classes of variational inclusions. For further study of these types of operators and their applications in variational inequalities and variational inclusions, see for example [3,[6][7][8][9][14][15][16]18,19,21,[25][26][27][30][31][32][33][34]. Motivated and inspired by the research work mentioned above, in this paper, we define the generalized resolvent operator associated with (H, ϕ)-η-monotone operator in semi-inner product spaces.…”