A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

For finite difference matrices that are monotone, a discretization error estimate in maximum norm follows from the truncation errors of the discretization. It enables also discretization error estimates for derivatives of the solution. These results are extended to convergent operator splittings of the difference matrix where the major, preconditioning part is monotone but the whole operator is...

In this paper, we study an elliptic obstacle problem with a generalized fractional Laplacian and multivalued operator which is described by gradient. Under quite general assumptions on the data, employ surjectivity theorem for mappings generated sum of maximal monotone bounded pseudomonotone mapping to prove that set weak solutions nonempty, closed. Then, introduce sequence penalized problems w...

We consider bifunctions F : C ×C → R where C is an arbitrary subset of a Banach space. We show that under weak assumptions, monotone bifunctions are locally bounded in the interior of their domain. As an immediate corollary, we obtain the corresponding property for monotone operators. Also, we show that in contrast to maximal monotone operators, monotone bifunctions (maximal or not maximal) can...

We introduce function spaces for the treatment of non-linear parabolic partial differential equations with variable log–Hölder continuous exponents that only incorporate information symmetric part a gradient. As an analogue Korn's inequality these functions is not available, construction appropriate smoothing method proves to be difficult. Using point-wise Poincaré near boundary bounded Lipschi...

An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is splitted into the sum of a single-valued operator F , possessing a kind of pseudo Dunn property, and a maximal monotone operator Q. The current auxiliary problem is constructed by fixing F at the...