We consider the functional equation f(xf(x)) = φ(f(x)) where φ : J → J is a given increasing homeomorphism of an open interval J ⊂ (0,∞) and f : (0,∞) → J is an unknown continuous function. In a series of papers by P.Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under φ and which contains in its interior no fixed point e...

A variational inequality problem (VIP) satisfying a constraint qual-iication can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity problems is generated. It is shown that, if the original problem is solvable, the sequence of computable i...

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

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...

Abstract We study nested variational inequalities, which are inequalities whose feasible set is the solution of another inequality. present a projected averaging Tikhonov algorithm requiring weakest conditions in literature to guarantee convergence solutions Specifically, we only need monotonicity upper- and lower-level inequalities. Also, provide first complexity analysis for considering optim...

In this paper, a common solution problem is investigated based on a Bregman projection. Strong convergence of the monotone projection algorithm for monotone operators and bifunctions is obtained in a reflexive Banach space.

We introduce and study a new system of nonlinear variational-like inclusions involving sG, η maximal monotone operators, strongly monotone operators, η-strongly monotone operators, relaxed monotone operators, cocoercive operators, λ, ξ -relaxed cocoercive operators, ζ, φ, g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique ...