A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...

We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Kreintype resolvent formulas for Schrödinger operators on bounded Lipschitz domains in R, n > 2. We also discuss the case of bounded C-domains, (1/2) < r < 1.

Recent perturbation results for exponentially dichotomous operators are generalized, in part by replacing compactness conditions on the perturbation by resolvent compactness. Both additive and multiplicative perturbations are considered. Mathematics Subject Classification (2000). Primary 47D06; Secondary 47A55.

In a recent paper [14], the fixed point and resolvent techniques have been used to give an iterative algorithm for solving generalized mixed equilibrium problem (GMEP). In this paper, an extended iterative algorithm, called generalized mean proximal algorithm (GMPA) is presented and its convergence to the solution of GMEP with θ-pseudomonotne and δLipschitz continuous mappings in Hilbert spaces...

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In particular, special attention is paid to the periodic generalized Jacobi operators. Finally, the spectral properties of generalized Jacobi operators are applied to pr...

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, η)-monotonicity generalizes A-monotoni...

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

In this paper, we study the logarithmic stability for the hyperbolic equations by arbitrary boundary observation. Based on Carleman estimate, we first prove an estimate of the resolvent operator of such equation. Then we prove the logarithmic stability estimate for the hyperbolic equations without any assumption on an observation sub-boundary.

with special accent on the case in which a(t) is unbounded. We use contraction mappings to establish close relations between a(t) and ∫ t 0 R(t, s)a(s)ds. This work gives us a fundamental understanding of the nature of R(t, s). It establishes numerous elementary boundedness results including some from a new point of view. And it tells us that one of our long-held basic assumptions is very incom...

In the paper stochastic Volterra equations of nonscalar type are studied using resolvent approach. The aim of this note is to provide some results on stochastic convolution and integral mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials.