The main goal of this paper is to discuss the recent advancements matrix means from positive matrices accretive in a more general setting. In particular, we present form governing well established definition geometric mean, then define arbitrary and functional calculus for matrices. Applications new discussion involve generalizations known inequalities setting that This includes arithmetic-harm...

This paper deals with Lavrentiev regularization for solving linear ill-posed problems, mostly with respect to accretive operators on Hilbert spaces. We present converse and saturation results which are an important part in regularization theory. As a byproduct we obtain a new result on the quasi-optimality of a posteriori parameter choices. Results in this paper are formulated in Banach spaces ...

We consider a two-player, zero-sum diierential game governed by an abstract nonlinear diierential equation of accretive type in an innnite dimensional space. We prove that the value function of the game is the unique viscosity solution of the corresponding Hamilton-Jacobi-Isaacs equation in the sense of Crandall-Lions 12]. We also discuss some properties of this notion of solution.