Let A be a positive self-adjoint operator and let B be an m-accretive operator which is A-small with a relative bound less than one. Let H = A + B, then H is well-deened on dom(H) = dom(A) and m-accretive. If B is a strictly m-accretive operator obeying dom((H)) dom(A) \ dom((B)) 6 = f0g for some 2 (0; 1]; (1) then for the Trotter product formula we prove that ?

In this paper, we first introduce a new Halpern-type iterative scheme to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings in a uniformly convex Banach space. We then apply our method to approximate zeros of an infinite family of accretive operators and derive a st...

In this paper we deal with methods for finding zeroes of set-valued operators A in Banach spaces. The first aim of this note is to show that the Yosida regularization may be combined with the schemes in [1, 2] keeping the strong convergence properties of the iterates and extending to set-valued operators two recent results by Chidume [1] and Chidume and Zegeye [2]. The second goal of the note i...

We consider the class of linear operator equations with operators admitting self-adjoint positive definite and m-accretive splitting (SAS). This splitting leads to an ADI-like iterative method which is equivalent to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of a minimal residual algorithm with Symmetric Gauss-Seidel and polynomi...