The Generalized Topological Degree For M-Accretive Operators And Its Applications

The concept of accretive mapping and pseudocontractive mapping was introduced in 1960(?) with the studying of nonlinear evolution equations. As we know, many physically significant problems and engineer problems can be modelled in terms of the form.The purpose of this paper is to construct a new generalized degree function for m-accretive operator by means of degree theory of Strictly Set-Contraction Field. We will prove this generalized degree function has the crucial properties of the general topological degree. Our work develop and extend the work of Li and Feng. We will prove some solvability theorems for m-accretive operators equation by applying our degree theory, these theorems improve and generalized the relevant results of and we can get some new results. We discuss the strong convergence to a solution of equations involving m- accretive operators. We point out that there is a mistake in . So we give a new and short proof to it.