| Using Ishikawa and Mann iterative sequences to converge nonlinear function's fixed point is applied widely in physics. Some conceptions of operator are introduced in this artide. We define the Ishikawa iterative sequence with error as: for any given x0,xn+1=αnxn+βnTyn+γnun (n≥0)yn=α^nxn+β^nTxn+γ^nνn (n≥0)where {un}and{γn} are two bounded sequences in Banach space Z, {αn},{βn},{γn},{α^n},{β^n} and {γ^n} are all real sequences in [0,1] satisfying the conditions: αn+βn+γn=α^n+β^n+γ^n=1(n≥0). In particular, if β^n=γ^n=0 for all (n≥0), for any given x0, the {xn} defined by xn+1=αnxn+βnTxn+γnun (n≥0)is called Mann iterative sequence with error. In this article, we mainly dicuss special nonlinear operator's and set-valued mapping's Ishikawa and Mann iteration in any Banach space. As whole, we mainly touch on some aspects as follow:①φ-strongly pseudocontractire operator's Ishikawa and Mann iteration in a cone.②Ishikawa and Mann iteration of nonlinear equations x±λTx=f③Ishikawa and Mann iterations of set-valued mapping.
|
PDF Full Text Request