scholarly journals Semilocal analysis of equations with smooth operators

1981 ◽  
Vol 4 (3) ◽  
pp. 553-563 ◽  
Author(s):  
George J. Miel
Keyword(s):  
Recent Work ◽  
Error Bounds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Kantorovich Theorem ◽  
Refined Version

Recent work on semilocal analysis of nonlinear operator equations is informally reviewed. A refined version of the Kantorovich theorem for Newton's method, with new error bounds, is presented. Related topics are briefly surveyed.

scholarly journals Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

1986 ◽  
Vol 9 (3) ◽  
pp. 583-587
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

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