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On the steepest descent approximation method for the zeros of generalized accretive operators. (English) Zbl 1220.47089
Summary: We present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space. Our study is based on an important result of S. Reich [Nonlinear Anal., Theory, Methods Appl. 2, 85–92 (1978; Zbl 0375.47032)] and the given results extend and improve some earlier results which involve the steepest descent approximation method.

##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47J05 Equations involving nonlinear operators (general) 47H06 Nonlinear accretive operators, dissipative operators, etc.
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##### References:
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