Abstract
Abstract We study the convergence of a more general Picard iterative sequence for nonexpansive and Lipschitz strongly accretive mappings in an arbitrary real Banach space. Our results improve the results of Ćirić et al. (Nonlinear Anal. 70(12):4332-4337, 2009). MSC:47H06, 47H09, 47J05, 47J25.
Highlights
1 Introduction and preliminaries Let E be a real Banach space with dual E∗, and J will denote the normalized duality map from E to E∗ defined by
The mapping T is called strongly pseudocontractive if there exists t > such that x – y ≤ ( + r)(x – y) – rt(Tx – Ty) for all x, y ∈ D(T) and r >
We study the convergence of a more general Picard iterative sequence for nonexpansive and Lipschitz strongly accretive mappings in an arbitrary real Banach space
Summary
The mapping T is called strongly pseudocontractive if there exists t > such that x – y ≤ ( + r)(x – y) – rt(Tx – Ty) for all x, y ∈ D(T) and r > . As a consequence of Kato [ ], this accretive condition can be expressed in terms of the duality mapping as follows: For each x, y ∈ D(A), there exists j(x – y) ∈ J(x – y) such that
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