A new iterative algorithm for common solutions of a finite family of accretive operators |
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Authors: | Lianggen Hu Liwei Liu |
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Institution: | 1. Department of Mathematics, Ningbo University, Ningbo, 315211, PR China;2. Department of Mathematics, Nanchang University, Nanchang, 330031, PR China |
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Abstract: | The purpose in this paper is to prove a theorem of strong convergence to a common solution for a finite family of accretive operators in a strictly convex Banach space by means of a new iterative algorithm, which is a generalization and extension of the results of Kim and Xu T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51–60], and Zegeye and Shahzad H. Zegeye, N. Shahzad, Strong convergence theorems for a common zero of a finite family of m-accretive mappings, Nonlinear Anal. 66 (2007) 1161–1169]. Further using the result, the theorem of strong convergence to a common fixed point is discussed for a finite family of pseudocontractive mappings under certain conditions. |
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Keywords: | 47H10 47H17 47J25 |
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