Visco-resolvent algorithms for monotone operators and nonexpansive mappings

Volume 7, Issue 5, pp 325--344 http://dx.doi.org/10.22436/jnsa.007.05.04

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Authors

Peize Li - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China. Shin Min Kang - Department of Mathematics and the RINS, Gyeongsang National University, Jinju 660-701, Korea. Li-Jun Zhu - School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan 750021, China.

Abstract

Two new type of visco-resolvent algorithms for finding a zero of the sum of two monotone operators and a fixed point of a nonexpansive mapping in a Hilbert space are investigated. The algorithms consist of the zeros and the fixed points of the considered problems in which one operator is replaced with its resolvent and a viscosity term is added. Strong convergence of the algorithms are shown. As special cases, we can approach to the minimum norm common element of the zero of the sum of two monotone operators and the fixed point of a nonexpansive mapping without using the metric projection. Some applications are included.

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Keywords

• Monotone operator
• nonexpansive mapping
• zero point
• fixed point
• resolvent.

MSC

•  49J40
•  47J20
•  47H09
•  65J15

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