期刊刊名：南台學報 　 卷期：38卷1期

篇名出版日期：2013年3月1日

作者：鄭志中,黃永裕,洪宗乾,Jyh-Chung Jeng, Young-Ye Huang, Chung-Chien Hong

語言：English

關鍵字：Fixed Point, Bregman Distance, Gâteaux Differentiable,定點理論,布雷格曼距離,加托可微

被點閱次數：6次

閱讀時間：434sec

摘要：
In this paper we define the class of firmly nonexpansive-type mappings relative to a Gâteaux differentiable function ƒ in a Banach space, and study the fixed point and convergence problem for this type of nonlinear mapping. We properly extend the Kohsaka-Takahashi fixed point theorem for firmly nonexpansive-type mappings to this much wider class of nonlinear mappings. As an application of our new fixed point theorem, the relation between the zero points of a monotone mapping and the fixed points of its associated resolvent relative to a Bregman function is studied. Using the Bregman distance associated with a well-chosen Bregman function instead of the norm in the scheme of a proximal-type algorithm, we extend the Solodov-Svaiter strong convergence theorem in Hilbert spaces to Banach spaces.

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