Asymptotically quasi-nonexpansive mappings with respect to the Bregman distance in the intermediate sense


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	Asymptotically quasi-nonexpansive mappings with respect to the Bregman distance in the intermediate sense


	Fixed Point Theory, Volume 18, No. 1, 2017, 391-406, March 1st, 2017 DOI: 10.24193/fpt-ro.2017.1.31 Authors: Yukino Tomizawa Abstract: The purpose of this paper is to introduce a new class of nonlinear mappings which is an extension of asymptotically quasi-nonexpansive mappings with respect to the Bregman distance in the intermediate sense. A strong convergence theorem of the shrinking projection method with the modified Mann iteration is established to find fixed points of the mappings in reflexive Banach spaces. Key Words and Phrases: Bregman distance, Bregman projection, asymptotically quasi-nonexpansive in the intermediate sense, fixed point, Legendre function, totally convex function. 2010 Mathematics Subject Classification: 26B25, 46T99, 47H09, 47H10, 47J25. Published on-line: March 1st, 2017. Abstract pdf Fulltext pdf Back to volume's table of contents