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Halpern's Iteration for Strongly Relatively Nonexpansive Mappings in Banach Spaces

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We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex anduniformly smooth Banach spaces. Our results extend those announced by many authors.

Abstract

We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex anduniformly smooth Banach spaces. Our results extend those announced by many authors.

참고문헌 (13)

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  10. F. Kohsaka, "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space", Abstr. Appl. Anal., 2004, pp.239~249 (2004)
  11. P. L. Lions, "Approximation de points fixes de contractions", C.R. Acad. Sci. Paris Ser. A-B., 284(A), pp.1357~1359 (1977)
  12. P. E. Mainge, "The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces", Comput. Math. Appl., 59, pp.74~79 (2010)
  13. S. Matsushita, "Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces", Fixed Point Theory Appl., 2004, pp.37~47 (2004)

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