Opial-Type Theorems and the Common Fixed Point Problem

Andrzej Cegielski and Yair Censor
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Andrzej Cegielski: University of Zielona Góra

Chapter Chapter 9 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 155-183 from Springer

Abstract: Abstract The well-known Opial theorem says that an orbit of a nonexpansive and asymptotically regular operator T having a fixed point and defined on a Hilbert space converges weakly to a fixed point of T. In this paper we consider recurrences generated by a sequence of quasi-nonexpansive operators having a common fixed point or by a sequence of extrapolations of an operator satisfying Opial’s demiclosedness principle and having a fixed point. We give sufficient conditions for the weak convergence of sequences defined by these recurrences to a fixed point of an operator which is closely related to the sequence of operators. These results generalize in a natural way the classical Opial theorem. We give applications of these generalizations to the common fixed point problem.

Keywords: Common fixed point; Opial theorem; Cutter operators; Dos Santos method; Quasi-nonexpansive operators (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-9569-8_9

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DOI: 10.1007/978-1-4419-9569-8_9

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