Rocky Mountain Journal of Mathematics

A weak convergence theorem for mean nonexpansive mappings

Torrey M. Gallagher

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Abstract

In this paper, we first prove that the iterates of a mean nonexpansive map defined on a weakly compact, convex set converge weakly to a fixed point in the presence of Opial's property and asymptotic regularity at a point. Next, we prove the analogous result for closed, convex (not necessarily bounded) subsets of uniformly convex Opial spaces. These results generalize the classical theorems for nonexpansive maps of Browder and Petryshyn in Hilbert space and Opial in reflexive spaces, satisfying Opial's condition.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 7 (2017), 2167-2178.

Dates
First available in Project Euclid: 24 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1514084423

Digital Object Identifier
doi:10.1216/RMJ-2017-47-7-2167

Mathematical Reviews number (MathSciNet)
MR3743709

Zentralblatt MATH identifier
06828635

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
Mean nonexpansive Opial's property asymptotically regular weak convergence

Citation

Gallagher, Torrey M. A weak convergence theorem for mean nonexpansive mappings. Rocky Mountain J. Math. 47 (2017), no. 7, 2167--2178. doi:10.1216/RMJ-2017-47-7-2167. https://projecteuclid.org/euclid.rmjm/1514084423


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References

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