Concepedia

Strongly relatively nonexpansive sequences generated by firmly nonexpansive-like mappings

Fixed Point Theory and Applications · 2014 · 29 citations · 15 references

Open access

Concepts

Banach SpaceNonexpansive SequencesSet-theoretic TopologyPartially Ordered SetFunctional AnalysisFirmly Nonexpansive-like MappingsNonexpansive Sequence

Abstract

We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this result, we study the problem of approximating common fixed points of such a sequence of mappings. MSC:47H09, 47H05, 65J15.

References

15

Monotone Operators and the Proximal Point Algorithm

R. T. Rockafellar · SIAM Journal on Control and Optimization · 1976 · 3.6K citations

Mathematical Programming, Numerical Analysis, Engineering +13

Nonlinear Functional Analysis

Wataru Takahashi · Tokyo Tech Research Repository (Tokyo Institute of Technology) · 2000 · 956 citations

Function Theory, Nonlinear Equation, Functional Analysis +2

On the maximality of sums of nonlinear monotone operators

R. T. Rockafellar · Transactions of the American Mathematical Society · 1970 · 898 citations

R. T. Rockafellar, Linear Operator, Monotone Operators.results +5

On the maximal monotonicity of subdifferential mappings

R. T. Rockafellar · Pacific Journal of Mathematics · 1970 · 726 citations · Full text

Variational Analysis, Subdifferential Mappings, Variational Inequality +2

Strong Convergence of a Proximal-Type Algorithm in a Banach Space

Shoji Kamimura, Wataru Takahashi · SIAM Journal on Optimization · 2002 · 651 citations

Mathematical Programming, Engineering, Variational Analysis +16