20 research outputs found
Strong Convergence Theorem for Bregman Strongly Nonexpansive Mappings and Equilibrium Problems in Reflexive Banach Spaces
By using a new hybrid method, a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of Bregman strongly nonexpansive mappings in a reflexive Banach space is proved
Compositions and Averages of Two Resolvents: Relative Geometry of Fixed Points Sets and a Partial Answer to a Question by C. Byrne
We show that the set of fixed points of the average of two resolvents can be
found from the set of fixed points for compositions of two resolvents
associated with scaled monotone operators. Recently, the proximal average has
attracted considerable attention in convex analysis. Our results imply that the
minimizers of proximal-average functions can be found from the set of fixed
points for compositions of two proximal mappings associated with scaled convex
functions. When both convex functions in the proximal average are indicator
functions of convex sets, least squares solutions can be completely recovered
from the limiting cycles given by compositions of two projection mappings. This
provides a partial answer to a question posed by C. Byrne. A novelty of our
approach is to use the notion of resolvent average and proximal average
A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space
In this paper, using a new shrinking projection method and generalized
resolvents of maximal monotone operators and generalized projections, we
consider the strong convergence for finding a common point of the fixed points
of a Bregman quasi-nonexpansive mapping, and common fixed points of a infinite
family of Bregman weak relatively nonexpansive mappings, and common zero points
of a finite family of maximal monotone mappings, and common solutions of an
equilibrium problem in a reflexive Banach space.Comment: 28 pages. arXiv admin note: substantial text overlap with
arXiv:2107.1325
Convergence Theorems of Iterative Schemes For Nonexpansive Mappings
In this paper, we give a type of iterative scheme for sequence of nonexpansive mappings and we study the strongly convergence of these schemes in real Hilbert space to common fixed point which is also a solution of a variational inequality. Also there are some consequent of this results in convex analysi