50 research outputs found
On the Strong Convergence of an Algorithm about Firmly Pseudo-Demicontractive Mappings for the Split Common Fixed-Point Problem
Based on the recent work by Censor and Segal (2009 J. Convex Anal.16), and
inspired by Moudafi (2010 Inverse Problems 26), we modify the algorithm of demicontractive operators proposed by Moudafi and study the modified algorithm for the class of firmly pseudodemicontractive operators to solve the split common fixed-point problem in a Hilbert space. We also give the strong convergence theorem under some appropriate conditions. Our work improves and/or develops the work of Moudafi, Censor and Segal, and other results
Strong Convergence of an Algorithm about Strongly Quasi-Nonexpansive Mappings for the Split Common Fixed-Point Problem in Hilbert Space
Based on the recent work by Censor and Segal (2009 J. Convex Anal.16), and inspired by Moudafi (2010 Inverse Problem 26), in this paper, we study the modified algorithm of Yu and Sheng [29] for the strongly quasi - nonexpansive operators to solve the split common fixed-point problem (SCFP) in the framework of Hilbert space. Furthermore we proved the strong convergence for the (SCFPP) by imposing some conditions. Our results extend and improved/developed some recent result announced. Keywords:Â Convex Feasibility, Split Feasibility, Split Common Fixed Point, Strongly Quasi-Nonexpansive Operator, Iterative Algorithm and Strong Convergence
Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems
The paper investigates two inertial extragradient algorithms for seeking a
common solution to a variational inequality problem involving a monotone and
Lipschitz continuous mapping and a fixed point problem with a demicontractive
mapping in real Hilbert spaces. Our algorithms only need to calculate the
projection on the feasible set once in each iteration. Moreover, they can work
well without the prior information of the Lipschitz constant of the cost
operator and do not contain any line search process. The strong convergence of
the algorithms is established under suitable conditions. Some experiments are
presented to illustrate the numerical efficiency of the suggested algorithms
and compare them with some existing ones.Comment: 25 pages, 12 figure
Strict pseudocontractions and demicontractions, their properties and applications
We give properties of strict pseudocontractions and demicontractions defined
on a Hilbert space, which constitute wide classes of operators that arise in
iterative methods for solving fixed point problems. In particular, we give
necessary and sufficient conditions under which a convex combination and
composition of strict pseudocontractions as well as demicontractions that share
a common fixed point is again a strict pseudocontraction or a demicontraction,
respectively. Moreover, we introduce a generalized relaxation of composition of
demicontraction and give its properties. We apply these properties to prove the
weak convergence of a class of algorithms that is wider than the
Douglas-Rachford algorithm and projected Landweber algorithms. We have also
presented two numerical examples, where we compare the behavior of the
presented methods with the Douglas-Rachford method.Comment: 27 pages, 3 figure
Iterative algorithms for approximating solutions of variational inequality problems and monotone inclusion problems.
Master of Science in Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Durban, 2017.In this work, we introduce and study an iterative algorithm independent of the operator
norm for approximating a common solution of split equality variational inequality prob-
lem and split equality xed point problem. Using our algorithm, we state and prove a
strong convergence theorem for approximating an element in the intersection of the set
of solutions of a split equality variational inequality problem and the set of solutions of
a split equality xed point problem for demicontractive mappings in real Hilbert spaces.
We then considered nite families of split equality variational inequality problems and
proposed an iterative algorithm for approximating a common solution of this problem and
the multiple-sets split equality xed point problem for countable families of multivalued
type-one demicontractive-type mappings in real Hilbert spaces. A strong convergence re-
sult of the sequence generated by our proposed algorithm to a solution of this problem was
also established. We further extend our study from the frame work of real Hilbert spaces
to more general p-uniformly convex Banach spaces which are also uniformly smooth. In
this space, we introduce an iterative algorithm and prove a strong convergence theorem for
approximating a common solution of split equality monotone inclusion problem and split
equality xed point problem for right Bregman strongly nonexpansive mappings. Finally,
we presented numerical examples of our theorems and applied our results to study the
convex minimization problems and equilibrium problems