The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.
In this paper, we introduce a new algorithm for solving the split equality
common null point problem and the equality fixed point problem for an
infinite family of Bregman quasi-nonexpansive mappings in reflexive Banach
spaces. We then apply this algorithm to the equality equilibrium problem and
the split equality optimization problem. In this way, we improve and
generalize the results of Takahashi and Yao [22], Byrne et al [9], Dong et
al [11], and Sitthithakerngkiet et al [21].
<p style='text-indent:20px;'>This paper analyzed the new extragradient type algorithm with inertial extrapolation step for solving self adaptive split null point problem and pseudomonotone variational inequality in real Hilbert space. Furthermore, in this study, a strong convergence result is obtained without assuming Lipschitz continuity of the associated mapping and the operator norm is self adaptive. Additionally, the proposed algorithm only uses one projections onto the feasible set in each iteration. More so, the strong convergence results are obtained under some relaxed conditions on the initial factor and the iterative parameters. Numerical results are presented to illustrate the performance of the proposed algorithm.The results obtained in this study improved and extended related studies in the literature.</p>
AbstractThis paper provides iterative construction of a common solution associated with the classes of equilibrium problems (EP) and split convex feasibility problems. In particular, we are interested in the EP defined with respect to the pseudomonotone bifunction, the fixed point problem (FPP) for a finite family of "Equation missing"-demicontractive operators, and the split null point problem. From the numerical standpoint, combining various classical iterative algorithms to study two or more abstract problems is a fascinating field of research. We, therefore, propose an iterative algorithm that combines the parallel hybrid extragradient algorithm with the inertial extrapolation technique. The analysis of the proposed algorithm comprises theoretical results concerning strong convergence under a suitable set of constraints and numerical results.
In this paper we introduce a new algorithm based on the viscosity iteration
method for solving the split common fixed point problem of two infinite
families of k-demicontractive mappings. We shall also study the split common
null point problem, and the split equilibrium problem for this class of
mappings. As an application, we obtain strong convergence theorems for the
split monotone variational inclusion problem and the split variational
inequality problem. Our results improve and extend the recent results of Cui
and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and
Vahidi [17], and many others.
A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm
