Current Issue : January - March Volume : 2011 Issue Number : 1 Articles : 5 Articles
We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept ofW-mappings for a finite family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces....
Using the idea of Tikhonov�s regularization, we present properties of the approximating curve for the split feasibility problem SFP and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, Byrne�s CQ algorithm Byrne, 2002 has only weak convergence. We introduce a modification of Byrne�s CQ algorithm in such a way that strong convergence is guaranteed and the limit is also the minimum norm solution of SFP....
The batch split-complex backpropagation BSCBP algorithm for training complex-valued neural networks is considered. For constant learning rate, it is proved that the error function of BSCBP algorithm is monotone during the training iteration process, and the gradient of the error function tends to zero. By adding a moderate condition, the weights sequence itself is also proved to be convergent. A numerical example is given to support the theoretical analysis....
Acommon method in solving ill-posed problems is to substitute the original problem by a family of well-posed i.e., with a unique solution regularized problems.We will use this idea to define and study a two-step algorithm to solve hierarchical fixed point problems under different conditions on involved parameters....
The purpose of this paper is to present a regularization variant of the inertial proximal point algorithm for finding a common element of the set of solutions for a variational inequality problem involving a hemicontinuous monotone mapping A and for a finite family of ?i-inverse strongly monotone mappings {Ai}Ni1 from a closed convex subset K of a Hilbert space H into H....
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