On the hierarchical variational inclusion problems in Hilbert spaces

Viscosity Approximation Methods for Split Variational Inclusion and Fixed Point Problems in Hilbert Spaces

The main objective of this paper is to find a common solution of split variational inclusion problem and fixed point problem of infinite family of nonexpansive operators in a setting of real Hilbert spaces. To reach this goal, the iterative algorithms which combine Moudafi’s viscosity approximation method with some fixed point technically proving methods are utilized for solving the problem. We...

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

On the Inclusion Relation of Reproducing Kernel Hilbert Spaces

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are...

On synchronal algorithm for fixed point and variational inequality problems in hilbert spaces

The aim of this article is to expand and generalize some approximation methods proposed by Tian and Di (J Fixed Point Appl, 2011. doi:10.1186/1687-1812-21) to the class of [Formula: see text]-total asymptotically strict pseudocontraction to solve the fixed point problem as well as variational inequality problem in the frame work of Hilbert space. Further, the results presented in this paper ext...

Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces