Systems of Variational Inequalities and Multiple-Set Split Equality Fixed-Point Problems for Countable Families of Multivalued Type-One Mappings of the Demicontractive Type

Ukrainian Mathematical Journal - Our main aim is to introduce an iterative algorithm for the approximation of a common solution to a splitequality problem for finite families of variational...     

Proximal-type algorithms for split minimization problem in P-uniformly convex metric spaces

Numerical Algorithms - In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete p-uniformly convex metric spaces. We also...     

Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity

Numerical Algorithms - In solving the split variational inequality problems, very few methods have been considered in the literature and most of these few methods require the underlying operators...     

Approximation of common solution of finite family of monotone inclusion and fixed point problems for demicontractive multivalued mappings in CAT(0) spaces

Ricerche di Matematica - In this paper, we use the gate condition on two multivalued k-demicontractive mappings to approximate a common solution of a finite family of monotone inclusion problem and...     

A viscosity iterative technique for split variational inclusion and fixed point problems between a Hilbert space and a Banach space

The main purpose of this paper is to introduce a viscosity-type iterative algorithm for approximating a common solution of a split variational inclusion problem and a fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common solution of a split variational inclusion problem and a fixed point problem for a multivalued quasi-nonexpansive mapping between a Hilbert space and a Banach space. Furthermore, we applied our results to study a split convex minimization problem. Also, a numerical example of our result is given. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13, 759–775, 2012), Moudafi (J. Optim. Theory Appl. 150, 275–283, 2011), Takahashi and Yao (Fixed Point Theory Appl. 2015, 87, 2015), and a host of other important results in this direction.