Approximation of the Solution of Split Equality Fixed Point Problem for Family of Multivalued Demicontractive Operators with Application

Abstract

In this paper, a new viscosity type iterative algorithm is used for obtaining a strong convergence result of split equality fixed point solutions for infinite families of multivalued demicontractive mappings in real Hilbert spaces. Our iterative scheme is based on choosing the step-sizes without calculating or estimating the operator norms and the condition of hemicompactness was relaxed to prove the strong convergence result. As an application, the solution of split convex minimization problem was approximated. The result presented herein unifies and extends several comparable results in the literature.

Keywords

• split equality fixed point problem
• multivalued demicontractive operator
• Hilbert spaces
• viscosity approximation