Strong and Weak Convergence Theorems for the Split Feasibility Problem of (<i>β</i>,<i>k</i>)-Enriched Strict Pseudocontractive Mappings with an Application in Hilbert Spaces

Abstract

The concept of symmetry has played a major role in Hilbert space setting owing to the structure of a complete inner product space. Subsequently, different studies pertaining to symmetry, including symmetric operators, have investigated real Hilbert spaces. In this paper, we study the solutions to multiple-set split feasibility problems for a pair of finite families of β-enriched, strictly pseudocontractive mappings in the setup of a real Hilbert space. In view of this, we constructed an iterative scheme that properly included these two mappings into the formula. Under this iterative scheme, an appropriate condition for the existence of solutions and strong and weak convergent results are presented. No sum condition is imposed on the countably finite family of the iteration parameters in obtaining our results unlike for several other results in this direction. In addition, we prove that a slight modification of our iterative scheme could be applied in studying hierarchical variational inequality problems in a real Hilbert space. Our results improve, extend and generalize several results currently existing in the literature.

Keywords

• strong convergence
• variational inequality
• enriched nonlinear mapping
• split feasibility problem
• multiple-set split feasibility problem
• fixed point