An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings

Abstract

Abstract We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in the literature from the class of nonexpansive or quasi-nonexpansive mappings to the larger class of demicontractive mappings. Examples to illustrate numerically the effectiveness of the new analytical results are presented.

Keywords

• Hilbert space
• Bounded linear operator
• Split feasibility problem
• Fixed point
• Variational inequality
• Banach contraction