Inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types

ABSTRACT

In this paper, inertial splitting algorithms for nonlinear operators of pseudocontractive and accretive types are proposed. Weak and strong convergence theorems are established in uniformly convex and q-uniformly smooth Banach spaces. Numerical examples are given to illustrate the effectiveness of our proposed algorithms.

KEYWORDS:

• Inertial algorithm
• accretive operator
• strict pseudocontraction
• strong convergence
• Banach space

MSC:

• 49H06
• 47H09
• 47N10
• 90C30

Acknowledgements

The authors are grateful to the referees for their valuable and constructive comments that greatly improved the readability and quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).