Generalized Hybrid Viscosity-Type Forward-Backward Splitting Method with Application to Convex Minimization and Image Restoration Problems

Abstract

Let E be a uniformly convex and q-uniformly smooth real Banach space. Let $A:E\to E$ be an α- inverse strongly accretive mapping of order q, $B:E⊸E$ be a set-valued m- accretive mapping and $S:E\to E$ be a nonexpansive mapping. In this article, a viscosity-type forward-backward splitting method for approximating a zero of (A + B) which is also a fixed point of S is introduced studied. Strong convergence theorem of the method is proved under suitable conditions. Furthermore, the convergence result obtained is applied to convex minimization and image restoration problems. Finally, numerical illustrations are presented to compare the convergence of the sequence of our algorithm and that of some recent important algorithms.

Keywords:

• α-inverse strongly accretive
• fixed point
• image restoration

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H20; 49M20; 49M25; 49M27; 47J25; 47H05

Acknowledgments

The authors would also like to thank the referees for their esteemed comments and suggestions. The authors acknowledge the African Development Bank (AfDB), the Pan African Material Institute (PAMI), AUST and the Center of Excellence in Theoretical and Computational Science (TaCS-CoE) for their financial support. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.

Competing interest

The authors declare that they have no conflict of interest.

Additional information

Funding

This work is supported from the African Development Bank (AfDB) research grant funds to AUST and the Center of Excellence in Theoretical and Computational Science (TaCS-CoE) research grant to KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.