A Tseng-type algorithm for approximating zeros of monotone inclusion and J -fixed-point problems with applications

In this paper, a Halpern–Tseng-type algorithm for approximating zeros of the sum of two monotone operators whose zeros are J -fixed points of relatively J -nonexpansive mappings is introduced and studied. A strong convergence theorem is established in Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorem to convex minimization and image-restoration problems are presented. In addition, the proposed algorithm is used in solving some classical image-recovery problems and a numerical example in a Banach space is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature.