An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems

In this work, an inertial Halpern-type algorithm involving monotone operators is proposed in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the iterates generated by the algorithm is proved to a zero of sum of two monotone operators. Furthermore, an application of the method to image recovery problems is presented. In addition, a numerical example on the classical Banach space l32(R) 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.