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In this article we present a modified S-iteration process that we combinewith inertial extrapolation to find a common solution to the split monotoneinclusion problem and the fixed point problem in real Hilbert space.Our goal isto establish a strong convergence theorem for approximating a commonsolution.Under some mild conditions,the problem can be solved. We also providea numerical example to show that our algorithms acceleration works well.

Inertial Modified S-Iteration Process for Split Monotone Inclusion and Fixed Point Problem In Real Hilbert Space