  We consider the monotone inclusion problems in real Hilbert spaces. Proximal
splitting algorithms are very popular technique to solve it and generally
achieve weak convergence under mild assumptions. Researchers assume the strong
conditions like strong convexity or strong monotonicity on the considered
operators to prove strong convergence of the algorithms. Mann iteration method
and normal S-iteration method are popular methods to solve fixed point
problems. We propose a new common fixed point algorithm based on normal
S-iteration method using Tikhonov regularization to find common fixed point of
nonexpansive operators and prove strong convergence of the generated sequence
to the set of common fixed points without assuming strong convexity and strong
monotonicity. Based on proposed fixed point algorithm, we propose a
forward-backward-type algorithm and a Douglas-Rachford algorithm in connection
with Tikhonov regularization to find the solution of monotone inclusion
problems. Further, we consider the complexly structured monotone inclusion
problems which are very popular these days. We also propose a strongly
convergent forward-backward-type primal-dual algorithm and a
Douglas-Rachford-type primal-dual algorithm to solve the monotone inclusion
problems. Finally, we conduct a numerical experiment to solve image deblurring
problems.
