Abstract
If S and T are two non-self-mappings, then a solution of equation Sa∗ = Ta∗ = a∗ does not
necessarily exist. The common best proximity point problem is to find the approximate
optimal solution of such type of equation and have a key role in theory of approximation
and optimization. The primary goal of this paper is to introduce an inertial-type selfadaptive
algorithm for solving the common best proximity point, generalized equilibrium
and split variational inclusion problems in Hilbert spaces. The strong convergence of
the proposed algorithm is given under some mild conditions. It is worth mentioning
that the step size in many existing algorithms requires the prior knowledge of operator
norms which is difficult to compute, whereas our proposed algorithm does not require this
condition. Numerical examples are given to illustrate the efficiency and applicability of
the proposed approach. We further apply the proposed algorithm to an image restoration
problem and show that it achieves a higher signal-to-noise ratio compared with the existing
algorithms considered in this study.