  This paper is to analyze the approximation solution of a split variational
inclusion problem in the framework of infinite dimensional Hilbert spaces. For
this purpose, several inertial hybrid and shrinking projection algorithms are
proposed under the effect of self-adaptive stepsizes which does not require
information of the norms of the given operators. Some strong convergence
properties of the proposed algorithms are obtained under mild constraints.
Finally, an experimental application is given to illustrate the performances of
proposed methods by comparing existing results.
