In this article, based on M-identity tensor, we establish some parameterized S-type inclusion intervals for fourth-order partially symmetric tensors. The new inclusion intervals are tighter than some existing results. Furthermore, some new S-type upper bounds on the M-spectral radius of fourth-order partially symmetric tensors are obtained. As applications, the new S-type upper bounds as the parameter of WQZ-algorithm can make the algorithm more rapidly converge to the largest M-eigenvalue of fourth-order partially symmetric tensors. Finally, we propose two sufficient conditions for the M-positive definiteness of fourth-order partially symmetric tensors.

We study a kind of split equality fixed point problem which is an extension of split equality problem. We propose a kind of simultaneous iterative algorithm with a way of selecting the step length which does not need any a priori information about the operator norms and prove that the sequences generated by the iterative method converge weakly to the solution of this problem. Some numerical results are shown to confirm the feasibility and efficiency of the proposed methods.