In this article, we introduce a split equality monotone yosida variational inclusion problem which is more general than the split equality monotone variational inclusion problem, split equality variational inclusion problem and yosida inclusion problem. We develop an iterative algorithm for approximating a common solution of split equality monotone yosida variational inclusion problem and split equality fixed point problems for infinite family of generalized $k$-strictly pseudocontractive multivalued mappings and infinite family of L-Lipschitzian and quasi-pseudocontractive mappings in the settings of infinite-dimensional Hilbert spaces. Using our iterative algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the solution set of the aforementioned problems. Our iterative algorithm is design in such a way that it does not require the prior knowledge of the operator norm. We apply our result to solve a variational inequality problem. Our result extends and complements some related results in literature.