Shrinking approximants for fixed point problem and generalized split null point problem in Hilbert spaces

This paper deals with the convergence analysis of a shrinking approximants for the computation of a common solution associated with the fixed point problem of ηη-demimetric operator and the generalized split null point problem in Hilbert spaces. The considered sequence of approximants is a variant of the parallel hybrid shrinking projection algorithm that converges strongly to the optimal common solution under suitable set of control conditions. The viability of the approximants with parallel implementation is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature.