  It is generally known that in order to solve the split equality fixed-point
problem (SEFPP), it is necessary to compute the norm of bounded and linear
operators, which is a challenging task in real life, to address this issue, we
studied the SEFPP involving the class of quasi-pseudocontractive mappings in
Hilbert spaces and constructed novel algorithms in this regards, and we proved
the algorithms' convergence both with and without prior knowledge of the
operator norm for bounded and linear mappings. Additionally, we gave
applications and numerical examples of our findings. A variety of well-known
discoveries revealed in the literature are generalized by the findings
presented in this work.
