LAUSR

In this paper, we propose some new parallel iterative methods by the hybrid and shrinking projection to find a common fixed point of a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces when the domain C satisfies $${{\mathrm{diam}}}(C)<\infty $$diam(C)<∞. We also give some applications of our main results for the problem of finding a common fixed point of nonexpansive mappings, nonexpansive semi-groups, the problem of finding a common zero point of monotone operators, the system of generalized mixed equilibrium problems and the system of variational inequalities without the condition $${{\mathrm{diam}}}(C)<\infty $$diam(C)<∞. Three numerical examples also are given to illustrate the effectiveness of the proposed algorithms.