Approximating common fixed points of a finite family of non-self mappings in Hilbert spaces

In this paper, we construct and study an iterative process involving a finite family of non-self mappings defined on a nonempty closed convex subset of a real Hilbert space. We approximate a common fixed point of a finite family of $$k_i$$ k i -strictly pseudocontractive non-self mappings for $$i=1,2,\ldots ,N$$ i = 1 , 2 , … , N by strong or weak convergence of the scheme depending on the nature of the iteration parameter. Also, we obtain strong convergence results for approximating a common fixed point of a finite family of $$k_i$$ k i -strictly pseudocontractive non-self mappings for $$i=1,2,\ldots , N$$ i = 1 , 2 , … , N under appropriate conditions. Moreover, we prove strong convergence results to a common fixed point of a finite family of quasi-nonexpansive non-self mappings. The results obtained in this paper improve, generalize and complement many of the results in the literature.

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