Weak and Strong Convergence Theorems for New Demimetric Mappings and the Split Common Fixed Point Problem in Banach Spaces

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In this paper, we consider the split common fixed point problem for new demimetric mappings in Banach spaces. Using the idea of Mann’s iteration, we prove a weak convergence theorem for finding a solution of the split common fixed point problem in Banach spaces. Furthermore, using the idea of Halpern’s iteration, we obtain a strong convergence theorem for finding a solution of the problem in Banach spaces. Using these results, we obtain well-known and new weak and strong convergence theorems in Hilbert spaces and Banach spaces.