MINIMUM-NORM FIXED POINT OF FINITE FAMILY OF -STRICTLY PSEUDOCONTRACTIVE MAPPINGS - Zegeye, H.; Thuto, M. V. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
Let K be a nonempty closed and convex subset of a real Hilbert space H and for each 1≤ i≤ N, let T_i: K→ K be λ_i-strictly pseudocontractive mapping. Then for β (0,2λ], where λ:={ λ_i:i=1,2,...,N}, and each t (0,1), it is proved that, there exists a sequence {y_t} K satisfying y_t= P_K[(1-t)(β Ty_t+(1-β) y_t)],where T:=θ_1T_1+θ_2T_2+...+θ_NT_N, for θ_1+θ_2+...+θ_N=1, which converges strongly, as t→ 0^+, to the common minimum-norm fixed point of {T_i: i=1,2,...,N}.Moreover, we provide an explicit iteration process which converges strongly to a common minimum-norm fixed point of {T_i:i=1,2,...,N}. Corresponding results, for a common minimum-norm solution of finite family of α-inverse strongly monotone mappings are also discussed. Our theorems improve several results in this direction.