Fixed point iterations for certain classes of nonlinear mappings

Abstract

Let X = L_p or L_p, 2≤p<∞, and let K be a nonempty closed convex bounded subset of X. It is proved that for some classes of nonlinear mappings T:K → K (more precisely, for T P₂ or C in the terminology of F.E. Browder and W.V. Pretryshyn; and B.E. Rhoades), the iteration process: x₁ ϵK,X_n+1 = (1-C_n)x_n+C_n Tx_n, n ≥1,under suitable conditions on K and the real sequence {C_n}_n=1 ^∞ converges strongly to a fixed point of T. While our thorems generalize serveral known results, our method is also of independent interest

AMS(MOS):

• 47H15

^*This research was supported by a grant from the third world Academy of Sciences (TWASRG 86-43), ICTP, Trieste, Italy

^*This research was supported by a grant from the third world Academy of Sciences (TWASRG 86-43), ICTP, Trieste, Italy

Notes

^*This research was supported by a grant from the third world Academy of Sciences (TWASRG 86-43), ICTP, Trieste, Italy