TY - JOUR

T1 - Approximation of fixed points of weakly contractive nonself maps in Banach spaces

AU - Chidume, C. E.

AU - Zegeye, H.

AU - Aneke, S. J.

PY - 2002/6/1

Y1 - 2002/6/1

N2 - Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).

AB - Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).

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U2 - 10.1016/S0022-247X(02)00063-X

DO - 10.1016/S0022-247X(02)00063-X

M3 - Article

AN - SCOPUS:0036600766

VL - 270

SP - 189

EP - 199

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -