Let E be a real q-uniformly smooth Banach space which is also uniformly convex (for example, Lp or lp spaces, 1 < p < ∞) and K be a nonempty closed convex and bounded subset of E with φ ≠ int (K). Let T: K → K be a Lipschitzian pseudocontractive mapping such that for z ∈ int (K), ∥z - Tz∥ < ∥x - Tx∥, for all x ∈ ∂(K). Then for z0 ∈ K arbitrary, the iteration process (zn) defined by zn+1: = (1 - μn+1)z+μn+1yn; yn: = (1 - αn)zn + αnTzn converges strongly to a fixed point of T, provided that (μn) and (αn) satisfy certain conditions. Moreover, if T is strictly pseudocontractive with a nonempty fixed-point set, then it is proved that the Mann type iteration scheme converges strongly to a fixed point of T.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics