Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings

Abstract EN

Let H be a real Hilbert space.

Let T1,T2:H→H be k1-, k2-strictly pseudononspreading mappings; let αn and βn be two real sequences in (0,1).

For given x0∈H, the sequence xn is generated iteratively by xn+1=βnxn+1-βnTw1αnγfxn+I-μαnBTw2xn, ∀n∈N, where Twi=1−wiI+wiTi with i=1,2 and B:H→H is strongly monotone and Lipschitzian.

Under some mild conditions on parameters αn and βn, we prove that the sequence xn converges strongly to the set FixT1∩FixT2 of fixed points of a pair of strictly pseudononspreading mappings T1 and T2.