Weak and Strong Convergence Theorems for Relatively Nonexpansive Mappings in Banach Spaces
نویسندگان
چکیده
where {rn} ⊂ (0,∞) and Jr = (I + rA)−1 for all r > 0. This algorithm was first introduced by Martinet [9]. In [16], Rockafellar proved that if liminfn→∞ rn > 0 and A−10 = ∅, then the sequence {xn} defined by (1.2) converges weakly to an element of solutions of (1.1). On the other hand, Kamimura and Takahashi [4] considered an algorithm to generate a strong convergent sequence in a Hilbert space. Further, Kamimura and Takahashi’s result was extended to more general Banach spaces by Kohsaka and Takahashi [7]. They introduced and studied the following iteration sequence: x = x0 ∈ E and xn+1 = J−1 ( αnJx+ ( 1−αn ) JJrnxn ) , n= 0,1,2, . . . , (1.3)
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