Simple projection algorithm for a countable family of weak relatively nonexpansive mappings and applications
نویسندگان
چکیده
*Correspondence: [email protected]; [email protected] Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China Abstract Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {Tn} : C→ C be a countable family of weak relatively nonexpansive mappings such that F = ⋂∞ n=1 F(Tn) = ∅. For any given gauss x0 ∈ C, define a sequence {xn} in C by the following algorithm: ⎪⎨⎪⎩ C0 = C, Cn+1 = {z ∈ Cn : φ(z, Tnxn) = φ(z, xn)}, n = 0, 1, 2, 3, . . . , xn+1 = Cn+1x0.
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