2012Thai Journal of MathematicsOpen access

General Cesaro mean approximation methods for nonexpansive mappings in Hilbert spaces

Pramote Markshoe, Rabian Wangkeeree

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Abstract

Let C be a nonempty closed convex subset of a real Hilbert space H, f a contraction on C and A a strongly bounded linear operator on H with coefficient γ > 0. Consider a general Cesaro mean iterative method x0 ∈ C, xn+1 = αnγf(xn) + βnxn + ((1 − βn)I + αnA) 1 n + 1 n

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Let C be a nonempty closed convex subset of a real Hilbert space H, f a contraction on C and A a strongly bounded linear operator on H with coefficient γ > 0. Consider a general Cesaro mean iterative method x0 ∈ C, xn+1 = αnγf(xn) + βnxn + ((1 − βn)I + αnA) 1 n + 1 n

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Available abstract

Let C be a nonempty closed convex subset of a real Hilbert space H, f a contraction on C and A a strongly bounded linear operator on H with coefficient γ > 0. Consider a general Cesaro mean iterative method x0 ∈ C, xn+1 = αnγf(xn) + βnxn + ((1 − βn)I + αnA) 1 n + 1 n

Key concepts: Mathematics, Hilbert space, Regular polygon, Bounded function, Bounded operator, Contraction (grammar), Linear operators, Operator (biology)

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