Steepest descent approximations in Banach space

Abstract

Let E be a real Banach space and let A : E → E be a Lipschitzian generalized strongly accretive operator. Let z ∈ E and x0 be an arbitrary initial value in E for which the steepest descent approximation scheme is defined by xn+1 = xn − αn(Ayn − z), yn = xn − βn(Axn − z), n = 0, 1, 2 . . . , where the sequences {αn} and {βn} satisfy the following conditions… (More)

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