S. Kusuoka, A. Yamazaki's Advances in Mathematical Economics, Vol. 10 PDF

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Sample text

The part of condition (11) which concerns the CES coefficients at the social level is introduced to ensure the possibiUty of local indeterminacy when the consumption good technology is Cobb-Douglas while the investment good technology is Leontief [see case (ii)]. This explains why such a condition does not occur under the assumption of symmetric elasticities. However, since the plausible values of 8 and g are close to zero, this condition does not imply a strong restriction on the CES coefficients.

2) where {r„} c (0, oo)andyr = (Z+rJ)"^ forallr > 0. This algorithm was first introduced by Martinet [5]. 1). Motivated by Rockafellar's result, Kamimura and Takahashi [6] proved the following two convergence theorems. 1 ([6]). Let H be a Hilbert space and letT c H x H be a maximal monotone operator. Let Jr — {I -\- rT)~^ for all r > 0 and let {xn} be a sequence defined as follows: x\ = x e H and Xn-\-\ = OinXn + (1 - an)^r„^Ai, « = 1, 2, . . , where {an\ C [0, 1] and {r^} C (0, oo) satisfy limsupa„ < 1 and liminf r^ > 0.

By the definition of dg, we have g{x) + 2{y,Jx-x*);,x*) for all JC,}' e E. 2). 2. Let Ebea uniformly convex and uniformly smooth Banach space and let B C E"^ X E be a maximal monotone operator Let Jr = (I -\-rBJ)~~^ for allr > 0 and let {Xn} be a sequence defined as follows: x\ = x e E and Xn-{-\ = GlnX + ( 1 - Otn)Jrn^n. H = 1, 2 , . . , where {Qf„} C [0, 1] and {r„} C (0, oo) satisfy \\mn-^ooOin = 0, X ^ i ^n = oo, and lim„_^oo^n = ^^- If B~^0 ^ 0, then the sequence {xn} converges strongly to R(BJ)-'^O(^^' where R(BJ)-^O ^^ ^ sunny generalized nonexpansive retraction of E onto (BJ)~^0.

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