SCIENTIFIC ABSTRACT SERGEYEV, A.B. - SERGEYEV, A.V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001548110002-9
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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B112/B229
AUTHORt Sergeyey, A.. - S_.
TITLE: The chord method
PERIODICAL: Sibirskiy matematicheskiy zhurnal, v. 2, no. 2, 1961, 282-289
TEXT: The author considers a nonlinear functional equation: P(X) = 0.
P(x) is supposed to be an abstract continuous function which effects a
linear map of the Banach space X on the Banach space Y. Besides, the
existence of abstract functions P(xl,xo), P(x2'xl'xo) is assumed which
map the spaces X ~x X and X x X x X on the subspaces (X Y) and Ix -P (X --.* Y)]
of Y. respectively, and satisfy the conditions: P(xl,xo)(Xl - xo)
= P(X 1) - P(xo ) and P(x 2' x11X 0)(X2 -x1) = P(x2'xo) - P(xlgxo)p respective-
ly. For the solution of the equation P(x) = 0 the author uses the
iterative method (chord method), starting from two approximation solutions
-'P(x,,). Re proves the following
X and x x x - [P(X x
0 n+1 n n' n-i
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S/199/61/002/002/004/004
The chord method B112/B229
'theorem 1: if 'r0 = [P(xolgxo)]-l exists and satisfies the conditions:
Poll < Bog 10, Jjr0P(x0')jj4 jo' (10~