Issue 2, Volume 16, December 1991

1991 · Open access

1. MULTIDIMENSIONAL QUANTIZATION AND $U(1)$-COVERING TRAN VUI PDF

   ▸ Abstract

   Abstract

   103-119
2. AN INTERSECTION THEOREM AND RELATED PROBLEMS BUI CONG CUONG PDF

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   Abstract

   121-132
3. OKA-WEIL THEOREM AND PLURISUBHARMONIC FUNCTIONS OF UNIFORM TYPE BUI DAC TAC, NGUYEN THU NGA PDF

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   Abstract

   133-145
4. ON THE CARDINALITY OF THE GROUP OF AUTOMORPHISMS OF ALGEBRAICALLY CLOSED EXTENSION FIELDS T. SOUNDARARAJAN PDF

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   Abstract

   147-153
5. A CLASS OF CALIBRATED FORMS ON $f$-MANIFOLDS HOANG XUAN HUAN PDF

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   Abstract

   155-170
6. ANALYTIC MULTIFUNCTION, UNIFORM FRECHET ALGEBRAS AND THEIR EXTENSION TRAN NGOC GIAO PDF

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   Abstract

   171-185
7. BANACH HYPERBOLICITY AND EXISTENCE OF HOLOMORPHIC MAPS IN INFINITE DIMENSION PHAM KHAC BAN PDF

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   Abstract

   187-199
8. ON NECESSARY OPTIMALITY CONDITIONS FOR DISCRETE MINIMAX PROBLEMS DO VAN LUU PDF

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   Abstract

   201-210
9. ON ANALYSIS AND DISCRETIZATION OF NONLINEAR ABEL INTEGRAL EQUATIONS OF FIRST KIND RUDOLF GORENFLO, ANDREAS PFEIFFER PDF

   ▸ Abstract

   For $0\leq x \leq B$, $0 < \beta <1$, we consider the integral equation $$\int_0^x (x-t)^{-\beta}K(x, t, y(y))dt=f(x)$$ under appropriate Lipschitz-like conditions on the function $K$ and some of its derivatives, the most essential condition being $$K_u(x,t,u)\geq c > 0\text{ for } 0\leq t\leq x\leq B, ~ u\in\mathbb R.$$ After a survey on theorems of existence, uniqueness and stability of the solution we generalize a numerical method, proposed and investigated 1976 by H. W. Branca for the particular case $\beta=1/2$, to all $\beta\in(0,1)$ and show it to be $O(h^2)$ convergent for all $\beta\in[0.2118, 1)$ if the solution $y$ is sufficiently smooth. The method is based on piecewise linear interpolation, one-point weighted Gauss quadrature on parition intervals of equal lenght $h$, and collocation.

   211-262