- P-ISSN1226-0657
- E-ISSN2287-6081
- KCI
ISSN : 1226-0657
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18권 2호
초록
Abstract
We provide a semilocal convergence result for approximating a solution of a singular system with constant rank derivatives, using Newton's method in an Euclidean space setting. Our approach uses more precise estimates and a combination of two Lipschitz-type conditions leading to the following advantages over earlier works [13], [16], [17], [29]: tighter bounds on the distances involved, and a more precise information on the location of the solution. Numerical examples are also provided in this study.
초록
Abstract
Let f : <TEX>${\mathbb{R}}{\rightarrow}{\mathbb{C}}$</TEX>. We consider the Hyers-Ulam stability of Jensen type functional inequality <TEX>$$|f(px+qy)-Pf(x)-Qf(y)|{\leq}{\epsilon}$$</TEX> in the half planes {(x, y) : <TEX>$kx+sy{\geq}d$</TEX>} for fixed d, k, <TEX>$s{\in}{\mathbb{R}}$</TEX> with <TEX>$k{\neq}0$</TEX> or <TEX>$s{\neq}0$</TEX>. As consequences of the results we obtain the asymptotic behaviors of f satisfying <TEX>$$|f(px+qy)-Pf(x)-Qf(y)|{\rightarrow}0$$</TEX> as <TEX>$kx+sy{\rightarrow}{\infty}$</TEX>.
초록
Abstract
We consider an optimal trading rule in this paper. We assume that the underlying asset follows a mean-reverting process and the transaction consists of one buying and one selling. To maximize the profit, we find price levels to buy low and to sell high. Associated HJB equations are used to formulate the value function. A verification theorem is provided for sufficient conditions. We conclude the paper with a numerical example.
초록
Abstract
We compute zeta functions of 1-solenoids. When our 1-solenoid is nonorientable, we compute Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid and its orientable double cover explicitly in terms of adjacency matrices and branch points. And we show that Artin-Mazur zeta function of orientable double cover is a rational function and a quotient of Artin-Mazur zeta function and Lefschetz zeta function of the 1-solenoid.
초록
Abstract
Main purpose of this note is to construct an example of a continuous one-to-one function f : <TEX>${\mathbb{Q}}^*{\rightarrow}{\mathbb{R}}$</TEX> whose inverse is nowhere continuous, and to show that the completeness is not necessary for the continuous inverse theorem.
초록
Abstract
In this paper we investigate the Hyers-Ulam stability of a Jensen type functional equation in multi-normed spaces and then extend the result to multi-normed left modules over a normed algebra A.
초록
Abstract
We study half lightlike submanifolds of an indefinite Sasakian manifold. The aim of this paper is to prove the following result: If a locally symmetric half lightlike submanifold of an indefinite Sasakian manifold is totally umbilical, then it is of constant positive curvature 1. In addition to this result, we prove three characterization theorems for such a half lightlike submanifold.