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Vol.11 No.4

Namdeo, R.-K ; Fisher, B pp.267-274
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Abstract

A related fixed point theorem for set valued mappings on two complete metric spaces is obtained.

Lee, Kang-Sup ; Kim, Young-Ja pp.275-285
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Abstract

In this paper, the time series models for the number of reported death claims of compulsory automobile liability insurance in Korea are studied. We found that IMA<TEX>${(0, 1, 1)}\;{\times}\;{(0, 1, 1)}_{12}$</TEX> would the most appropriate model for the number of reported claims by the Box-Jenkins method.

Duggal, B.P. ; Jeon, In-Ho pp.287-292
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Abstract

The operator <TEX>$A \; {\in} \; L(H_{i})$</TEX>, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space <TEX>$\cal H_{i}$</TEX>, is said to be p-hyponormal if <TEX>$(A^\ast A)^P \geq (AA^\ast)^p$</TEX> for <TEX>$p\; \in \; (0,1]$</TEX>. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let <TEX>$I_{i}$</TEX> be the identity operator on <TEX>$H_{i}$</TEX>. Letting (equation omitted), where each <TEX>$A_{i}$</TEX> is p-hyponormal, it is proved that the commuting n-tuple T = (<TEX>$T_1$</TEX>,..., <TEX>$T_{n}$</TEX>) satisfies Bishop's condition (<TEX>$\beta$</TEX>) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

Liu, Zeqing ; Ume, Jeong-Sheok ; Kang, Shin-Min pp.293-308
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Abstract

Let K be a nonempty convex subset of an arbitrary Banach space X and <TEX>$T\;:\;K\;{\rightarrow}\;K$</TEX> be a uniformly continuous strictly hemi-contractive operator with bounded range. We prove that certain Ishikawa iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. We also establish similar convergence and almost stability results for strictly hemi-contractive operator <TEX>$T\;:\;K\;{\rightarrow}\;K$</TEX>, where K is a nonempty convex subset of arbitrary uniformly smooth Banach space X. The convergence results presented in this paper extend, improve and unify the corresponding results in Chang [1], Chang, Cho, Lee & Kang [2], Chidume [3, 4, 5, 6, 7, 8], Chidume & Osilike [9, 10, 11, 12], Liu [19], Schu [25], Tan & Xu [26], Xu [28], Zhou [29], Zhou & Jia [30] and others.

Kim, Tae-Soon ; Jeon, Myung-Jin pp.309-321
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Abstract

For a complete open Riemannian manifold, the ideal boundary consists of points at infinity. The so-called Busemann-functions play the role of distance functions for points at infinity. We study the similarity and difference between Busemann-functions and ordinary distance functions.

Jun, Kil-Woung ; Kim, Hark-Mann ; Lee, Don-O pp.323-335
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Abstract

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

Jeong, Jae-Ug ; Noor, M.-Aslam ; Rafig, A. pp.337-348
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Abstract

In this paper, we suggest and analyze Noor (three-step) iterative scheme for solving nonlinear strongly accretive operator equation Tχ = f. The results obtained in this paper represent an extension as well as refinement of previous known results.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics