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Vol.11 No.4
Abstract
A related fixed point theorem for set valued mappings on two complete metric spaces is obtained.
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.
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.
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.
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.
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.
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.