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East Asian mathematical journal
Journal Basic Information
pISSN :
1226-6973
eISSN :
2287-2833
Journal DOI :
10.7858/eamj
Frequency :
Others
Publisher:
Youngnam Mathematical Society
Editor in Chief :
Jong-Kyu Kim
Volume & Issues
Volume 24, Issue 5 - Dec 2008
Volume 24, Issue 4 - Sep 2008
Volume 24, Issue 3 - Jun 2008
Volume 24, Issue 2 - Apr 2008
Volume 24, Issue 1 - Jan 2008
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1
A SYSTEM OF NONLINEAR VARIATIONAL INCLUSIONS WITH (A,
)-MONOTONE MAPPINGS IN HILBERT SPACES
Shang, Meijuan ; Qin, Xiaolong ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 1~6
Abstract
In this paper, we introduce a system of nonlinear variational inclusions involving (A,
)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A,
)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Our results improve and extend the recent ones announced by many others.
2
LOCALIZATION OF AZUKAWA PSEUDOMETRIC
Lee, Sun-Hong ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 7~10
Abstract
We prove a localization theorem of Azukawa pseudometric at a local plurisubharmonic peak point of a domain in the complex Euclidean space.
3
RECENT RESULTS AND CONJECTURES IN ANALYTICAL FIXED POINT THEORY
Park, Se-Hie ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 11~20
Abstract
We survey recent results and some conjectures in analytical fixed point theory. We list the known fixed point theorems for Kakutani maps, Fan-Browder maps, locally selectionable maps, approximable maps, admissible maps, and the better admissible class
of maps. We also give 16 conjectures related to that theory.
4
LOCAL CONVERGENCE OF THE SECANT METHOD UPPER
CONTINUOUS DIVIDED DIFFERENCES
Argyros, Ioannis K. ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 21~25
Abstract
The semilocal convergence of the secant method under
continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].
5
WEAK CONVERGENCE OF MANN ITERATIVE SEQUENCE FOR NONEXPANSIVE MAPPINGS IN PROBABILISTIC HILBERT SPACES
Su, Yongfu ; Wang, Xiuzhen ; Gao, Junyu ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 27~33
Abstract
The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.
6
STRONG CONVERGENCE OF COMPOSITE IMPLICIT ITERATIVE PROCESS FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS
Gu, Feng ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 35~43
Abstract
Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let
be N nonexpansive self-mappings of K with
(here
denotes the set of fixed points of
). Suppose that one of the mappings in
is semi-compact. Let
for some
and
for some
. For arbitrary
, let the sequence {
} be defined iteratively by
, where
. Then {
} convergence strongly to a common fixed point of the mappings family
. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of
or N=1 are also new.
7
OPTIMAL CONTROL OF A QUEUEING SYSTEM WITH
-SERVICE POLICY
Kim, Sung-Gon ; Bae, Jong-Ho ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 45~55
Abstract
We consider an M/G/1 queue with
-service policy, which is a two-stage service policy. The server starts to serve with rate 1 if a job arrives to the sever in idle state. If the workload of the system upcrosses
, then the service rate is changed to M and this rate continues until the system is empty. It costs to change the service rate to M and maintaining the rate. When the expectation of the stationary workload is supposed to be less than a given value, we derive the optimal value of M.
8
GENERALIZED PROJECTION AND APPROXIMATION FOR GENERALIZED VARIATIONAL INEQUALITIES SYSTEM IN BANACH SPACES
He, Xin-Feng ; Xu, Yong-Chun ; He, Zhen ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 57~65
Abstract
The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.
9
ON CHAOTIC OPERATOR ORDER
IN HILBERT SPACES
Lin, C.S. ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 67~79
Abstract
In this paper, we characterize the chaotic operator order
. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing
, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order
in terms of operator equalities.
10
CONVERGENCE OF VISCOSITY APPROXIMATIONS TO FIXED POINTS OF NONEXPANSIVE NONSELF-MAPPINGS IN BANACH SPACES
Jung, Jong-Soo ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 81~95
Abstract
Let E be a uniformly convex Banach space with a uniformly
differentiable norm, C a nonempty closed convex subset of E, and
a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For
a contraction and
, let
be a unique fixed point of a contraction
, defined by
,
. It is proved that if {
} is bounded, then
converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly
differentiable norm.
11
FIXED POINT THEORY FOR PERMISSIBLE MAPS VIA INDEX THEORY
Balaj, Mircea ; Cho, Yeol-Je ; O'Regan, Donal ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 97~103
Abstract
New fixed point theorems for permissible maps between
spaces are presented. The proof relies on index theory developed by Dzedzej and on viewing a
space as the projective limit of a sequence of Banach spaces.
12
STRONG CONVERGENCE OF AN IMPLICIT ITERATION PROCESS FOR A FINITE FAMILY OF STRONG SUCCESSIVELY
-PSEUDOCONTRACTIVE MAPS
Chen, Rudong ; Miao, Qian ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 105~110
Abstract
The aim of this paper is to prove convergence of implicit iteration process to a common fixed point for a finite family of strong successive
-pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of S. S. Chang [On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 313(2006), 273-283], M. O. Osilike[Implicit iteration process for common fixed points of a finite finite family of strictly pseudocontractive maps, Appl. Math. Comput. 189(2) (2007), 1058-1065].
13
A SYSTEM OF FIRST-ORDER IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS
Lan, Heng-You ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 111~123
Abstract
In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.
14
APPROXIMATIONS OF THE ITERATIVE SEQUENCES FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES
Chang, Shih-Sen ; Cho, Yeol-Je ; Zhou, Haiyun ;
East Asian mathematical journal , volume 24, issue 1, 2008, Pages 125~137
Abstract
In this paper, we first introduce some iterative sequences of Halpern type for asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces and then we discuss strong convergence for the iterative processes. The results presented in this paper extend, supplement and improve the correspoding main results of Reich [11], Shimizu and Takahashi [13], Shioji and Takahashi [15], [16] and Wittmann [18].