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Communications of the Korean Mathematical Society
Journal Basic Information
pISSN :
1225-1763
eISSN :
2234-3024
Journal DOI :
10.4134/CKMS
Frequency :
Others
Publisher:
The Korean Mathematical Society
Editor in Chief :
Volume & Issues
Volume 28, Issue 4 - Oct 2013
Volume 28, Issue 3 - Jul 2013
Volume 28, Issue 2 - Apr 2013
Volume 28, Issue 1 - Jan 2013
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1
CUBIC FORMULA AND CUBIC CURVES
Woo, Sung Sik ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 209~224
DOI : 10.4134/CKMS.2013.28.2.209
Abstract
The problem of finding rational or integral points of an elliptic curve basically boils down to solving a cubic equation. We look closely at the cubic formula of Cardano to find a criterion for a cubic polynomial to have a rational or integral roots. Also we show that existence of a rational root of a cubic polynomial implies existence of a solution for certain Diophantine equation. As an application we find some integral solutions of some special type for
.
2
ON KERNEL OF ORDERED SEMIGROUPS - A CORRIGENDUM
Kehayopulu, Niovi ; Tsingelis, Michael ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 225~229
DOI : 10.4134/CKMS.2013.28.2.225
Abstract
According to the paper in [3], the kernel of an ordered semigroup S is a completely regular subsemigroup of S. In this note we show that the kernel of an ordered semigroup S is not a completely regular subsemigroup of S, in general.
3
A COUNTEREXAMPLE FOR IMPROVED SOBOLEV INEQUALITIES OVER THE 2-ADIC GROUP
Chamorro, Diego ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 231~241
DOI : 10.4134/CKMS.2013.28.2.231
Abstract
On the framework of the 2-adic group
, we study a Sobolev-like inequality where we estimate the
norm by a geometric mean of the BV norm and the
norm. We first show, using the special topological properties of the
-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙
. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.
4
GENERAL NONLINEAR RANDOM SET-VALUED VARIATIONAL INCLUSION PROBLEMS WITH RANDOM FUZZY MAPPINGS IN BANACH SPACES
Balooee, Javad ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 243~267
DOI : 10.4134/CKMS.2013.28.2.243
Abstract
This paper is dedicated to study a new class of general nonlinear random A-maximal
-relaxed
-accretive (so called (A,
)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in
-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal
-relaxed
-accretive mappings due to Lan et al. and Chang's lemma [13], some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.
5
A FIXED POINT APPROACH TO THE STABILITY OF THE GENERALIZED POLYNOMIAL FUNCTIONAL EQUATION OF DEGREE 2
Jin, Sun-Sook ; Lee, Yang-Hi ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 269~283
DOI : 10.4134/CKMS.2013.28.2.269
Abstract
In this paper, we investigate a stability of the functional equation
by using the fixed point theory in the sense of L. C
dariu and V. Radu.
6
A NOTE ON RADON-NIKODYM THEOREM FOR OPERATOR VALUED MEASURES AND ITS APPLICATIONS
Ahmed, Nasiruddin ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 285~295
DOI : 10.4134/CKMS.2013.28.2.285
Abstract
In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.
7
A REDUCIBILITY OF SRIVASTAVA'S TRIPLE HYPERGEOMETRIC SERIES F
^{(3)}
[x, y, z]
Choi, Junesang ; Wang, Xiaoxia ; Rathie, Arjun K. ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 297~301
DOI : 10.4134/CKMS.2013.28.2.297
Abstract
When certain general single or multiple hypergeometric functions were introduced, their reduction formulas have naturally been investigated. Here, in this paper, we aim at presenting a very interesting reduction formula for the Srivastava's triple hypergeometric function
by applying the so-called Beta integral method to the Henrici's triple product formula for hypergeometric series.
8
SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION
Rao, Snehal B. ; Patel, Amit D. ; Prajapati, Jyotindra C. ; Shukla, Ajay K. ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 303~317
DOI : 10.4134/CKMS.2013.28.2.303
Abstract
In present paper, we obtain functions
and
by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function
and some special cases have also been discussed.
9
APPROXIMATE EULER-LAGRANGE-JENSEN TYPE ADDITIVE MAPPING IN MULTI-BANACH SPACES: A FIXED POINT APPROACH
Moradlou, Fridoun ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 319~333
DOI : 10.4134/CKMS.2013.28.2.319
Abstract
Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:
.
10
A HYBRID METHOD FOR A COUNTABLE FAMILY OF LIPSCHITZ GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS AND AN EQUILIBRIUM PROBLEM
Cholamjiak, Prasit ; Cholamjiak, Watcharaporn ; Suantai, Suthep ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 335~351
DOI : 10.4134/CKMS.2013.28.2.335
Abstract
In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.
11
NON-EXISTENCE OF TOTALLY GEODESIC SCREEN DISTRIBUTIONS ON LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS
Jin, Dae Ho ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 353~360
DOI : 10.4134/CKMS.2013.28.2.353
Abstract
We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.
12
A NIELSEN TYPE NUMBER OF FIBRE PRESERVING MAPS
Lee, Seoung Ho ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 361~369
DOI : 10.4134/CKMS.2013.28.2.361
Abstract
We introduce a Nielsen type number of a fibre preserving map, and show that it is a lower bound for the number of
-orbits in the homotopy class. Under suitable conditions we show that it is equal to the Nielsen type relative essential
-orbit number. We also give necessary and sufficient conditions for it and the essential
-orbit number to coincide.
13
ON θ-(
,
)-CONTINUOUS FUNCTIONS IN GRILL TOPOLOGICAL SPACES
Al-Omari, Ahmad ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 371~381
DOI : 10.4134/CKMS.2013.28.2.371
Abstract
In this paper, we investigate some properties of
-(
,
)-continuous functions in a grill topological spaces. Moreover, the relationships with other related functions are investigated.
14
M/PH/1 QUEUE WITH DETERMINISTIC IMPATIENCE TIME
Kim, Jerim ; Kim, Jeongsim ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 383~396
DOI : 10.4134/CKMS.2013.28.2.383
Abstract
We consider an M/PH/1 queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.
15
AN IMPROVED BINOMIAL METHOD FOR PRICING ASIAN OPTIONS
Moon, Kyoung-Sook ; Kim, Hongjoong ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 397~406
DOI : 10.4134/CKMS.2013.28.2.397
Abstract
We present an improved binomial method for pricing European- and American-type Asian options based on the arithmetic average of the prices of the underlying asset. At each node of the tree we propose a simple algorithm to choose the representative averages among all the effective averages. Then the backward valuation process and the interpolation are performed to compute the price of the option. The simulation results for European and American Asian options show that the proposed method gives much more accurate price than other recent lattice methods with less computational effort.
16
ON A FAST ITERATIVE METHOD FOR APPROXIMATE INVERSE OF MATRICES
Soleymani, Fazlollah ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 407~418
DOI : 10.4134/CKMS.2013.28.2.407
Abstract
This paper studies a computational iterative method to find accurate approximations for the inverse of real or complex matrices. The analysis of convergence reveals that the method reaches seventh-order convergence. Numerical results including the comparison with different existing methods in the literature will also be considered to manifest its superiority in different types of problems.
17
ROBUST DUALITY FOR GENERALIZED INVEX PROGRAMMING PROBLEMS
Kim, Moon Hee ;
Communications of the Korean Mathematical Society, volume 28, issue 2, 2013, Pages 419~423
DOI : 10.4134/CKMS.2013.28.2.419
Abstract
In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.