Showing papers in "Kyungpook Mathematical Journal in 2006"

Classes of Multivalent Functions Defined by Dziok-Srivastava Linear Operator and Multiplier Transformation

Abstract: In this paper, the authors introduce new classes of p-valent functions defined by Dziok-Srivastava linear operator and the multiplier transformation and study their properties by using certain first order differential subordination and superordination. Also certain inclusion relations are established and an integral transform is discussed.

Weighted Sharing of Two Sets

Abstract: Using the notion of weighted sharing of sets we improve two results of H. X. Yi on uniqueness of meromorphic functions.

Uniqueness of Meromorphic Functions and a Question of Gross

Abstract: . In this paper, we deal with the uniqueness of meromorphic functions con-cerning one question of Gross (see [5, Question 6]), and obtain some results that areimprovements of that of former authors. Moreover, the example shows that the result issharp. 1. Introduction and main resultsIn this paper, the term \meromorphic" will always mean meromorphic in thecomplex plane C. We assume that the reader is familiar with the basic results andnotations of Nevanlinna's value distribution theory (see [6]), such as T (r;f ), N (r;f )and m (r;f ). Meanwhile, we need the following notations. Let f (z) be a meromor-phic function. We denote by n 1) (r;f ) the number of simple poles of f in jzj · r,N 1) (r;f ) is de¯ned in terms of n 1) (r;f ) in the usual way (see [19]). We furtherde¯ne± 1) (1 ; f ) = 1 i limsup r !1 N 1) (r;f )T (r;f ):By the de¯nition of N 1) (r;f ), we haveN 1) (r;f ) · N (r;f ) ·12N 1) (r;f )+12N (r;f ) ·12N 1) (r;f )+12T (r;f ):From this we obtain(1)12± 1) (1 ;f ) ·12±

Ideal Theory in Commutative A-semirings

Abstract: In this paper, we investigate and characterize the class of A-semirings. A characterization of the Thierrin radical of a proper ideal of an A-semiring is given. More- over, when P is a Q-ideal in the semiring R, it is shown that P is primary if and only if R=P is nilpotent. The concept of semirings was introduced by H. S. Vandiver in 1935 and has since then been studied by many authors (e.g., (1)-(5), (11)-(13)). In several papers from 1956 to 1958, K. Iseki ((7)-(10)) developed a large amount of ideal theory for semirings that are not necessarily commutative under either operation. Many of Iseki's results were topological in nature; however, he gave several characterizations of prime ideals and has defined and studied the Thierrin radical of an ideal. It is the purpose of this paper to present a development of ideal theory for commutative semirings and to connect this theory with the theory developed by Iseki. P. J. Allen ((1)) introduced the notion of a Q-ideal and a construction process was presented by which one can build the quotient structure of a semiring modulo a Q-ideal. Maximal homomorphisms were defined and examples of such homomorphisms were given. Using these notions, the Fundamental Theorem of Homomorphisms for rings was generalized to include a large class of semirings. The results proven in (1) will be used throughout this paper. Since the theory of ideals plays an important role in the theory of quotient semirings, in this paper, we will make an intensive study of the notions of prime, completely prime, and primary ideals in commutative semrings. The notion of an A-semiring will be defined and a characterization of an A-semiring will be presented. With the aid of these notions, further algebraic properties of the radical of an ideal in an A-semiring will be given. It will also be shown that a proper Q-ideal I in the semiring R is primary if and only if every zero divisor in

A Note on Regular Ternary Semirings

Abstract: This paper is a sequel of our previous paper (1). In this paper, we introduce the notions of regular ideal and partial ideal (p-ideal) in a ternary semiring and using these two notions we characterize regular ternary semiring.

On Almost Continuity

Abstract: A new class of functions is introduced in this paper. This class is called almost -precontinuity. This type of functions is seen to be strictly weaker than almost precontinuity. By using -preopen sets, many characterizations and properties of the said type of functions are investigated.

Nonlinear Functional Boundary Value Problems in Banach Algebras Involving Caratheodories

Abstract: In this paper, an existence theorem for a nonlinear two point boundary value problem of second order dierential equations in Banach algebras is proved using a nonlinear alternative based on Leray-Schauder alternative

On Applications of Weyl Fractional q-integral Operator to Generalized Basic Hypergeometric Functions

Abstract: Applications of Weyl fractional q-integral operator to various generalized ba- sic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper Certain interesting special cases have also been deduced

On the Value Distribution of ff (k)

Abstract: This paper proves the following results: Let f be a transcendental entire function, and let k(‚ 2) be a positive integer. If T(r;f) 6 N1)(r;1=f)+S(r;f); then ff (k) assumes every finite nonzero value infinitely often. Also the case when f is a transcenden- tal meromorphic function has been considered and some results are obtained.

Characterization of Function Rings Between C * (X) and C(X)

Abstract: . Let X be a Tychonoff space andP( X ) the set of all the subrings of C ( X ) that contain C ⁄ ( X ). For any A ( X ) inP( X ) suppose A A X is the largest sub-space of flX containing X to which each function in A ( X ) can be extended continu-ously. Let us write A ( X ) » B ( X ) if and only if A A X = A B X , thereby defining anequivalence relation onP( X ). We have shown that an A ( X ) inP( X ) is isomorphicto C ( Y ) for some space Y if and only if A ( X ) is the largest member of its equiv-alence class if and only if there exists a subspace T of flX with the property that A ( X ) = ff 2 C ( X ) : f ⁄ ( p ) is real for each p in Tg , f being the unique continuous exten-sion of f in C ( X ) from flX to R ⁄ , the one point compactification of R. As a consequenceit follows that if X is a realcompact space in which every C ⁄ -embedded subset is closed,then C ( X ) is never isomorphic to any A ( X ) inP( X ) without being equal to it. 1. IntroductionIt is well known in the theory of rings of continuous functions that for a Ty-chonoff space

The Action of the Handlebody Group on the First Homology Group of the Surface

Abstract: The action of mapping class groups of a handlebody on the first homology group is investigated. A homological analogy of mapping class groups of a handlebody is defined and its system of generators is given.

Conformally Flat Quasi-Einstein Spaces

Abstract: The object of the present paper is to study a conformally flat quasi-Einstein space and its hypersurface.

Sensitivity Analysis for Generalized Nonlinear Implicit Quasi-variational Inclusions

Abstract: In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a new class of parametric generalized nonlinear implicit quasi-variational inclusion problem in spaces. The results presented in this paper are new and generalize many known results in this field.

On Idempotent Reflexive Rings

Abstract: We introduce in this paper the concept of idempotent reflexive right ideals and concern with rings containing an injective maximal right ideal. Some known results for reflexive rings and right HI-rings can be extended to idempotent reflexive rings. As applications, we are able to give a new characterization of regular right self-injective rings with nonzero socle and extend a known result for right weakly regular rings. Throughout this paper, R denotes an associative ring not necessarily with unity unless otherwise stated. A right ideal I is said to be reflexive (2) if aRb µ I implies bRa µ I for a;b 2 R. A ring R is called reflexive if 0 is a reflexive ideal. In this paper we define an idempotent reflexive right ideal which is a nontrivial generaliza- tion of a reflexive right ideal. Some known results of Mason (2) are extended. For an idempotent reflexive ring R with unity, we prove that if R contains an injective maximal right ideal, then R is right self-injective. As a byproduct of this result, we obtain a new characterization of regular right self-injective rings with nonzero socle. This characterization is then used to prove that an idempotent reflexive right HI-ring is semisimple Artinian. Consequently we extend nontrivially a result in (7). Moreover we show that if R is an idempotent reflexive ring with unity and every simple singular right R-module is p-injective then R is a right weakly regular ring. Definition 1. A right ideal I is called idempotent reflexive if aRe µ I if and only if eRa µ I for a;e = e 2 2 R. We say that R is an idempotent reflexive ring when 0 is an idempotent reflexive ideal.

Topological Imitations and Reni-Mecchia-Zimmermann's Conjecture

Abstract: M. Reni has shown that there are at most nine mutually inequivalent knots in the 3-sphere whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds. By observing that the Z-homology sphere version of M. Reni's result still holds, M. Mecchia and B. Zimmermann showed that there are exactly nine mutually inequivalent, knots in Z-homology 3-spheres whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds, and conjectured that there exist exactly nine mutually inequivalent, knots in the true 3-sphere whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds. Their proof used an argument of AID imitations published in 1992. The main result of this paper is to solve their conjecture affirmatively by combining their argument with a theory of strongly AID imitations published in 1997.

On Direct Sums of Lifting Modules and Internal Exchange Property

Abstract: Let R be a ring with identity and let be an amply supplemented R-module. Then it is proved that has () and is for , i = 1, 2, if and only if for any coclosed submodule X of M, there exist and such that .

Noor Iterations with Error for Non-Lipschitzian Mappings in Banach Spaces

Abstract: Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T.

L p Boundedness for Singular Integral Operators with L(log + L) 2 Kernels on Product Spaces

Abstract: In this paper, we study the mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to . Our results extend as well as improve some known results on singular integrals.

Permuting Tri-Derivations in Prime and Semi-Prime Gamma Rings

Abstract: We study permuting tri-derivations in Γ-rings and give an example.

Some New Hilbert Type Inequalities

Abstract: In this paper, we obtain some inequalities similar to Hilbert type. Some new inequalities are also given.

The First Four Terms of Kauffman's Link Polynomial

Abstract: We give formulas for the first four coefficient polynomials of the Kauffman's link polynomial involving linking numbers and the coefficient polynomials of the Kauffman polynomials of the one- and two-component sublinks. We use mainly the Dubrovnik polynomial, a version of the Kauffman polynomial.

Symmetry Properties of 3-dimensional D'Atri Spaces

Abstract: We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the -Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

Generalized Weyl's Theorem for Some Classes of Operators

Abstract: Let A be a bounded linear operator acting on a Hilbert space H. The B-Weyl spectrum of A is the set aeBw(A) of all ‚ 2C such that Ai‚I is not a B-Fredholm operator of index 0. Let E(A) be the set of all isolated eigenvalues of A. Recently in (6) Berkani showed that if A is a hyponormal operator, then A satisfies generalized Weyl's theorem aeBw(A) = ae(A) n E(A), and the B-Weyl spectrum aeBw(A) of A satisfies the spectral mapping theorem. In (51), H. Weyl proved that weyl's theorem holds for hermitian op- erators. Weyl's theorem has been extended from hermitian operators to hyponormal and Toeplitz operators (12), and to several classes of operators including semi-normal operators ((9), (10)). Recently W. Y. Lee (35) showed that Weyl's theorem holds for algebraically hyponormal operators. R. Curto and Y. M. Han (14) have extended Lee's results to al- gebraically paranormal operators. In (19) the authors showed that Weyl's theorem holds for algebraically p-hyponormal operators. As Berkani has shown in (5), if the generalized Weyl's theorem holds for A, then so does Weyl's theorem. In this paper all the above re- sults are generalized by proving that generalized Weyl's theorem holds for the case where A is an algebraically (p;k)-quasihyponormal or an algebarically paranormal operator which includes all the above mentioned operators.

Centroaffine Minimal Surfaces with Constant Curvature Metric

Abstract: We classify centroaffine minimal surfaces with constant curvature metric under some natural conditions on the cubic differentials.

On Partitioning Ideals of Semirings

Abstract: . We prove the following results:(1) Let R be a strongly euclidean semiring. Then an ideal A of R n£n is a partitioningideal if and only if it is a subtractive ideal.(2) A monic ideal M of R [ x ], where R is a strongly euclidean semiring, is a partitioningideal if and only if it is a subtractive ideal. 1. IntroductionThroughout this paper all semirings are with a multiplicative identity. Z + willdenote the set of all non negative integers. For the terminology, we refer [1], [2] and[4]. A right ideal I of a semiring R is called subtractive if a , a + b 2 I , b 2 R then b 2 I . An ideal I of a semiring R is called partitioning ideal if there exists a subset Q of R such that:1. R = [fq + I : q 2 Qg .2. If q 1 ; q 2 2 Q then q 1 = q 2 if and only if ( q 1 + I ) \ ( q 2 + I ) 6= ; .A commutative semiring R is called strongly euclidean [5] if there exists a function d : Rif 0 g ! Z + such that (1) d ( ab ) ‚ d ( a ) for all a;b 2 Rif 0 g , and (2) if a;b 2 R with b 6= 0 then there exist unique q;r 2 R

Oscillation of Second Order Nonlinear Elliptic Differential Equations

Abstract: By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.

Weighted L p Boundedness for the Function of Marcinkiewicz

Abstract: In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator when satisfies a mild regularity condition and belongs to , . We also prove the weighted boundedness for a class of Marcinkiewicz integral operators and related to the Littlewood-Paley -function and the area integral S, respectively.

New Lacunary Strong Convergence Difference Sequence Spaces Defined by Sequence of Moduli

Abstract: . In this paper, we define 4 m -Lacunary strongly convergent sequences definedby sequence of moduli and give various properties and inclusion relations on these sequencespaces. 1. IntroductionLet ! be the set of all sequences of real or complex numbers and l 1 ; c and c 0 be the sets of all bounded, convergent sequences and sequences convergent to zerorespectively, normed by jjxjj 1 = sup k jx k j; where k 2 N= f 1 ; 2 ;¢¢¢g , the set of positive integers.The difference sequence space X ( 4 ) was introduced by Kizmaz [3] as follows X ( 4 ) = fx = ( x k ) 2 ! : ( 4x k ) 2 Xg for X = l 1 ; c and c 0 ; where 4x k = ( x k ix k +1 ) for all k 2 N.The difference sequence spaces were generalized by Et and Colak [1] as follows X ( 4 m ) = fx = ( x k ) 2 ! : 4 m x = ( 4 m x k ) 2 Xg for X = l 1 ; c and c 0 ; where 4 m x k = ( 4 mi 1 x k i4 mi 1 x k +1 ).A sequence of positive integers µ = ( k r ) is called “lacunary” if k 0 = 0, 0

Asymptotic Results for a Class of Fourth Order Quasilinear Difference Equations

Abstract: In this paper, the authors first classify all nonoscillatory solutions of equation (1) into six disjoint classes according to their asymptotic behavior, and then they obtain necessary and sufficient conditions for the existence of solutions in these classes. Examples are inserted to illustrate the results.

Commutative Semigroups whose Proper Homomorphic Images are All of Smaller Cardinality

Abstract: We characterize those commutative semigroups S such that every non- isomorphic homomorphic image of S has smaller cardinality than S. We also characterize commutative groups with the same property. In (3) Kaplansky posed the following problem for an infinite commutative group G: Show that every proper (not isomorphic) homomorphic image of G is finite if and only if G is an infinite cyclic group. In (2) Jensen and Miller characterized all infinite commutative semigroups S such that every proper homomorphic image of S is finite; they called such semigroups homomorphically finite or HF semigroups. In this note we characterize those infinite commutative semigroups S such that ev- ery proper homomorphic image of S is of smaller cardinality than S. We call such semigroups H-smaller. Surprisingly, the H-smaller semigroups are precisely those in Jensen and Miller's Theorem. As part of the proof of this fact we also generalize the exercise in Kaplansky by showing that, if G is an infinite commutative group, then every proper homomorphic image of G is of smaller cardinality than G if and only if G is an infinite cyclic group. For any semigroup S let S 0 , S 1 , and S 0;1 denote S with zero adjoined, S with identity adjoined, and S with both zero and identity adjoined, respectively. The group of integers is denoted Z. The symbol N 0 stands for any subsemigroup of (N;+), the semigroup of positive integers under addition. We now state Jensen and Miller's theorem. Theorem 1 (2, Theorem 3). Let S be an infinite commutative semigroup. Then every proper homomorphic image of S is finite if and only if S is either Z, Z 0 , N 0 , (N 0 ) 0 , (N 0 ) 1 , or (N 0 ) 0;1 . We let jXj denote the cardinality of X for any set X. Throughout the rest of this note S will denote an infinite commutative H-smaller semigroup. Our result follows easily from the following lemmas, which are taken almost without change from (2).