Showing papers in "Kyungpook Mathematical Journal in 2009"
TL;DR: In this article, some coecient estimates in the subclass SL ⁄ of strongly starlike functions deflned by a certain geometric condition are considered. But they do not consider the case where the functions are strongly star-like.
Abstract: In this paper we consider some coe-cient estimates in the subclass SL ⁄ of strongly starlike functions deflned by a certain geometric condition.
65 citations
TL;DR: Theorem 1.1 (Hardy-Littlewood-Sobolev inequality as discussed by the authors for 1 < p < n, where p is the number of vertices in the Riesz potential.
Abstract: . Let T ˆ be the generalized fractional integral operator associated to a functionˆ: (0;1) !(0;1), as de ned in [16]. For a function Won R n , we shall be interested inthe boundedness of the multiplication operator f7!WT ˆ fon generalized Morrey spaces.Under some assumptions on ˆ, we obtain an inequality for WT ˆ , which can be viewed asan extension of Olsen’s and Kurata-Nishigaki-Sugano’s results. 1. IntroductionFor 0 <
59 citations
TL;DR: In this paper, the authors define the weighted geometric mean as an extension of the geometric mean of two operators for three positive operators, in particular, for all integers by induction, and define reasonable geometric means of k operators by induction.
Abstract: Based on Ricatti equation for two (positive invertible) operators A and B which has the geometric mean as its solution, we consider a cubic equation for A, B and C. The solution X = is a candidate of the geometric mean of the three operators. However, this solution is not invariant under permutation unlike the geometric mean of two operators. To supply the lack of the property, we adopt a limiting process due to Ando-Li-Mathias. We define reasonable geometric means of k operators for all integers by induction. For three positive operators, in particular, we define the weighted geometric mean as an extension of that of two operators.
28 citations
TL;DR: In this paper, the uniqueness problems of meromorphic functions that share a small function with one of their derivatives are investigated, and some results to improve some previous results are given. But the results are limited.
Abstract: In this paper, we investigate uniqueness problems of meromorphic functions that share a small function with one of their derivatives, and give some results to improve some previous results.
20 citations
TL;DR: In this article, the uniqueness problem on entire functions sharing one value was studied, and the authors improved and generalized some previous results of Zhang and Lin (11), and relaxed the nature of sharing value from CM to IM.
Abstract: In this paper, we study the uniqueness problems on entire functions sharing one value. We improve and generalize some previous results of Zhang and Lin (11). On the one hand, we consider the case for some more general differential polynomials (f n P (f )) (k) where P (w) is a polynomial; on the other hand, we relax the nature of sharing value from CM to IM.
20 citations
TL;DR: In this article, the authors define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and consider invariant, non-invariant and anti-inverse hypersurfaces of an almost RiemANNian manifold endowed with such a connection.
Abstract: We define a quarter symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection.
19 citations
TL;DR: In this article, the authors considered φ conformally at, conharmonically at, projectively at and concircularly at Lorentzian α Sasakian manifolds.
Abstract: In this study we consider φ conformally at, φ conharmonically at, φ projectively at and φ concircularly at Lorentzian α Sasakian manifolds. In all cases, we get the manifold will be an η Einstein manifold.
18 citations
TL;DR: In this paper, the existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example.
Abstract: The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.
18 citations
TL;DR: By introducing a parameter and estimating the weight coefficient, a new Hilbert-type integral inequality with a composite kernel and a best constant factor was obtained in this article, where the authors also considered its equivalent forms and reverse forms.
Abstract: By introducing a parameter and estimating the weight coefficient, we obtain a new Hilbert-type integral inequality with a composite kernel and a best constant factor. As applications, we also consider its equivalent forms and reverse forms.
17 citations
TL;DR: In this paper, the authors established a new method to prove Hyers-Ulam-Rassias stability of the quartic functional equation f(2x + y) + f( 2x y + 6f(y) = 4(f(x+ y)+ f(x y) plus 6 f(y)) in non-Archimedean normed linear spaces.
Abstract: We establish a new method to prove Hyers-Ulam-Rassias stability of the quartic functional equation f(2x + y) + f(2x y) + 6f(y) = 4(f(x + y) + f(x y) + 6f(x)) in non-Archimedean normed linear spaces.
17 citations
TL;DR: In this paper, the authors derived several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V(q 3) and also established some explicit evaluations using the values of remarkable product of theta-function.
Abstract: On page 366 of his lost notebook 15, Ramanujan recorded a cubic contin- ued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V (q 3) and also establish some explicit evaluations using the values of remarkable product of theta-function.
TL;DR: In this article, the signless Laplacian spectral radius of unicyclic graphs with a prescribed number of pendant vertices or independence number was studied. And the extremal graphs were characterized completely.
Abstract: In this paper, we study the signless Laplacian spectral radius of unicyclic graphs with prescribed number of pendant vertices or independence number. We also characterize the extremal graphs completely.
TL;DR: In this article, the uniqueness of meromorphic as well as entire functions has been studied, and some results related to the uniqueness and uniqueness of entire functions have been proved, which will improve and supplement several known results.
Abstract: In the paper we prove some results related to the uniqueness of meromorphic as well as entire functions. Our results will improve and supplement several known results .
TL;DR: A comprehensive family of harmonic univalent functions which contains various well-known classes of harmonicunivalent functions as well as many new ones is introduced and studied.
Abstract: In this paper, we introduce and study a comprehensive family of harmonic univalent functions which contains various well-known classes of harmonic univalent functions as well as many new ones. Also, we improve some results obtained by Frasin [3] and obtain coefficient bounds, distortion bounds and extreme points, convolution conditions and convex combination are also determined for functions in this family. It is worth mentioning that many of our results are either extensions or new approaches to those corresponding previously known results.
TL;DR: In this paper, it was shown that the class of commutative semirings S such that S has nonzero characteristic and every zero-divisor of S is nilpotent can be partitioned into zerosumfree semidomains and rings.
Abstract: . In this article, we generalize a well-known result of Hebisch and Weinert thatstates that a finite semidomain is either zerosumfree or a ring. Specifically, we show thatthe class of commutative semirings S such that S has nonzero characteristic and everyzero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. Inaddition, we demonstrate that if S is a finite commutative semiring such that the set ofzero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpo-tent or S must be a ring. An example is given to establish the existence of semirings in thislatter category with both nontrivial zero-sums and zero-divisors that are not nilpotent. 1. IntroductionThis article is devoted to an exploration of how ideal-theoretic considerations incommutative semirings, particularly finite commutative semirings, impact the mul-tiplicative behavior of those elements of the semiring that have additive inversesin the semiring. The general question as to the algebraic nature of these so-called“zero-sums” of a semiring is one of the most central in the theory of semirings. Weare especially motivated by a result of Hebisch and Weinert [9, Corollary 3.4, p. 81]that establishes that the class of finite semidomains can be partitioned by the an-tipodal properties of being zerosumfree (that is, only the zero element is a zero-sumof the semiring) and being a ring (where, by definition, every element is a zero-sumof the semiring). Of course, there exist infinite semidomains with nontrivial zero-sums that are not rings; for example, the polynomial semiring XZ[X] + N, where
TL;DR: In this paper, the Stancu and Post-Widder operators have been shown to have better approximation properties than the classical post-widder operator and post-stancu operator in polynomial weighted spaces.
Abstract: . In the papers [5]-[7] was examined approximation of functions by the modi edSzasz-Mrakyan operators and other positive linear operators preserving e 2 (x) = x 2 : In thispaper we introduce the Post-Widder and Stancu operators preserving x 2 in polynomialweighted spaces. We show that these operators have better approximation properties thanclassical Post-Widder and Stancu operators. 1. Introduction1.1. The Post-Widder operators(1) P n (f;x) P n (f(t);x) :=Z 10 f(t)p n (x;t)dt; x 2I; n 2N;(2) p n (x;t) :=(n=x) n t n 1 (n 1)!expntx;I = (0;1), N = f1;2;g , were examined in many papers and monographs (e.g.[4]) for real-valued functions f bounded on I. It is known ([4], Chapter 9) that P n are well de ned also for functions e k (x) = x k , k 2N 0 = N [f0g, and(3) P n (e 0 ;x) = 1; P n (e 1 ;x) = x; P n (e 2 ;x) =n+ 1nx 2 and generally(4) P n (e k ;x) =n(n+ 1) (n+ k k1)xn k ; k 2N; Corresponding author.Received 19 June 2007; accepted 23 October 2007.2000 Mathematics Subject Classi cation: 41A25, 41A36.Key words and phrases: Post-Widder operator, Stancu operator, polynomial weightedspace, approximation theorem.
TL;DR: In this paper, the Riccati inequality was generalized to the algebraic case, where the geometric mean is the unique positive de nite solution of (1) XB 1 X TX XT = C for positive operators B; C and arbitrary T.
Abstract: . We show that for an algebraic Riccati equation X B 1 X T X X T = C,its solutions are given by X = W + BT for some solution W of X B 1 X = C + T BT.To generalize this, we give an equivalent condition forB WW A 0 for given positiveoperators B and A, by which it can be regarded as Riccati inequality X B 1 X A.As an application, the harmonic mean B ! C is explicitly written even if B and C arenoninvertible. 1. IntroductionThe following equation is said to be the algebraic Riccati equation:(1) XB 1 X TX XT = Cfor positive de nite matrices B; C and arbitrary T. The simple case T = 0 in (1)(2) XB 1 X = Cis called the Riccati equation by several authors. It is known that the geometricmean B ] C is the unique positive de nite solution of (2), see [6] and [4]. RecallAndo’s de nition of it in terms of operator matrix [2]; for positive operators B; C Corresponding author.Received April 5, 2009; accepted May 4, 2009.2000 Mathematics Subject Classi cation: 47A63, 47A64, 47B15.Key words and phrases: Riccati equation, operator matrix, geometric mean and harmonicmean.
TL;DR: In this article, generalized ϕ-recurrent and concircular ϕrecurrent LP-Sasakian manifolds were studied, and generalized concircularity was considered.
Abstract: In this paper we studied generalized ϕ-recurrent and generalized concircular ϕ-recurrent LP-Sasakian manifolds.
TL;DR: In this article, a theorem dealing with local property of summability of factored Fourier series has been proved, which generalizes a result of Mazhar [8] and some new results have also been obtained.
Abstract: In the present paper, a theorem dealing with local property of summability of factored Fourier series which generalizes a result of Mazhar [8], has been proved. Some new results have also been obtained.
TL;DR: In this article, real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a certain cyclic condition are classified as hypersurface surfaces with Jacobi operators.
Abstract: We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies a certain cyclic condition.
TL;DR: In this article, it was shown that a direct summand of an SIP-extending module inherits this property under some conditions, and the question about direct summands of SIPextending modules is open.
Abstract: A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not neces- sarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about C11 and SIP-modules.
TL;DR: In this paper, the convergence of an iterated transform of a quasiaffine hyponormal operator converges to a normal operator under the strong operator topology for a bounded operator T = $U{\mid}T{mid}$ (polar decomposition).
Abstract: 【For a bounded operator T = $U{\mid}T{\mid}$ (polar decomposition), we consider a transform b $\widehat{T}$ = ${\mid ${\mid}T{\mid}U$ and discuss the convergence of iterated transform of $\widehat{T}$ under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.】
TL;DR: In this article, a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform which is also square integral is given.
Abstract: We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in .
TL;DR: In this paper, it was shown that the Mordell-weil group J(M) is the direct sum of a torsion group and a free Z-module of infinite rank.
Abstract: . Let J be the Jacobian variety of a hyperelliptic curve over Q. Let M be thefield generated by all square roots of rational integers over a finite number field K. Thenwe prove that the Mordell-Weil group J(M) is the direct sum of a finite torsion groupand a free Z-module of infinite rank. In particular, J(M) is not a divisible group. On theother hand, if Mf is an extension of M which contains all the torsion points of J over Q,then J(Mf sol )/J(Mf ) tors is a divisible group of infinite rank, where Mf sol is the maximalsolvable extension of Mf. 1. IntroductionLet K be a number field. Let A be a nonzero abelian variety defined over K.For an extension M over K, we denote the group of M-rational points by A(M)and its torsion subgroup by A(M) tors . We call A(M) is the Mordell-Weil group ofA over M. In [1], Frey and Jarden have asked whether the Mordell-Weil group ofevery nonzero abelian variety A defined over K has infinite Mordell-Weil rank overthe maximal abelian extension K ab of K. They proved that for elliptic curves Edefined over Q, the Mordell-Weil group E(Q
TL;DR: In this article, the authors give formulae for sums of products of two Horadam type generalized Fibonacci numbers with the same recurrence equation and with possibly different initial conditions.
Abstract: In this paper we give formulae for sums of products of two Horadam type generalized Fibonacci numbers with the same recurrence equation and with possibly different initial conditions. Analogous improved alternating sums are also studied as well as various derived sums when terms are multiplied either by binomial coefficients or by members of the sequence of natural numbers. These formulae are related to the recent work of Belbachir and Bencherif, erin and erin and Gianella.
TL;DR: In this article, the authors consider the case where the algebra of operators on a complex Banach space is an algebra, and define a mapping x! x from J(X) into itself by x = x 1 ix2 (= (x 1 +ix2) ): J(x) with the operator norm ||.
Abstract: Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h 2 B(X) : h is hermitian}, and J(X) = {x 2 B(X) : x = x1 + ix2,x1 and x2 2 H(X)}. Let a 2 B(B(X)) denote the derivation a(x) = ax xa. If J(X) is an algebra and a 1 (0) 1 a (0) for some a 2 J(X), then ||a|| || a (x x xx )|| for all x 2 J(X)\ a 1 (0). The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = Cp, the von Neumann-Schatten p-class, are considered. Then each x 2 J(X) has a unique representation x = x1 +ix2, x1 and x2 2 H(X), and we may define a mapping x ! x from J(X) into itself by x = x1 ix2 (= (x1 +ix2) ): J(X) with the operator norm ||.|| of B(X) is a complex Banach space such that is a continuous linear involution on J(X) (3, Lemma 8, Page 50). Recall that an operator a 2 B(X) is normal if a = a1 + ia2 2 J(X) and (a1,a2) = a1a2 a2a1 = 0. We say that an operator a 2 J(X) satisfies the PF- property, short for the Putnam-Fuglede property, if a 1 (0) a 1 (0). Normal operators satisfy the PF-property: if a = a1 +ia2 is normal, then ax = 0 implies a1x = a2x = 0 =) a x = 0 (4, Page 124). Let a 2 B(B(X)) denote the derivation a(x) = ax xa = (La Ra)x, where La and Ra denote, respectively, the operators of left multiplication and right multiplication by a. If a 2 H(X), then La, Ra and La Ra 2 H(X). Evidently, if a = a1 + ia2, then a = a1 + i a2 , where ( a1 , a2 ) = 0 whenever (a1,a2) = 0.
TL;DR: In this paper, the envelopes of homotopies were introduced to explain a dynamics on homotopy on the compact metric space, and it was shown that any -limit set, as well as any attractor, for an envelope of homotoopies is an empty set.
Abstract: This paper is indented to explain a dynamics on homotopies on the compact metric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes of flows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the ow geometry and the discrete geometry will be illustrated. In particular, it is shown that any -limit set, as well as any attractor, for an envelope of homotopies is an empty set (provided the homotopies that we treat are not trivial), whereas it is nonempty in general in discrete case.
TL;DR: In this article, the diameter of the boundary slope set of a Montesinos knot is given in terms of the minimal crossing numbers of the knots and the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.
Abstract: In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.
TL;DR: In this paper, a comprehensive class of starlike univalent functions de ned by Dziok-Srivastava operator is introduced, and necessary and sufficient bounds are given for functions in this class to be starlike.
Abstract: . A comprehensive class of starlike univalent functions de ned by Dziok-Srivastava operator is introduced. Necessary and sucient coecient bounds are givenfor functions in this class to be starlike. Further distortion bounds, extreme points andresults on partial sums are investigated. 1. IntroductionLet Adenote the class of functions of the form(1) f(z) = z+X 1n=2 a n z n which are analytic in the open unit disc U= fz: jzj<1g:Denote by Sthe subclassof Aconsisting functions normalized by f(0) = 0 = f 0 (0) 1 which are univalentin Uand STand CV the subclasses of Sthat are respectively, starlike and convex.Also denote by V;the class of analytic functions with varying arguments introducedby Silverman [13] consisting of functions fof the form (1) in Sfor which there existsa real number such that(2) n + (n 1)= ˇ(mod2ˇ);where arg(a n ) = n for all n 2:Goodman [4], [5] introduced and de ned the following subclasses of CV and ST:De nition 1. A function f(z) is uniformly convex (uniformly starlike) in Uif f(z)is in CV (ST) and has the property that for every circular arc contained in U;with center ˘also in U;the arc f() is convex (starlike) with respect to f(˘):The
TL;DR: In this paper, the authors introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence, respectively, and study their relations with shadowing property.
Abstract: In this paper we introduce the notions of strict persistence and weakly strict persistence which are stronger than those of persistence and weak persistence, respectively, and study their relations with shadowing property. In particular, we show that the weakly strict persistence and the weak inverse shadowing property are locally generic in Z(M).