• 대한수학회지
• /
• 제49권3호
• /
• pp.537-547
• /
• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• Korean Journal of Mathematics
• /
• 제23권2호
• /
• pp.249-257
• /
• 2015

For a positive integer k, an operator T is said to be k-quasi-*-paranormal if ${\parallel}T^{k+2}x{\parallel}{\parallel}T^kx{\parallel}{\geq}{\parallel}T^*T^kx{\parallel}^2$ for all x $\in$ H, which is a generalization of *-paranormal operator. In this paper, we give a necessary and sufficient condition for T to be a k-quasi-*-paranormal operator. We also prove that the spectrum is continuous on the class of all k-quasi-*-paranormal operators.

• 한국정보통신학회논문지
• /
• 제10권9호
• /
• pp.1612-1616
• /
• 2006

모바일 환경에서 지도 서비스를 위해서는 휴대 단말기의 제한된 자원을 고려한 접근방법 이 요구된다. 모바일 서비스 전용 지도 데이터 베이스를 별도로 개발하여 사용하지 않는다면 지도 데이터를 축소하여 휴대 단말기로 전송할 필요가 있다. 본 논문은 기존의 유선 지도 데이터 베이스로부터 검색한 지도를 휴대 단말기에 출력이 가능하도록 하는 필터링(filtering) 기법을 제안하고 성능을 평가한다. 이 필터링 기법은 지도 일반화(generalization) 기법의 'selection' 연산에 기반하여 휴대폰 환경에 적합하도록 변형 한 것이다.

• 대한수학회지
• /
• 제32권3호
• /
• pp.593-608
• /
• 1995

The study of self-adjoint operator algebras on Hilbert space is well established, with a long history including some of the strongest mathematicians of the twentieth century. By contrast, non-self-adjoint CSL-algebras, particularly reflexive algebras, are only begins to be studied by W. B. Wrveson [1] 1974.

• Korean Journal of Mathematics
• /
• 제32권2호
• /
• pp.297-314
• /
• 2024

Fractional integral operators have been studied extensively in the last few decades by various mathematicians, because it plays a vital role in the developments of new inequalities. The main goal of the current study is to establish some new Milne-type inequalities by using the special type of fractional integral operator i.e Caputo Fabrizio operator. Additionally, generalization of these developed Milne-type inequalities for s-convex function are also given. Furthermore, applications to some special means, quadrature formula, and q-digamma functions are presented.

• Kyungpook Mathematical Journal
• /
• 제47권3호
• /
• pp.311-322
• /
• 2007

This paper deals with space Beltrami system with three characteristic matrices in even dimensions, which can be regarded as a generalization of space Beltrami system with one and two characteristic matrices. It is transformed into a nonhomogeneous $p$-harmonic equation $d^*A(x,df^I)=d^*B(x,Df)$ by using the technique of out differential forms and exterior algebra of matrices. In the process, we only use the uniformly elliptic condition with respect to the characteristic matrices. The Lipschitz type condition, the monotonicity condition and the homogeneous condition of the operator A and the controlled growth condition of the operator B are derived.

• Kyungpook Mathematical Journal
• /
• 제58권3호
• /
• pp.489-494
• /
• 2018

The first purpose of this note is to generalize two nice theorems of H. J. Kim concerning hyperinvariant subspaces for certain classes of operators on Hilbert space, proved by him by using the technique of "extremal vectors". Our generalization (Theorem 1.2) is obtained as a consequence of a new theorem of the present authors, and doesn't utilize the technique of extremal vectors. The second purpose is to use this theorem to obtain the existence of hyperinvariant subspaces for a class of $2{\times}2$ operator matrices (Theorem 3.2).

• Journal of applied mathematics & informatics
• /
• 제41권6호
• /
• pp.1209-1225
• /
• 2023

In this paper, we defined some new classes of analytic functions in conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness and distortion for functions in these classes. It is important to mentioned that our results are generalization of number of existing results in the literature.

• 호남수학학술지
• /
• 제46권2호
• /
• pp.267-278
• /
• 2024

In this paper, we investigate the uniqueness of a meromorphic function f(z) and its difference polynomial of difference operator with two sharing values counting multiplicities. Our two results improve and generalize the recent results of Barki Mahesh, Dyavanal Renukadevi S and Bhoosnurmath Subhas S [4] and for the case q ≥ 2, this allows for a highly unique generalization. To further demonstrate the validity of our main result, we provide an example.

• Korean Journal of Mathematics
• /
• 제17권1호
• /
• pp.53-66
• /
• 2009

We show the existence of a nontrivial periodic solution for the superquadratic parabolic equation with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear term at infinity which have continuous derivatives. We use the critical point theory on the real Hilbert space $L_2({\Omega}{\times}(0 2{\pi}))$. We also use the variational linking theorem which is a generalization of the mountain pass theorem.