• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.395-404
• /
• 2012

Our first aim of this paper is to define maximal operators a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ${\leq}$ a < $\infty$ by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.

• Journal of the Chungcheong Mathematical Society
• /
• v.1 no.1
• /
• pp.71-76
• /
• 1988

For each continuous convex function ${\phi}$ defined on an open convex subset $A_{\phi}$ of a Banach space X, if we define a positively homogeneous sublinear functional ${\sigma}_x$ on X by ${\sigma}_x(y)=\sup{\lbrace}f(y)\;:\;f{\in}{\partial}{\phi}(x){\rbrace}$, where ${\partial}{\phi}(x)$ is a subdifferential of ${\phi}$ at x, then we get the following characterization theorem of Gateaux differentiability (weak Asplund) sapce. THEOREM. For every ${\phi}$ above, $D_{\phi}={\lbrace}x{\in}A\;:\;\sup_{||u||=1}\;{\sigma}_x(u)+{\sigma}_x(-u)=0{\rbrace}$ contains dense (dense $G_{\delta}$) subset of $A_{\phi}$ if and only if X is a Gateaux differentiability (weak Asplund) space.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.13 no.4
• /
• pp.635-641
• /
• 2010

In this paper, we propose an efficient public key broadcast encryption system which can also extend traitor trace and revoke system. Although the proposed system has limited collusion size, the ciphertext size in the system can be sublinear in the number of total users, the private key size is constant, the computational cost can be sublinear and it can support black-box tracing algorithm, therefore, our system can be an option to applications where reducing the ciphertext size, private key size is a top priority. Furthermore, we can also apply our system to military document broadcast system, because it has such an efficient measurement.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.227-235
• /
• 2004

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.

• Journal of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.545-566
• /
• 1999

In this paper we describe normal quintic surfaces in P which are birationally isomorphic to Enriques surfaces. especially we characterize the sublinear systems which give rise to one of two Stagnaro's normal quintic surfaces in P3.

• Kyungpook Mathematical Journal
• /
• v.47 no.4
• /
• pp.569-578
• /
• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• East Asian mathematical journal
• /
• v.38 no.1
• /
• pp.33-41
• /
• 2022

In this paper, we study singular Dirichlet boundary value problems involving ϕ-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity f = f(u) has a positive falling zero and is either superlinear or sublinear at u = 0.

• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.241-258
• /
• 2006

This paper gives conditions under which necessary optimality conditions in a locally Lipschitz program can be expressed as the invexity of the active constraint functions or the type I invexity of the objective function and the constraint functions on the feasible set of the program. The results are nonsmooth extensions of those of Hanson and Mond obtained earlier in differentiable case.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.125-144
• /
• 2017

Three nontrivial nonnegative solutions for some critical quasilinear elliptic systems with lower-order negative perturbations are obtained by using the Ekeland's variational principle and the mountain pass theorem.

• East Asian mathematical journal
• /
• v.38 no.1
• /
• pp.13-20
• /
• 2022

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.