• Honam Mathematical Journal
• /
• v.29 no.3
• /
• pp.455-464
• /
• 2007

We consider existence theorems for a new class of mixed vector F-implicit complementarity problems and the corresponding mixed vector F-implicit variational inequality problems.

• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.401-410
• /
• 2007

Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.779-789
• /
• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• The Pure and Applied Mathematics
• /
• v.20 no.1
• /
• pp.51-57
• /
• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• East Asian mathematical journal
• /
• v.26 no.3
• /
• pp.389-395
• /
• 2010

In this paper, a class of g-demi-pseudomonotone mappings is introduced and the solvability of a class of generalized vector F-complementarity problems with the mappings in Banach spaces is considered.

• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.165-171
• /
• 2021

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.531-538
• /
• 2014

Concentric hyperspheres in the n-dimensional Euclidean space $\mathbb{R}^n$ are the level hypersurfaces of a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$. The magnitude $||{\nabla}f||$ of the gradient of such a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ is a function of the function f. We are interested in the converse problem. As a result, we show that if the magnitude of the gradient of a function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with isolated critical points is a function of f itself, then f is either a radial function or a function of a linear function. That is, the level hypersurfaces are either concentric hyperspheres or parallel hyperplanes. As a corollary, we see that if the magnitude of a conservative vector field with isolated singularities on $\mathbb{R}^n$ is a function of its scalar potential, then either it is a central vector field or it has constant direction.

• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.237-251
• /
• 2011

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We dene the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

• Journal of Power Electronics
• /
• v.11 no.6
• /
• pp.846-855
• /
• 2011

This paper proposes a control mode switching scheme between vector control and constant V/f control for induction machine (IM) drives for maximum torque utilization in a higher speed region. For the constant V/f scheme, a smooth transition method from the linear range of PWM up to the six-step mode is applied, by which the machine flux and torque can be kept constant in a high-speed range. Also, a careful consideration of the initial phase angle of the voltage in the transient state of the control mode change between the vector control and V/f schemes is described. The validity of the proposed strategy is verified by the experiment result for a 3-kW induction motor drives.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.393-400
• /
• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)