• Communications of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.147-161
• /
• 2016

In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang [4], Zhang [31] and many others.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.1019-1045
• /
• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.2
• /
• pp.155-171
• /
• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• Journal of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.899-912
• /
• 2011

We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1331-1345
• /
• 2016

A K-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator K in Hilbert spaces. K-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a K-g-frame, which is different from a g-frame, is discussed. Several construction methods of K-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of K-g-frames are obtained.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.163-169
• /
• 2011

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.

• Kyungpook Mathematical Journal
• /
• v.58 no.4
• /
• pp.733-746
• /
• 2018

The concept of f-statistical convergence which is, in fact, a generalization of statistical convergence, has been introduced recently by Aizpuru et al. (Quaest. Math. 37: 525-530, 2014). The main object of this paper is to prove an f-statistical analog of the classical Korovkin type approximation theorem of Boyanov and Veselinov. It is shown that the f-statistical analog is intermediate between the classical theorem and its statistical analog. As an application, we estimate the rate of f-statistical convergence of the sequence of positive linear operators defined from $C^*[0,{\infty})$ into itself.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2018.05a
• /
• pp.157-157
• /
• 2018

A reliable and accurate downscaling model which can provide climate change information, obtained from global climate models (GCMs), at finer resolution has been always of great interest to researchers. In order to achieve this model, linear methods widely have been studied in the past decades. However, nonlinear methods also can be potentially beneficial to solve downscaling problem. Therefore, this study explored the applicability of some nonlinear machine learning techniques such as neural network (NN), extreme learning machine (ELM), and ELM autoencoder (ELM-AE) as well as a linear method, least absolute shrinkage and selection operator (LASSO), to build a reliable temperature downscaling model. ELM is an efficient learning algorithm for generalized single layer feed-forward neural networks (SLFNs). Its excellent training speed and good generalization capability make ELM an efficient solution for SLFNs compared to traditional time-consuming learning methods like back propagation (BP). However, due to its shallow architecture, ELM may not capture all of nonlinear relationships between input features. To address this issue, ELM-AE was tested in the current study for temperature downscaling.

• Korean Journal of Mathematics
• /
• v.32 no.2
• /
• pp.219-228
• /
• 2024

In this paper, we compute the generalized 𝛼-Köthe Toeplitz duals of the X-valued (Banach space) difference sequence spaces E(X, ∆), E(X, ∆_𝜐) and obtain a generalization of the existing results for 𝛼-duals of the classical difference sequence spaces E(∆) and E(∆_𝜐) of scalars, E ∈ {ℓ_∞, c, c₀}. Apart from this, we compute the generalized 𝛼-Köthe Toeplitz duals for E(X, ∆^r) r ≥ 0 integer and observe that the results agree with corresponding results for scalar cases.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
• /
• 2004.10a
• /
• pp.27-40
• /
• 2004

When we derive multi-scale databases from a source spatial database, thegeometries and topological relations in the source database are transformed according to a predefined set of constraints. This means that the derived databases should be checked to see if the constraints are respected during the construction or updates of databases and to maintain the consistency of multi-scale databases. In this paper, we focus on the topological consistency between the source and derived databases, which is one of the important constraints to respect. In particular, we deal with the method of assessment of topological consistency, when 2-dimensional objects are collapsed to 1-dimensional ones. We introduce eight types of topological relations between 2-dimensional objects and 19 topological ones between 1-dimensional objects and propose four different strategies to convert 2-dimensional topological relations in the source database to 1-dimensional ones objects in the target database. With these strategies, we guarantee the topological consistency between multi-scale databases.