• Communications of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.247-258
• /
• 2007

In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.

• Speech Sciences
• /
• v.13 no.1
• /
• pp.117-128
• /
• 2006

The two-channel Generalized Sidelobe Canceller (GSC) scheme suffers from the presence of leakage signal in the reference channel. The leakage signal is caused by the dissimilar impulse responses between microphones, and different paths from speech source to microphones. Such leakage is detrimental to speech enhancement of the GSC since the desired reference signal becomes corrupted. In order to suppress the signal leakage, two matrix injection methods are proposed. In the first method, a simple gain compensation matrix is used. In the second, a projection matrix for reducing the error between the actual and the ideal primary and reference signals, is used. This paper describes the performance degradation resulting from leakage, and proposes effective methods to resolve the problem. Representative experiments were conducted to demonstrate the effectiveness of the proposed methods on recorded speech and noise in an actual automobile environment.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.431-440
• /
• 2009

In this paper, we introduce and consider a new system of relaxed cocoercive variational inequalities involving three different operators and the concept of projective nonexpansive mapping. Base on the projection technique, we suggest two kinds of new iterative methods for the approximate solvability of this system. The results presented in this paper extend and improve the main results of [S.S. Chang, H.W.J. Lee, C.K. Chan, Generalized system for relaxed co coercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329-334] and [Z. Huang, M. Aslam Noor, An explicit projection method for a system of nonlinear variational inequalities with different ($\gamma,r$)-cocoercive mappings, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.01.032].

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.885-894
• /
• 2009

In this paper, we consider a hybrid projection algorithm for a pair of inverse-strongly monotone mappings and a quasi-$\phi4-nonexpansive mapping. Strong convergence theorems are established in the framework of Banach spaces.

• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.561-567
• /
• 2012

The approximate solvability of a generalized system for relaxed cocoercive extended general variational inequalities is studied by using the project operator technique. The results presented in this paper are more general and include many previously known results as special cases.

• Korean Journal of Mathematics
• /
• v.15 no.2
• /
• pp.135-148
• /
• 2007

We prove the stability of generalized Jensen's equations in a Hilbert module over a unital $C^*$-algebra. This is applied to show the stability of a projection, a unitary operator, a self-adjoint operator, a normal operator, and an invertible operator in a Hilbert module over a unital $C^*$-algebra.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.89-98
• /
• 1999

We propose some new iterative methods for solving the generalized variational inequalities where the underlying operator T is monotone. These methods may be viewed as projection-type meth-ods. Convergence of these methods requires that the operator T is only monotone. The methods and the proof of the convergence are very simple. The results proved in this paper also represent a signif-icant improvement and refinement of the known results.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.515-531
• /
• 1997

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.6
• /
• pp.1355-1375
• /
• 2021

The n-dimensional generalized Hartogs triangles ℍⁿ_𝐩 with n ≥ 2 and 𝐩 := (p₁, …, p_n) ∈ (ℝ⁺)ⁿ are the domains defined by ℍⁿ_𝐩 := {z = (z₁, …, z_n) ∈ ℂⁿ : |z₁|^p₁ < ⋯ < |z_n|^p_n < 1}. In this paper, we study the L^p Sobolev mapping properties for the Bergman projections on the n-dimensional generalized Hartogs triangles ℍⁿ_𝐩, which can be viewed as a continuation of the work by S. Zhang in [25] and a higher-dimensional generalization of the work by L. D. Edholm and J. D. McNeal in [16].

• Communications for Statistical Applications and Methods
• /
• v.15 no.5
• /
• pp.667-674
• /
• 2008

We develop new family of the t distributions for modeling semicircular data. It has convenient mathematical features. It is extended to the l-axial t distribution and a generalized semicircular t distribution.