• East Asian mathematical journal
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• 제4권
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• pp.139-150
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• 1988

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.545-555
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• 2009

In this paper, we investigate a generalized family of complex-valued harmonic functions that are multivalent, sense-preserving, and are associated with k-uniformly harmonic functions in the unit disk. The results obtained here include a number of known and new results as their special cases.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.129-140
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• 2020

In this paper, we introduce an efficient algorithm for the non-convex penalized multinomial logistic regression that can be uniformly applied to a class of non-convex penalties. The class includes most non-convex penalties such as the smoothly clipped absolute deviation, minimax concave and bridge penalties. The algorithm is developed based on the concave-convex procedure and modified local quadratic approximation algorithm. However, usual quadratic approximation may slow down computational speed since the dimension of the Hessian matrix depends on the number of categories of the output variable. For this issue, we use a uniform bound of the Hessian matrix in the quadratic approximation. The algorithm is available from the R package ncpen developed by the authors. Numerical studies via simulations and real data sets are provided for illustration.

• 대한수학회보
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• 제49권4호
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• East Asian mathematical journal
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• 제6권1호
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• pp.9-28
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• 1990

• Kyungpook Mathematical Journal
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• 제34권1호
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• pp.11-19
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• 1994

• 대한수학회보
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• 제45권4호
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• pp.671-680
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• 2008

Necessary conditions for the existence of common fixed points for noncommuting mappings satisfying generalized contractive conditions in a Menger convex metric space are obtained. As an application, related results on best approximation are derived. Our results generalize various well known results.

• Korean Journal of Mathematics
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• 제18권2호
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• pp.105-118
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• 2010

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

• 대한수학회지
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• 제27권1호
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• pp.25-32
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• 1990

• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.189-193
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• 1978