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Kim, Jong-Kyu;Anh, Pham Ngoc;Hyun, Ho-Geun
- Bulletin of the Korean Mathematical Society
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- v.49 no.4
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- pp.749-759
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- 2012
A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, ${\nabla}({\parallel}x{\parallel}^2_M)$. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.
https://doi.org/10.4134/BKMS.2012.49.4.749 인용 PDF KSCI

Huang, Xingfeng;Li, Shiqi;An, Shuhua
- Research in Mathematical Education
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- v.16 no.3
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- pp.177-194
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- 2012
What strategies are used to help students understand quadratic functions in mathematics classroom? In specific, how does Chinese teacher highlight a connection between algebraic representation and graphic representation? From October to November 2009, an experienced teacher classroom was observed. It was found that when students started learning a new type of quadratic function in lessons, the teacher used two different teaching strategies for their learning: (1) Eliciting students to plot the graphs of quadratic functions with pointwise approaches, and then construct the function image in their minds with global approaches; and (2) Presenting a specific mathematical problem, or introducing conception to elicit students to conjecture, and then encouraging them to verify it with appoint approaches.
https://doi.org/10.7468/jksmed.2012.16.3.177 인용 PDF KSCI