• Journal of the Optical Society of Korea
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• v.5 no.3
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• pp.70-75
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• 2001

Next Generation Space Telescope (NGST) is under design study for proposed launch around 2008. It will take over the task of Hubble Space Telescope (HST) and provide much more detailed information about celestial objects. Present large telescopes both in space and on the ground contain aspheric mirrors, called Ritchey-Chretien type. As the size of the telescope becomes larger and the optical quality is requested to be higher, reaching the diffraction limit, more accurate optical testing methods are required. However, there are few testing methods which can achieve the required accuracy for aspheric optics, and none of them has achieved it with certainty. The failure of producing the primary mirror of the Hubble Space Telescope to meet specification is a good example. Moreover, testing aspheric mirrors of large convex form adds the difficulty to extreme. In this paper, space telescopes and large ground-based telescopes are surveyed and testing methods for aspheric optics are reviewed. a method of testing aspheric convex mirrors is suggested.

• East Asian mathematical journal
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• v.15 no.1
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• pp.19-28
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• 1999

• Bulletin of the Korean Space Science Society
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• 2004.10b
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• pp.67-67
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• 2004

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.83-95
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• 2014

In a uniformly convex Banach space, we introduce a iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings and utilize a new inequality to prove several convergence results for the iterative sequence. The results generalize and unify many important known results of relevant scholars.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.161-168
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• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• East Asian mathematical journal
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• v.26 no.1
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• pp.81-93
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• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.175-192
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• 2004

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's unique-ness theorem.