• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.469-485
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• 2023

In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

• 대한수학회논문집
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• 제26권4호
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• pp.575-584
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• 2011

We provide a semilocal convergence analysis for a Newtonlike method under weak conditions in a Banach space setting. In particular, we only assume that the Gateaux derivative of the operator involved is hemicontinuous. An application is also provided.

• 대한수학회지
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• 제54권1호
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• pp.17-33
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• 2017

We present a new local as well as a semilocal convergence analysis for Steffensen's method in order to locate fixed points of operators on a Banach space setting. Using more precise majorizing sequences we show under the same or less computational cost that our convergence criteria can be weaker than in earlier studies such as [1-13], [21, 22]. Numerical examples are provided to illustrate the theoretical results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.283-287
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• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.207-215
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• 2006

Using more precise majorizing sequences than before [6], [10], [11], [14] we provide a finer semilocal convergence analysis for a certain class of Euler-Halley type methods for approximating a solution of an equation in a Banach space setting.

• East Asian mathematical journal
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• 제25권2호
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• pp.153-157
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• 2009

Motivated by optimization considerations we revisit the work by Dontchev in [7] involving the convergence of Newton's method to a solution of a generalized equation in a Banach space setting. Using the same hypotheses and under the same computational cost we provide a finer convergence analysis for Newton's method by using more precise estimates.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.219-230
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• 2011

We determine the radius of convergence for some Newton{type methods (NTM) for approximating a locally unique solution of an equation in a Banach space setting. A comparison is given between the radii of (NTM) and Newton's method (NM). Numerical examples further validating the theoretical results are also provided in this study.

• 한국콘텐츠학회논문지
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• 제6권5호
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• pp.29-34
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• 2006

본 연구에서는, Banach 공간의 값을 갖는 확률요소들의 합 $S_n=\sum_{i=1}^nV-i$ 수렴하는 경우에, Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$에 대한 대수의 법칙을 고찰하여 $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 확률변수들의 Tail 합과 확률요소들의 Tail 합에 대한 극한 성질의 유사성을 연구하여, Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 약 대수의 법칙과 하나의 수렴법칙이 동등함을 기술하는 기존의 정리를 다른 대체적인 방법으로 증명한다.

• 대한수학회보
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• 제30권2호
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• pp.201-212
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• 1993

It is our purpose in this paper to first establish an inequality in real uniformly smooth Banach spaces with modulus of smoothness of power type q > 1 that generalizes a well known Hilbert space inequality. Using our inequality, we shall then extend the above result of Qihou [15] on the Ishikawa iteration process from Hilbert spaces to these much more general Banach spaces. Furthermore, we shall prove that the Mann iteration process converges strongly to the unique fixed point of a quasi-contractive map in this general setting. No compactness assumption on K is required in our theorems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권1호
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• pp.35-45
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• 2008

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.