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Enlarging the ball of convergence of secant-like methods for non-differentiable operators
IOANNISK.ARGYROS,Hongmin Ren 대한수학회 2018 대한수학회지 Vol.55 No.1
In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using $\omega$-condition and centered-like $\omega$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.
A RELATIONSHIP BETWEEN THE LIPSCHITZ CONSTANTS APPEARING IN TAYLOR'S FORMULA
Ioannis K. Argyros,Hongmin Ren 한국수학교육학회 2011 純粹 및 應用數學 Vol.18 No.4
Taylor's formula is a powerful tool in analysis. In this study, we as-sume that an operator is m-times Fr¶echet-di®erentiable and satis¯es a Lipschitz condition. We then obtain some Taylor formulas using only the Lipschitz constants. Applications are also provided.
ON THE CONVERGENCE OF A NEWTON-LIKE METHOD UNDER WEAK CONDITIONS
Argyros, Ioannis K.,Ren, Hongmin Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.4
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.
Ioannis K. Argyros,Hongmin Ren 대한수학회 2017 대한수학회지 Vol.54 No.1
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 \cite{1,2,3,4,5,6,7,8,9,10,11,12,13}, \cite{21,22}. Numerical examples are provided to illustrate the theoretical results.
Argyros, Ioannis K.,Ren, Hongmin Korean Mathematical Society 2017 대한수학회지 Vol.54 No.1
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.
ENLARGING THE BALL OF CONVERGENCE OF SECANT-LIKE METHODS FOR NON-DIFFERENTIABLE OPERATORS
Argyros, Ioannis K.,Ren, Hongmin Korean Mathematical Society 2018 대한수학회지 Vol.55 No.1
In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.