Certain first-order iterative methods for mixed variational inequalities in a Hilbert space

2011 ◽  
Vol 51 (5) ◽  
pp. 713-721
Author(s):  
I. P. Ryazantseva
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Iterative Methods ◽  
First Order ◽  
Mixed Variational Inequalities

scholarly journals Iterative methods for solving extended general mixed variational inequalities

2011 ◽  
Vol 62 (2) ◽  
pp. 804-813 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Saleem Ullah ◽  
Khalida Inayat Noor ◽  
Eisa Al-Said
Keyword(s):  
Variational Inequalities ◽  
Iterative Methods ◽  
Mixed Variational Inequalities

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

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