| Brief introduction |
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In future We have developed local as well as semi-local convergence analysis of third order iterative methods such as Chebyshev's, Chebyshev-Halley and modified Newton-like methods used to find zeros of non-linear operator equations in Banach spaces. For showing local and semi-local convergence of above mentioned methods we used new type of majorant conditions which were earlier introduced by Argyros and Ren (2012) and Ling and Xu (2014). Moreover, two particular cases of the convergence analysis namely under Kantorovich-type, Smale-type and Nesterov-Nemirovskii condition have also presented for both local and semi-local convergence analysis.
We will study convergence of another higher order iterative methods in Banach spaces by using majorant conditions, recurrence relations under different continuity conditions on the operator. We will also study local and semi-local convergence of these methods under Riemannian manifold settings. |
| Articles Published/ Accepted |
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Research publications
Articles in Journals (Published/ Accepted)
- Chandni Kumari & P. K. Parida, 2018. Local convergence analysis for Chebyshev's method, Journal of Applied Mathematics and Computing, 59 (1-2), 405-421. https://link.springer.com/article/10.1007/s12190-018-1185-9
- Swet Nisha, P. K. Parida & Chandni Kumari, 2019. Convergence of a Continuation method under majorant conditions, Korean Journal of Mathematics, 27 (4), 1005–1025. http://koreascience.or.kr/article/JAKO201908559988539.page
- Chandni Kumari and P. K. Parida, 2020. Convergence theorems of a new multiparametric family of Newton-like method in Banach spaces, International Journal of Nonlinear Analysis and Applications, Scopus, ESCI (Accepted).
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| Seminar/ Workshop/ Conference Participation |
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- 2nd Bi-Annual Conference of JSMS, Ranchi, November 21-23, 2015.
- Short Term Course on Dynamical System: Theory & Applications, organized by Department of Applied Mathematics, ISM, Dhanbad, India during June 26-30, 2016.
- Science & Technology Sensitization Programme for the Women, Leading Towards Entrepreneurship (STSP-2017), organized by CSIR-National Metallurgical Laboratory (NML) Jamshedpur, India during October 05-06, 2017.
- Referencing Tools, organized by central University of Jharkhand, Ranchi, India during November 27-28, 2017.
- Chandni Kumari and P. K. Parida: Local convergence of Chebyshev's method in Banach space under majorant condition, International Conference on Mathematical Sciences and Applications, organized by Guru Ghasidas Vishwavidyalaya, Bilaspur, India during February 23-25, 2018.
- Chandni Kumari and P. K. Parida: Convergence theorems for modified Newton's method in Banach Space, International Conference on Emerging Technologies, Systems & Applications, organized by Jharkhand Rai University, Ranchi, India during April 21-22, 2018.
- Chandni Kumari and P. K. Parida: Ball convergence theorems for Chebyshev's method in Banach space, International Conference on Mathematical Modelling and Scientific Computing, organized by Indian Institute of Technology Indore, Indore, India during July 19-21, 2018.
- One day workshop on Research Methodology and Latex Learning, organized by Central University of Jharkhand, during December 14, 2018.
- Chandni Kumari and P. K. Parida: The semilocal convergence behavior for Chebyshev's method, 34th Annual National Conference of The Mathematica Society Banaras Hindu University on Emerging Trends in Combinatorics and Its Application, organized by Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India during February 22-23, 2019.
- Advanced Training School on Numerical PDEs and inverse Problems (ATSNPDEIP-19), organized by Department of Mathematics and Statistics, Indian Institute of Technology Tirupati, Renigunta Road, Tirupati (AP),India during December 9-20, 2019.
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