Some New Classes of General Harmonic-like Nonlinear Equations
References
- F. Al-Azemi, O. Calin, Asian options with harmonic average, Appl. Math. Inform. Sci., vol. 9, 2015, 1-9.
- G. D. Anderson, M. K. Vamanamurthy, M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl., vol. 335, no. 2, 2007, 1294-1308.
- K. Ashish, M. Rani, R. Chugh, Julia sets and Mandelbrot sets in Noor orbit, Appl. Math. Comput., vol. 228, no. 1, 2014, 615-631.
- Ashish, J. Cao, M. A. Noor, Stabilization of fixed points in chaotic maps using Noor orbit with applications in cardiac arrhythmia, J. Appl. Anal. Computation, vol. 13, no. 5, 2023, 2452-2470.
- Ashish, R. Chugh, M. Rani, Fractals and Chaos in Noor Orbit: a four-step Feedback Approach, Lap Lambert Academic Publishing, Saarbrucken, Germany, 2021.
- A. Barbagallo, S. G. Lo Bainco, A random elastic traffic equilibrium problem via stochastic quasi-variational inequalities, Commun. Nonlin. Sci. Numer. Simul. vol. 131, 2024, 107798.
- R. L. Burden, J. D. Faires, Numerical Analysis, 9 th Edition, Brooks-Cole, Boston, MA, USA, 2005.
- C. Chairatsiripong, T. Thianwan, Novel Noor iterations technique for solving nonlinear equations, AIMS Math., vol. 7, no. 6, 2022, 10958-10976.
- G. Cristescu, L. Lupsa, Non-Connected Convexities and Applications, Kluwer Academic Publishers, Dordrecht, Holland, 2002.
- P. Dupuis, A. Nagurney, Dynamical systems and variational inequalities, Annals Oper. Research, vol. 44, 1993, 7-42.
- A. S. Householder, The Numerical Treatment of a Single Nonlinear Equation, McGraw-Hill, New York, USA, 1970.
- A. G. Khan, M. A. Noor, K. I. Noor, Dynamical systems for general quasi variational inequalities, Annal. funct. Analysis, vol. 6, no. 1, 2015, 193-209.
- Y. C. Kwuni, A. A. Shahid, W. Nazeer, S. I. Butt, M. Abbas, S. M. Kang, Tri-corns and multicorns in Noor Orbit with s-convexity, IEEE Access, vol. 7, 2019, DOI − 10.1109/ACCESS.2019.2928796.
- A. Nagurney, D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications, Kluwer Academic Publishers, Boston, Dordrecht, London 1996.
- C. P. Niculescu, L. E. Persson, Convex Functions and Their Applications, Springer-Verlag, New York, 2018.
- K. I. Noor M. A. Noor, S. Momani, Modified Householder iterative method for nonlinear equations, Appl. Math. Computation, vol. 190, 2007, 1534-1539.
- M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., vol. 251, 2000, 217-230.
- M. A. Noor, Some dvelopments in general variational inequalites, Appl. Math. Comput., vol. 152, 2004, 199-277.
- M. A. Noor, Stability of the modified projected dynamical systems, Computers Math. Appl. vol. 44, 2002, 1-5.
- M. A. Noor, New classes of itertaive methods for nonlinear equations, Appl. Math. Comput., 191, 2007, 128-131.
- M. A. Noor, K. I. NoorIterative schemes for solving nonlinear equations, Appl. Math. Comput., vol. 183, 2006, 774-779.
- M. A. Noor, K. I. Noor, Some new iterative schemes for solving general quasi variational inequalities, Le Matematiche, vol. 79, no. 2, 2024, 327-370.
- M. A. Noor, K. I. Noor, Some novel aspects and applications of Noor iterations and Noor orbits, J. Advan. Math. Stud., vol. 17, no. 3, 2024, 276-284.
- M. A. Noor, K. I. Noor, New iterative methods for solving general harmoniclike variational inequalities, Inter. J. Value Engineer., vol. 2, no. 1, 2025, doi : https://doi.org/10.59429/ijve.v2i1.9171
- M. A. Noor, K. I. Noor, K. Kankam, On a new generalization of the Lax-Milgram Lemma, Earth. J. Mah. Sci., vol. 15, no. 1, 2025, 23-34.
- M. A. Noor, K. I. Noor, Some new classes of general harmonic-like variational inequalities, Earth. J. Math. Sci., vol. 15, no. 6, 2025, 951-988.
- , M. A. Noor, K. I. Noor, General hamonic-like variational inequalities, U.P.B. Sci. Bull., Series A, vol. 87, no. 3, 2025, 49-58.
- M. A. Noor, K. I. Noor, M. Th. Rassias, New trends in general variational inequalities, Acta Appl. Mathematica, vol. 170, no. 1, 2020, 981-1064.
- P. Paimsangan, T. Thianwan, Signal recovery and polynomiographic visualization of modified Noor iteration of operators with property(E), Demonst. Math., vol. 57, 2024.
- S. Suantai, M. A. Noor, K. Kankam, P. Cholamjiak, Novel forward-backward algorithms for optimization and applications to compressive sensingand image inpainting, Advan. Differ. Eqs., 2021, Id-265, doi : 10.1186/s13662−021−03422−9.
- J. F. Traub, Iterative Methods for Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, USA, 1964.
- P. T. Vuong, X. He, D. V. Thong, Global exponential stability of a neural network for inverse variational inequalities, J. Optim. Theory Appl., vol. 190, 2021, 915-930.
- Y. S. Xia, J. Wang, A recurrent neural network for solving linear projection equations, Neural Network, vol. 13, 2000, 337-350.
- Y. S. Xia, J. Wang, On the stability of globally projected dynamical systems, J. Optim. Theory Appl., vol. 106, 2000, 129-150.
- A. Yadav, K. Jha, Parrondo ’ s paradox in the Noor logistic map, Int. J. Adv. Research Eng.Technology, vol. 7, no. 5, 2016, 01-06.
Language: English
Page range: 17 - 35
Submitted on: May 2, 2025
Accepted on: Aug 24, 2025
Published on: Apr 8, 2026
Published by: Lucian Blaga University of Sibiu
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2026 Muhammad Aslam Noor, Khalida Inayat Noor, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.