Abstract
In this study, we prove some convergence results for generalized \(\alpha \)-Reich–Suzuki non-expansive mappings via a fast iterative scheme. We validate our result by constructing a numerical example. Also, we compare our results with the other well known iterative schemes. Finally, we calculate the approximate solution of nonlinear fractional differential equation.
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Acknowledgements
Authors are very thankful to both the learned referees for pointing out many omissions and valuable comments. The first author is indebted to Dr. Faeem Ali for his all out help. The first author is grateful to University Grants Commission, India for providing financial assistance in the form of the Junior Research Fellowship.
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Khatoon, S., Uddin, I. & Baleanu, D. Approximation of fixed point and its application to fractional differential equation. J. Appl. Math. Comput. 66, 507–525 (2021). https://doi.org/10.1007/s12190-020-01445-1
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DOI: https://doi.org/10.1007/s12190-020-01445-1
Keywords
- Generalized \(\alpha \)-Reich–Suzuki non-expansive mappings
- Nonlinear fractional differential equation
- Fixed point