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A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings

Author

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  • Thakur, Balwant Singh
  • Thakur, Dipti
  • Postolache, Mihai

Abstract

In this paper, we propose a new iterative algorithm to approximate fixed point of Suzuki’s generalized nonexpansive mappings. We establish some weak and strong convergence theorems in a uniformly convex Banach space. We also provide examples to illustrate the convergence behavior of the proposed algorithm.

Suggested Citation

  • Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:147-155
    DOI: 10.1016/j.amc.2015.11.065
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    Citations

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    Cited by:

    1. Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    2. Yuanheng Wang & Mingyue Yuan & Bingnan Jiang, 2021. "Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems," Mathematics, MDPI, vol. 9(13), pages 1-13, July.
    3. Hasanen A. Hammad & Habib ur Rehman & Manuel De la Sen, 2022. "A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations," Mathematics, MDPI, vol. 10(22), pages 1-26, November.
    4. Maryam Gharamah Alshehri & Faizan Ahmad Khan & Faeem Ali, 2022. "An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    5. Ali Abkar & Mohsen Shekarbaigi, 2017. "A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces," Mathematics, MDPI, vol. 5(1), pages 1-13, February.
    6. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    7. Javid Ali & Faeem Ali & Puneet Kumar, 2019. "Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    8. Konrawut Khammahawong & Parin Chaipunya & Kamonrat Sombut, 2022. "Approximating Common Fixed Points of Nonexpansive Mappings on Hadamard Manifolds with Applications," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    9. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    10. Usurelu, Gabriela Ioana & Turcanu, Teodor, 2021. "Best proximity points of (EP)-operators with qualitative analysis and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 215-230.
    11. Gdawiec, Krzysztof & Kotarski, Wiesław, 2017. "Polynomiography for the polynomial infinity norm via Kalantari’s formula and nonstandard iterations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 17-30.
    12. Austine Efut Ofem & Jacob Ashiwere Abuchu & Reny George & Godwin Chidi Ugwunnadi & Ojen Kumar Narain, 2022. "Some New Results on Convergence, Weak w 2 -Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces," Mathematics, MDPI, vol. 10(20), pages 1-26, October.
    13. Chanchal Garodia & Afrah A. N. Abdou & Izhar Uddin, 2021. "A New Modified Fixed-Point Iteration Process," Mathematics, MDPI, vol. 9(23), pages 1-10, December.
    14. Wissam Kassab & Teodor Ţurcanu, 2019. "Numerical Reckoning Fixed Points of ( ρE )-Type Mappings in Modular Vector Spaces," Mathematics, MDPI, vol. 7(5), pages 1-13, April.
    15. Mujahid Abbas & Muhammad Waseem Asghar & Manuel De la Sen, 2022. "Approximation of the Solution of Delay Fractional Differential Equation Using AA -Iterative Scheme," Mathematics, MDPI, vol. 10(2), pages 1-20, January.

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