Generalization of Fixed Point Approximation of Contraction and Suzuki Generalized Non-Expansive Mappings in Banach Domain

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-20-2022-65
Published: Dec 6, 2022
Cite as:
N. Muhammad, A. Asghar, M. Aslam, S. Irum, M. Iftikhar, M. M. Abbas, A. Qayyum, Generalization of Fixed Point Approximation of Contraction and Suzuki Generalized Non-Expansive Mappings in Banach Domain, Int. J. Anal. Appl., 20 (2022), 65.

Main Article Content

N. Muhammad, A. Asghar, M. Aslam, S. Irum, M. Iftikhar, M. M. Abbas, A. Qayyum

Abstract

By principal motivation from the results of the new iterative scheme that produces faster results than K-iteration. In this article, we study generalized results by a new iteration scheme to approximate fixed points of generalized contraction and Suzuki non-expansive mappings. We establish strong convergence results of generalized contraction mappings of closed convex Banach space and also deduce data dependent results. Furthermore, we prove some weak and strong convergence theorems in the sense of generalized Suzuki non-expansive mapping by applying condition (C).

Article Details

References

  1. A. Asghar, A. Qayyum, N. Muhammad, Different Types of Topological Structures by Graphs, Eur. J. Math. Anal. 3 (2022), 3. https://doi.org/10.28924/ada/ma.3.3.
  2. F.e. Browder, Nonexpansive Nonlinear Operators in a Banach Space, Proc. Natl. Acad. Sci. U.S.A. 54 (1965), 1041–1044. https://doi.org/10.1073/pnas.54.4.1041.
  3. T. Suzuki, Fixed Point Theorems and Convergence Theorems for Some Generalized Nonexpansive Mappings, J. Math. Anal. Appl. 340 (2008), 1088–1095. https://doi.org/10.1016/j.jmaa.2007.09.023.
  4. J. Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed Point Theory for a Class of Generalized Nonexpansive Mappings, J. Math. Anal. Appl. 375 (2011), 185–195. https://doi.org/10.1016/j.jmaa.2010.08.069.
  5. V.K. Sahu, H.K. Pathak, R. Tiwari, Convergence Theorems for New Iteration Scheme and Comparison Results, Aligarh Bull. Math. 35 (2016), 19-42.
  6. W. Kassab, T. Turcanu, Numerical Reckoning Fixed Points of (%E)-Type Mappings in Modular Vector Spaces, Mathematics, 7 (2019), 390. https://doi.org/10.3390/math7050390.
  7. S. Dhompongsa, W. Inthakon, A. Kaewkhao, Edelstein’s Method and Fixed Point Theorems for Some Generalized Nonexpansive Mappings, J. Math. Anal. Appl. 350 (2009), 12–17. https://doi.org/10.1016/j.jmaa.2008.08.045.
  8. J. Garcia-Falset, E. Llorens-Fuster, T. Suzuki, Fixed Point Theory for a Class of Generalized Nonexpansive Mappings, J. Math. Anal. Appl. 375 (2011), 185–195. https://doi.org/10.1016/j.jmaa.2010.08.069.
  9. I. Uddin, M. Imdad, J. Ali, Convergence Theorems for a Hybrid Pair of Generalized Nonexpansive Mappings in Banach Spaces, Bull. Malays. Math. Sci. Soc. 38 (2014), 695–705. https://doi.org/10.1007/s40840-014-0044-6.
  10. M. De la Sen, M. Abbas, On Best Proximity Results for a Generalized Modified Ishikawa’s Iterative Scheme Driven by Perturbed 2-Cyclic Like-Contractive Self-Maps in Uniformly Convex Banach Spaces, J. Math. 2019 (2019), 1356918. https://doi.org/10.1155/2019/1356918.
  11. N. Muhammad, A. Asghar, S. Irum, A. Akgül, E.M. Khalil, M. Inc, Approximation of Fixed Point of Generalized Non-Expansive Mapping via New Faster Iterative Scheme in Metric Domain, AIMS Math. 8 (2023), 2856–2870. https://doi.org/10.3934/math.2023149.
  12. Z. Opial, Weak Convergence of the Sequence of Successive Approximations of Non-Expansive Mappings, Bull. Amer. Math. Soc. 73 (1967), 595-597.
  13. J. Schu, Weak and Strong Convergence to Fixed Points of Asymptotically Nonexpansive Mappings, Bull. Austral. Math. Soc. 43 (1991), 153–159. https://doi.org/10.1017/s0004972700028884.
  14. H.F. Senter, W.G. Dotson, Approximating Fixed Points of Nonexpansive Mappings, Proc. Amer. Math. Soc. 44 (1974), 375–380. https://doi.org/10.1090/s0002-9939-1974-0346608-8.
  15. S.M. Soltuz, Data Dependence of Mann Iteration, Octogon Math. Mag. 9 (2001), 825-828. https://dl.acm.org/doi/10.5555/605858.605878.
  16. V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, (2007).
  17. A. Qayyum, A weighted Ostrowski-Grüss Type Inequality of Twice Differentiable Mappings and Applications, Int. J. Math. Comput. 1 (2008), 63-71.
  18. M.M. Saleem, Z. Ullah, T. Abbas, M.B. Raza, A. Qayyum, A New Ostrowski’s Type Inequality for Quadratic Kernel, Int. J. Anal. Appl. 20 (2022), 28. https://doi.org/10.28924/2291-8639-20-2022-28.
  19. T. Hussain, M.A. Mustafa, A. Qayyum, A New Version of Integral Inequalities of a Linear Function of Bounded Variation, Turk. J. Inequal. 6 (2022), 7-16.
  20. J. Amjad, A. Qayyum, S. Fahad, M. Arslan, Some New Generalized Ostrowski Type Inequalities With New Error Bounds, Innov. J. Math. 1 (2022), 30–43. https://doi.org/10.55059/ijm.2022.1.2/23.