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Approximating fixed points of \(\left( \lambda ,\rho \right) \)-firmly nonexpansive mappings in modular function spaces

  • Safeer Hussain Khan
Open Access
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Abstract

In this paper, we first introduce an iterative process in modular function spaces and then extend the idea of a \(\lambda \)-firmly nonexpansive mapping from Banach spaces to modular function spaces. We call such mappings as \( \left( \lambda ,\rho \right) \)-firmly nonexpansive mappings. We incorporate the two ideas to approximate fixed points of \(\left( \lambda ,\rho \right) \) -firmly nonexpansive mappings using the above-mentioned iterative process in modular function spaces.

Mathematics Subject Classification

46A80 47H09 47H10 

Notes

References

  1. 1.
    Dehaish, B.A.B.; Kozlowski, W.M.: Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in modular function spaces. Fixed Point Theory Appl. 2012, 118 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Dhompongsa, S.; Benavides, T.D.; Kaewcharoen, A.; Panyanak, B.: Fixed point theorems for multivalued mappings in modular function spaces. Sci. Math. Jpn. 63(2), 161–169 (2006)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Khamsi, M.A.; Kozlowski, W.M.: Fixed Point Theory in Modular Function Spaces. Birkhauser, Basel (2015)CrossRefzbMATHGoogle Scholar
  4. 4.
    Khan, S.H.: A Picard-Mann hybrid iterative process. Fixed Point Theory Appl. 2013, 69 (2013).  https://doi.org/10.1186/1687-1812-2013-69 MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Khan, S.H.; Abbas, M.: Approximating fixed points of multivalued rho-nonexpansive mappings in modular function spaces. Fixed Point Theory Appl. 2014, 34 (2014)CrossRefzbMATHGoogle Scholar
  6. 6.
    Ruiz, D.A.; Acedo, G.L.; Marquez, V.M.: Firmly nonexpansive mappings. J. Nonlinear Convex Anal. 15(1), 61–87 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Schu, J.: Weak and strong convergence to fixed points of asymptotically non expansive mappings. Bull. Aust. Math. Soc. 43, 153–159 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Senter, H.F.; Dotson, W.G.: Approximating fixed points of nonexpansive mappings. Proc. Am. Math. Soc. 44(2), 375–380 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Thakur, B.S.; Thakur, D.; Postolache, M.: A new iterative scheme for numerical reckoning xed points of Suzuki’s generalized nonexpansive mappings. Appl. Math. Comput. 275, 147–155 (2016)MathSciNetGoogle Scholar
  10. 10.
    Thakur, B.S.; Thakur, D.; Postolache, M.: New iteration scheme for numerical reckoning xed points of nonexpansive mappings. J. Inequal. Appl. 2014, 328 (2014)CrossRefzbMATHGoogle Scholar
  11. 11.
    Yao, Y.; Postolache, M.; Liou, Y.C.; Yao, Z.: Construction algorithms for a class of monotone variational inequalities. Optim. Lett. 10(7), 1519–1528 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Yao, Y.; Agarwal, R.P.; Postolache, M.; Liu, Y.C.: Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem. Fixed Point Theory Appl. 2014, 183 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Yao, Y., Liou, Y.C., Postolache, M.: Self-adaptive algorithms for the split problem of the demicontractive operators. Optimization.  https://doi.org/10.1080/02331934.2017.1390747
  14. 14.
    Yao, Y.; Leng, L.; Postolache, M.; Zheng, X.: Mann-type iteration method for solving the split common fixed point problem. J. Nonlinear Convex Anal. 18(5), 875–882 (2017)MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and PhysicsQatar UniversityDohaQatar

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