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Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 162 - 174, 28.02.2020

Osman Alagoz Birol Gündüz Sezgin Akbulut

Abstract

References

  • Abbas, M. and Nazir, T. 2014. “A new faster iteration process applied to constrained minimization and feasibility problems”, Mathematificki Vesnik, 66(2), 223-234.
  • Agarwal, R. P., O'Regan, D. and Sahu, D.R. 2007. “Iteraitve construction of fixed points of nearly asymptotically nonexpansive mappings”, J. Nonlinear Convex Anal. 8 (1), 61-79.
  • Berinde, V. 2001. “Picard iteration converges faster than Mann iteration for a class of quasicontractive operators”, Fixed Point Theory and Applications, 2, 97-105.
  • Goebel, K. and Kirk, W.A. (1990). “Topic in Metric Fixed Point Theory”, Cambridge University Press.
  • Ishikawa, S., 1974. “Fixed points by a new iteration method”, Proc. Am. Math. Soc. 44, 147-150.
  • Karaca, N. and Yildirim, I. 2015. “Approximating fixed points of nonexpansive mappings by a faster iteration process”, J. Adv. Math. Stud. Vol. 8(2), 257-264.
  • Khan, S. H. 2013. “A Picard-Man hybrid iterative process”, Fixed Point Theory and appl., doi:10.1186/1687-1812-2013-69.
  • Mann, W. R. 1953. “Mean value methods in iteration”, Proc. Am. Math. Soc. 4, 506-510.
  • Noor, M. A. 2000. “New approximation schemes for general variational inequalities”, Journal of Mathematical Analysis and Applicaitons, 251(1), 217-229.
  • Opial, Z. 1967. “Weak convergence of the sequence of successive approximations for nonexpansive mappings”, Bull. Am. Math. Soc. 73, 595-597.
  • Picard, E., 1890. “Memoire sur la theorie des equation aux derivees partielles la methode des approximations successives”, J. Math. Pures Appl. 6, 145-210.
  • Phuengrattana, W. 2011. “Approximating fixed points of Suzuki-generalized nonexpansive mappings”, Nonlinear Anal. Hybrid Syst. 5(3), 583-590.
  • Schu, J. 1991. “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings”, Bull. Aust. Math. Soc. 43(1), 153-159.
  • Senter, H. F. and Dotson, W. G. 1974. “Approximating fixed points of nonexpansive mappings”, Proc. Am. Math. Soc., 44(2), 375-380.
  • Sintunavarat, W. and Pitea, A. “On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis”, J. Nonlinear Sci. Appl., 9, 2553-2562.
  • Suzuki, T. 2008. “Fixed point theorems and convergence theorems for some generalized nonexpansive mappings”, J. Math. Anal. Appl., 340(2), 1088-1095.
  • Thakur et al., 2014. “New iteraiton schme for numerical reckoning fixed points of nonexpansive mappings”, Journal of inequalities and applicaitons, 238,1-15.
  • Thakur et al., 2016. “E new iteraiton scheme for approximating fixed points of nonexpansive mappings”, Filomat, 30(10), 2711-2720.
  • Zamfirescu, T. 1972. “Fixed point theorems in metric spaces”, Archive 23 (1972), 292-298.1

Convergence Theorems with a Faster Iteration Process for Suzuki’s Generalized Non-expansive Mapping with Numerical Examples

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 162 - 174, 28.02.2020

Osman Alagoz Birol Gündüz Sezgin Akbulut

Abstract

In this paper firstly, we compared rates of convergences of some
iteration processes which converge faster than Picard, Mann, Ishikawa and
S-iteration processes. Then, we proved some strong and weak convergence
theorems for the fastest iteration process for Suzuki’s generalized
non-expansive mapping in Banach spaces. We also supported our theoretical
findings via numerical examples. 

Keywords

Suzuki’s non-expansive mapping rate of convergence fixed point

References

  • Abbas, M. and Nazir, T. 2014. “A new faster iteration process applied to constrained minimization and feasibility problems”, Mathematificki Vesnik, 66(2), 223-234.
  • Agarwal, R. P., O'Regan, D. and Sahu, D.R. 2007. “Iteraitve construction of fixed points of nearly asymptotically nonexpansive mappings”, J. Nonlinear Convex Anal. 8 (1), 61-79.
  • Berinde, V. 2001. “Picard iteration converges faster than Mann iteration for a class of quasicontractive operators”, Fixed Point Theory and Applications, 2, 97-105.
  • Goebel, K. and Kirk, W.A. (1990). “Topic in Metric Fixed Point Theory”, Cambridge University Press.
  • Ishikawa, S., 1974. “Fixed points by a new iteration method”, Proc. Am. Math. Soc. 44, 147-150.
  • Karaca, N. and Yildirim, I. 2015. “Approximating fixed points of nonexpansive mappings by a faster iteration process”, J. Adv. Math. Stud. Vol. 8(2), 257-264.
  • Khan, S. H. 2013. “A Picard-Man hybrid iterative process”, Fixed Point Theory and appl., doi:10.1186/1687-1812-2013-69.
  • Mann, W. R. 1953. “Mean value methods in iteration”, Proc. Am. Math. Soc. 4, 506-510.
  • Noor, M. A. 2000. “New approximation schemes for general variational inequalities”, Journal of Mathematical Analysis and Applicaitons, 251(1), 217-229.
  • Opial, Z. 1967. “Weak convergence of the sequence of successive approximations for nonexpansive mappings”, Bull. Am. Math. Soc. 73, 595-597.
  • Picard, E., 1890. “Memoire sur la theorie des equation aux derivees partielles la methode des approximations successives”, J. Math. Pures Appl. 6, 145-210.
  • Phuengrattana, W. 2011. “Approximating fixed points of Suzuki-generalized nonexpansive mappings”, Nonlinear Anal. Hybrid Syst. 5(3), 583-590.
  • Schu, J. 1991. “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings”, Bull. Aust. Math. Soc. 43(1), 153-159.
  • Senter, H. F. and Dotson, W. G. 1974. “Approximating fixed points of nonexpansive mappings”, Proc. Am. Math. Soc., 44(2), 375-380.
  • Sintunavarat, W. and Pitea, A. “On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis”, J. Nonlinear Sci. Appl., 9, 2553-2562.
  • Suzuki, T. 2008. “Fixed point theorems and convergence theorems for some generalized nonexpansive mappings”, J. Math. Anal. Appl., 340(2), 1088-1095.
  • Thakur et al., 2014. “New iteraiton schme for numerical reckoning fixed points of nonexpansive mappings”, Journal of inequalities and applicaitons, 238,1-15.
  • Thakur et al., 2016. “E new iteraiton scheme for approximating fixed points of nonexpansive mappings”, Filomat, 30(10), 2711-2720.
  • Zamfirescu, T. 1972. “Fixed point theorems in metric spaces”, Archive 23 (1972), 292-298.1
There are 19 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Osman Alagoz

Birol Gündüz

Sezgin Akbulut

Publication Date February 28, 2020
Published in Issue Year 2020 Volume: 13 Issue: ÖZEL SAYI I

Cite

APA Alagoz, O., Gündüz, B., & Akbulut, S. (2020). Convergence Theorems with a Faster Iteration Process for Suzuki’s Generalized Non-expansive Mapping with Numerical Examples. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 162-174.