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Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma

Year 2018, Volume: 18 Issue: 3, 852 - 860, 30.12.2018

Kadri Doğan

Abstract

Bu çalışmada, Mann yineleme yönteminden daha hızlı olan Mann tipinde bir yineleme
tanımlanmış ve bu yineleme yönteminin Banach uzaylarında hemen hemen büzülme dönüşümleri
için sabit noktaya yakınsadığı gösterilmiştir. Ayrıca düzenlenmiş Mann yineleme yönteminin
literatürdeki diğer sabit nokta yineleme yöntemlerine yakınsaklık denklikleri ispatlanmıştır. Son
olarak, Mann tipindeki yineleme yönteminin, klasik Mann yineleme yönteminden daha hızlı
olduğu gösterilmiştir.

Keywords

Mann sabit nokta yineleme yöntemi Yakınsaklık hızı Yakınsaklık denkliği Kuvvetli yakınsaklık.

References

  • Abbas, M. and Nazir, T., 2014. A new faster iteration process applied to constrained minimization and feasibility problems, Matematicki Vesnik 66 (2014) 223-234.
  • Berinde, V., 2004. Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2014 :1.
  • Fukhar-ud-din, H. and Berinde, V., 2016. Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat 30, 223-230.
  • Harder, A.M. and Hicks, T. L., 1988. Stability results for fixed point iteration procedures, Mathematica Japonica, 33, 693-706.
  • Chugh, R., Malik, P. and Kumar, V., 2015. On a new faster implicit fixed point iterative scheme in convex metric spaces, J. Function Spaces , 2015, Article ID 905834.
  • Gursoy, F. and Karakaya, V., 2014. A Picard-S hybrid type iteration method for solving a diferential equation with retarded argument, arXiv preprint arXiv:1403.2546
  • Karahan, I. and Ozdemir, M., 2013. A general iterative method for approximation of fixed points and their applications, Advances in Fixed Point Theory, 3, 510-526.
  • Karakaya, V., Dogan, K., Gursoy, F. and Erturk, M., 2013. Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstract and Applied Analysis, 2013, 9 pages.
  • Dogan, K. and Karakaya, V., 2014. On the convergence and stability results for a new general iterative process, The Scienti_c World Journal, 2014, 8 pages.
  • Sintunavarat, W. and Pitea, A., 2016. On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis, J. Nonlinear Science Appl. 9, 2553-2562.
  • Suantai, S., 2005. Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311, 506-517. Reich, S. and Safrir, I., 1990. Nonexpansive iteration in hyperbolic spaces, Nonlinear. Anal. 15, 537-558
  • Qihou, L., 2001. Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, Journal of Mathematical Analysis and applications, 259(1), 18-24.
  • Berinde, V., 2003. On the approximation of fixed points of weak contractive mappings, Carpathian J. Math, 19, 7 - 22.
  • Berinde, V., 2007. Iterative Approximation of Fixed Points, Springer, Berlin, (2007). Phuengrattana, W. and Suantai, S., 2013. Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach Spaces, Thai J. Math. 11, 217-226.
  • Krasnoselkii, M. A., 1961. On solving the equations with self-adjoint operators by the method of successive approximations, Progress of mathematical sciences, vol.15. Issue. 3. Picard, E., 1890. Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl., 6, 145-210.
  • Karakaya,V., Atalan, Y., DoganK., and El Houda Bouzara,N., 2017. Some fixed point results for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18, No. 2, 625-640
  • . Mann, W.R., 1953. Mean value methods in iterations, Proc. Amer. Math. Soc., 4, 506-510.
  • Ishikawa, S., 1974. Fixed point by a new iteration method, Proceedings of the American Mathematical Society, 44, 147-150.
  • Noor, M.A., 2000. New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, 251, 217-229.
  • Phuengrattana, W. and Suantai, S., 2011. On the rate of convergence of Mann, Ishikawa, Noor and SP iterations for continuous on an arbitrary interval, Journal of Computational and Applied Mathematics, 235, 3006-3914.
  • Chugh, R. Kumar, V. and Kumar, S., 2012. Strong convergence of a new three step iterative scheme in Banach spaces, American Journal of Computational Mathematics, 2, 345-357.
  • Khan, S.H., 2013. A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications, 1, 1-10.

Year 2018, Volume: 18 Issue: 3, 852 - 860, 30.12.2018

Kadri Doğan

Abstract

References

  • Abbas, M. and Nazir, T., 2014. A new faster iteration process applied to constrained minimization and feasibility problems, Matematicki Vesnik 66 (2014) 223-234.
  • Berinde, V., 2004. Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2014 :1.
  • Fukhar-ud-din, H. and Berinde, V., 2016. Iterative methods for the class of quasi-contractive type operators and comparsion of their rate of convergence in convex metric spaces, Filomat 30, 223-230.
  • Harder, A.M. and Hicks, T. L., 1988. Stability results for fixed point iteration procedures, Mathematica Japonica, 33, 693-706.
  • Chugh, R., Malik, P. and Kumar, V., 2015. On a new faster implicit fixed point iterative scheme in convex metric spaces, J. Function Spaces , 2015, Article ID 905834.
  • Gursoy, F. and Karakaya, V., 2014. A Picard-S hybrid type iteration method for solving a diferential equation with retarded argument, arXiv preprint arXiv:1403.2546
  • Karahan, I. and Ozdemir, M., 2013. A general iterative method for approximation of fixed points and their applications, Advances in Fixed Point Theory, 3, 510-526.
  • Karakaya, V., Dogan, K., Gursoy, F. and Erturk, M., 2013. Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstract and Applied Analysis, 2013, 9 pages.
  • Dogan, K. and Karakaya, V., 2014. On the convergence and stability results for a new general iterative process, The Scienti_c World Journal, 2014, 8 pages.
  • Sintunavarat, W. and Pitea, A., 2016. On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis, J. Nonlinear Science Appl. 9, 2553-2562.
  • Suantai, S., 2005. Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311, 506-517. Reich, S. and Safrir, I., 1990. Nonexpansive iteration in hyperbolic spaces, Nonlinear. Anal. 15, 537-558
  • Qihou, L., 2001. Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, Journal of Mathematical Analysis and applications, 259(1), 18-24.
  • Berinde, V., 2003. On the approximation of fixed points of weak contractive mappings, Carpathian J. Math, 19, 7 - 22.
  • Berinde, V., 2007. Iterative Approximation of Fixed Points, Springer, Berlin, (2007). Phuengrattana, W. and Suantai, S., 2013. Comparison of the rate of convergence of various iterative methods for the class of weak contractions in Banach Spaces, Thai J. Math. 11, 217-226.
  • Krasnoselkii, M. A., 1961. On solving the equations with self-adjoint operators by the method of successive approximations, Progress of mathematical sciences, vol.15. Issue. 3. Picard, E., 1890. Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl., 6, 145-210.
  • Karakaya,V., Atalan, Y., DoganK., and El Houda Bouzara,N., 2017. Some fixed point results for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18, No. 2, 625-640
  • . Mann, W.R., 1953. Mean value methods in iterations, Proc. Amer. Math. Soc., 4, 506-510.
  • Ishikawa, S., 1974. Fixed point by a new iteration method, Proceedings of the American Mathematical Society, 44, 147-150.
  • Noor, M.A., 2000. New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, 251, 217-229.
  • Phuengrattana, W. and Suantai, S., 2011. On the rate of convergence of Mann, Ishikawa, Noor and SP iterations for continuous on an arbitrary interval, Journal of Computational and Applied Mathematics, 235, 3006-3914.
  • Chugh, R. Kumar, V. and Kumar, S., 2012. Strong convergence of a new three step iterative scheme in Banach spaces, American Journal of Computational Mathematics, 2, 345-357.
  • Khan, S.H., 2013. A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications, 1, 1-10.
There are 22 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Kadri Doğan

Publication Date December 30, 2018
Submission Date January 10, 2018
Published in Issue Year 2018 Volume: 18 Issue: 3

Cite

APA Doğan, K. (2018). Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 18(3), 852-860.
AMA Doğan K. Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2018;18(3):852-860.
Chicago Doğan, Kadri. “Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18, no. 3 (December 2018): 852-60.
EndNote Doğan K (December 1, 2018) Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18 3 852–860.
IEEE K. Doğan, “Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 3, pp. 852–860, 2018.
ISNAD Doğan, Kadri. “Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18/3 (December 2018), 852-860.
JAMA Doğan K. Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18:852–860.
MLA Doğan, Kadri. “Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 3, 2018, pp. 852-60.
Vancouver Doğan K. Daha Hızlı Mann Sabit Nokta Yinelemesi Üzerine Bir Çalışma. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18(3):852-60.