Araştırma Makalesi
BibTex RIS Kaynak Göster

Bazı sabit nokta yineleme yöntemlerinin yakınsama davranışlarının incelenmesi

Yıl 2017, Cilt: 21 Sayı: 3, 540 - 544, 01.06.2017
https://doi.org/10.16984/saufenbilder.278071

Öz

Bazı sabit nokta yineleme yöntemlerinin, belirli bir büzülme şartını sağlayan operatörlerin sınıfından seçilen
elemanların karakterlerine bağlı olarak farklı yakınsama davranışları sergiledikleri nümerik bir örnek verilerek
gösterilecektir.

Kaynakça

  • Berinde, V. (2004). Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators. Fixed Point Theory Appl., 97-105.
  • Chugh, R., Preety, M., & Kumar, V. (2015). On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces. Journal of Function Spaces, 2015, 1-11.
  • Ćirić, L., Rafiq, A., Radenović, S., Rajović, M., & Ume, J. S. (2008). On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings,”. Applied Mathematics and Computation, 198(1), 128–137.
  • Doğan, K., & Karakaya, V. (2014). On the Convergence and Stability Results for a New General Iterative Process. The Scientific World Journal, 1-8.
  • Gürsoy, F. (2016). A Picard-S iterative method for approximating fixed point of weak-contraction mappings. Filomat, 30(10), 2829-2845.
  • Gürsoy, F., Khan, A. R., & Fukhar-ud-din, H. (2016). Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics, 1-16.
  • Imoru, C. O., & Olatinwo, M. O. (2003). On the stability of Picard and Mann iteration processes. Carpathian Journal of Mathematics, 19(2), 155–160.
  • Ishikawa, S. (1974). Fixed points by a new iteration method. Proc. Amer. Math. Soc., 44, 147-150.
  • Karakaya, V., Gürsoy, F., & Ertürk, M. (2016). Some convergence and data dependence results for various fixed point iterative methods. Kuwait Journal of Science, 43(1), 112-128.
  • Khan, A. R., Khamsi, M. A., & Fukhar-ud-din, h. (2011). Strong convergence of a general iteration scheme in CAT(0)−spaces. Nonlinear Anal., 74(3), 783–791.
  • Kirk, W. A. (1981). Krasnoselskii’s iteration process in hyperbolic space. Numer. Funct. Anal. Optim., 4(4), 371–381.
  • Kohlenbach, U. (2005). Some logical metatheorems with applications in functional analysis. Trans. Amer. Math. Soc., 357(1), 89-128.
  • Mann, W. (1953). Mean value methods in iteration. Proc. Amer. Math. Soc., 4, 506-510.
  • Noor, M. A. (2000). New approximation schemes for general variational inequalities. J. Math. Anal. Appl., 251(1), 217-229.
  • Phuengrattana, W., & 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., 217-226.
  • Şahin, A., & Başarır, M. (2016). Convergence and data dependence results of an iteration process in a hyperbolic space. Filomat, 30(3), 569–582.
  • Takahashi, W. (1970). A convexity in metric spaces and nonexpansive mappings I. Kodai Math. Sem. Rep., 22(2), 142-149.

Investigation of convergency behaviors of some fixed point iteration methods

Yıl 2017, Cilt: 21 Sayı: 3, 540 - 544, 01.06.2017
https://doi.org/10.16984/saufenbilder.278071

Öz

It will be shown by providing a numerical example that some fixed point iteration methods exhibit different
convergency behaviors depending on the characters of the members chosen from a class of operators satisfying a
certain contractive condition.

Kaynakça

  • Berinde, V. (2004). Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators. Fixed Point Theory Appl., 97-105.
  • Chugh, R., Preety, M., & Kumar, V. (2015). On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces. Journal of Function Spaces, 2015, 1-11.
  • Ćirić, L., Rafiq, A., Radenović, S., Rajović, M., & Ume, J. S. (2008). On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings,”. Applied Mathematics and Computation, 198(1), 128–137.
  • Doğan, K., & Karakaya, V. (2014). On the Convergence and Stability Results for a New General Iterative Process. The Scientific World Journal, 1-8.
  • Gürsoy, F. (2016). A Picard-S iterative method for approximating fixed point of weak-contraction mappings. Filomat, 30(10), 2829-2845.
  • Gürsoy, F., Khan, A. R., & Fukhar-ud-din, H. (2016). Convergence and data dependence results for quasi-contractive type operators in hyperbolic spaces. Hacettepe Journal of Mathematics and Statistics, 1-16.
  • Imoru, C. O., & Olatinwo, M. O. (2003). On the stability of Picard and Mann iteration processes. Carpathian Journal of Mathematics, 19(2), 155–160.
  • Ishikawa, S. (1974). Fixed points by a new iteration method. Proc. Amer. Math. Soc., 44, 147-150.
  • Karakaya, V., Gürsoy, F., & Ertürk, M. (2016). Some convergence and data dependence results for various fixed point iterative methods. Kuwait Journal of Science, 43(1), 112-128.
  • Khan, A. R., Khamsi, M. A., & Fukhar-ud-din, h. (2011). Strong convergence of a general iteration scheme in CAT(0)−spaces. Nonlinear Anal., 74(3), 783–791.
  • Kirk, W. A. (1981). Krasnoselskii’s iteration process in hyperbolic space. Numer. Funct. Anal. Optim., 4(4), 371–381.
  • Kohlenbach, U. (2005). Some logical metatheorems with applications in functional analysis. Trans. Amer. Math. Soc., 357(1), 89-128.
  • Mann, W. (1953). Mean value methods in iteration. Proc. Amer. Math. Soc., 4, 506-510.
  • Noor, M. A. (2000). New approximation schemes for general variational inequalities. J. Math. Anal. Appl., 251(1), 217-229.
  • Phuengrattana, W., & 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., 217-226.
  • Şahin, A., & Başarır, M. (2016). Convergence and data dependence results of an iteration process in a hyperbolic space. Filomat, 30(3), 569–582.
  • Takahashi, W. (1970). A convexity in metric spaces and nonexpansive mappings I. Kodai Math. Sem. Rep., 22(2), 142-149.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Faik Gürsoy

Yayımlanma Tarihi 1 Haziran 2017
Gönderilme Tarihi 7 Ocak 2017
Kabul Tarihi 28 Mart 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 21 Sayı: 3

Kaynak Göster

APA Gürsoy, F. (2017). Investigation of convergency behaviors of some fixed point iteration methods. Sakarya University Journal of Science, 21(3), 540-544. https://doi.org/10.16984/saufenbilder.278071
AMA Gürsoy F. Investigation of convergency behaviors of some fixed point iteration methods. SAUJS. Haziran 2017;21(3):540-544. doi:10.16984/saufenbilder.278071
Chicago Gürsoy, Faik. “Investigation of Convergency Behaviors of Some Fixed Point Iteration Methods”. Sakarya University Journal of Science 21, sy. 3 (Haziran 2017): 540-44. https://doi.org/10.16984/saufenbilder.278071.
EndNote Gürsoy F (01 Haziran 2017) Investigation of convergency behaviors of some fixed point iteration methods. Sakarya University Journal of Science 21 3 540–544.
IEEE F. Gürsoy, “Investigation of convergency behaviors of some fixed point iteration methods”, SAUJS, c. 21, sy. 3, ss. 540–544, 2017, doi: 10.16984/saufenbilder.278071.
ISNAD Gürsoy, Faik. “Investigation of Convergency Behaviors of Some Fixed Point Iteration Methods”. Sakarya University Journal of Science 21/3 (Haziran 2017), 540-544. https://doi.org/10.16984/saufenbilder.278071.
JAMA Gürsoy F. Investigation of convergency behaviors of some fixed point iteration methods. SAUJS. 2017;21:540–544.
MLA Gürsoy, Faik. “Investigation of Convergency Behaviors of Some Fixed Point Iteration Methods”. Sakarya University Journal of Science, c. 21, sy. 3, 2017, ss. 540-4, doi:10.16984/saufenbilder.278071.
Vancouver Gürsoy F. Investigation of convergency behaviors of some fixed point iteration methods. SAUJS. 2017;21(3):540-4.

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