Araştırma Makalesi
BibTex RIS Kaynak Göster

A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations

Yıl 2020, Cilt: 10 Sayı: 1, 563 - 575, 01.03.2020
https://doi.org/10.21597/jist.583528

Öz

In this study, by using the iterative method discussed in (Kang et al., 2013) and adopting a technique given in details (Biazar and Amirteimoori, 2006) introduced a new hybrid third-order iterative method to solve nonlinear equations derived from the Picard-Mann fixed-point iterative method. Some problems have been solved in order to demonstrate the performance of the established iterative method for the solution of the nonlinear equations.

Destekleyen Kurum

Artvin Coruh Univesity

Kaynakça

  • Abbas M, Nazir T, 2014. A new faster iteration process applied to constrained minimization and feasibility problems, Matematicki Vesnik 66(2): 223-234.
  • Ashiq A, Qaisar M, Tanveer M, Aslam A, NazeerW, 2015. Modified new third-order iterative method for non-linear equations, Sci.Int.(Lahore), 27(3), 1741-1744, 2015.
  • Babolian E, Biazar J, 2002. Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 132 (1): 167–172.
  • Berinde V, 2014. Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2014 (2004):1.
  • Biazar J, Amirteimoori A, 2006. An improvement to the fixed point iterative method, Appl. Math. Comput. 182 (1): 567–571.
  • Chugh R, Malik P, Kumar V, 2015. On a new faster implicit xed point iterative scheme in convex metric spaces, J. Function Spaces (2015), Article ID 905834.
  • Dogan K, Karakaya V, 2018. A study in the fixed point theory for a new iterative scheme and a class of generalized mapings, Creat. Math. Inform. 27(2018), No. 2, 151-160.
  • Fukhar-ud-din H, 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 (2016) 223-230.
  • Isaacson E, Keller HB, 1966. Analysis of Numerical Methods, John Wiley & Sons, Inc., No:1, 106-108 New York, USA.
  • Khan SH, 2013. A Picard-Mann hybrid iterative process. Fixed Point Theory Appl. (2013). doi:10.1186/1687-1812-2013-69.
  • Kang SM, Rafiq A, and Kwun Y C, 2013. A New Second-Order Iteration Method for Solving Nonlinear Equations, Abstract and Applied Analysis. Volume 2013, Article ID 487062, 4 pages.
  • Karakaya V, Dogan K, Gursoy F, Erturk M, 2013. Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstract and Applied Analysis, 2013(2013), 9 pages.
  • Karakaya V, Dogan K, 2014. On the convergence and stability results for a new general iterative process, The Scientific World Journal, 2014(2014), 8 pages.
  • Karakaya V, Atalan Y, Dogan K, Bouzara N. El Houda, 2017. Some fixed point results for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18(2017), No. 2, 625-640.
  • Picard E, 1890. Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl., 6(1890), 145-210.
  • 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. 11 (2013) 217-226.

A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations

Yıl 2020, Cilt: 10 Sayı: 1, 563 - 575, 01.03.2020
https://doi.org/10.21597/jist.583528

Öz

In this study, by using the iterative method discussed in (Kang et al., 2013) and adopting a technique given in details (Biazar and Amirteimoori, 2006) introduced a new hybrid third-order iterative method to solve nonlinear equations derived from the Picard-Mann fixed-point iterative method. Some problems have been solved in order to demonstrate the performance of the established iterative method for the solution of the nonlinear equations.

Kaynakça

  • Abbas M, Nazir T, 2014. A new faster iteration process applied to constrained minimization and feasibility problems, Matematicki Vesnik 66(2): 223-234.
  • Ashiq A, Qaisar M, Tanveer M, Aslam A, NazeerW, 2015. Modified new third-order iterative method for non-linear equations, Sci.Int.(Lahore), 27(3), 1741-1744, 2015.
  • Babolian E, Biazar J, 2002. Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 132 (1): 167–172.
  • Berinde V, 2014. Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators, Fixed Point Theory Appl. 2014 (2004):1.
  • Biazar J, Amirteimoori A, 2006. An improvement to the fixed point iterative method, Appl. Math. Comput. 182 (1): 567–571.
  • Chugh R, Malik P, Kumar V, 2015. On a new faster implicit xed point iterative scheme in convex metric spaces, J. Function Spaces (2015), Article ID 905834.
  • Dogan K, Karakaya V, 2018. A study in the fixed point theory for a new iterative scheme and a class of generalized mapings, Creat. Math. Inform. 27(2018), No. 2, 151-160.
  • Fukhar-ud-din H, 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 (2016) 223-230.
  • Isaacson E, Keller HB, 1966. Analysis of Numerical Methods, John Wiley & Sons, Inc., No:1, 106-108 New York, USA.
  • Khan SH, 2013. A Picard-Mann hybrid iterative process. Fixed Point Theory Appl. (2013). doi:10.1186/1687-1812-2013-69.
  • Kang SM, Rafiq A, and Kwun Y C, 2013. A New Second-Order Iteration Method for Solving Nonlinear Equations, Abstract and Applied Analysis. Volume 2013, Article ID 487062, 4 pages.
  • Karakaya V, Dogan K, Gursoy F, Erturk M, 2013. Fixed point of a new three-step iteration algorithm under contractive-like operators over normed spaces, Abstract and Applied Analysis, 2013(2013), 9 pages.
  • Karakaya V, Dogan K, 2014. On the convergence and stability results for a new general iterative process, The Scientific World Journal, 2014(2014), 8 pages.
  • Karakaya V, Atalan Y, Dogan K, Bouzara N. El Houda, 2017. Some fixed point results for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18(2017), No. 2, 625-640.
  • Picard E, 1890. Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl., 6(1890), 145-210.
  • 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. 11 (2013) 217-226.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Kadri Doğan 0000-0002-6622-3122

Yayımlanma Tarihi 1 Mart 2020
Gönderilme Tarihi 28 Haziran 2019
Kabul Tarihi 23 Ekim 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

Kaynak Göster

APA Doğan, K. (2020). A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations. Journal of the Institute of Science and Technology, 10(1), 563-575. https://doi.org/10.21597/jist.583528
AMA Doğan K. A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations. Iğdır Üniv. Fen Bil Enst. Der. Mart 2020;10(1):563-575. doi:10.21597/jist.583528
Chicago Doğan, Kadri. “A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations”. Journal of the Institute of Science and Technology 10, sy. 1 (Mart 2020): 563-75. https://doi.org/10.21597/jist.583528.
EndNote Doğan K (01 Mart 2020) A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations. Journal of the Institute of Science and Technology 10 1 563–575.
IEEE K. Doğan, “A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 1, ss. 563–575, 2020, doi: 10.21597/jist.583528.
ISNAD Doğan, Kadri. “A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations”. Journal of the Institute of Science and Technology 10/1 (Mart 2020), 563-575. https://doi.org/10.21597/jist.583528.
JAMA Doğan K. A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:563–575.
MLA Doğan, Kadri. “A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations”. Journal of the Institute of Science and Technology, c. 10, sy. 1, 2020, ss. 563-75, doi:10.21597/jist.583528.
Vancouver Doğan K. A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(1):563-75.