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On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme

Yıl 2019, Cilt: 7 Sayı: 1, 97 - 106, 15.04.2019

Öz

The aim of this paper is to obtain results of the strong convergence, rate of convergence and data dependence for a new three step iterative scheme using contraction mappings and to give examples for the rate of convergence and data dependence results. After these numerical approachs, it can be seen that the new iterative scheme has a better rate of convergence with respect to the other iterative schemes in the literature. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.


Kaynakça

  • [1] R. P. Agarwal, D. O Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. Vol:8, No:1 (2007), 61-79.
  • [2] S. Ishikawa, Fixed Point By a New Iteration Method, Proc. Amer. Math. Soc. Vol:44 (1974), 147-150.
  • [3] W. R. Mann, Mean Value Methods in Iteration, Proc. Amer. Math. Soc., Vol:4 (1953), 506-510.
  • [4] M.A Noor, New Approximation Schemes for General Variational Inequalities, J. Math. Anal. Appl. Vol:251, (2000), 217-229.
  • [5] V. Karakaya, Y. Atalan, K. Dogan, NEH. Bouzara, Some Fixed Point Results for a new three steps iteration process in Banach spaces, Fixed Point Theory, Vol:18 No:2 (2017) 625-640.
  • [6] R.Chugh, V. Kumar, S. Kumar, Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces, Amer. J. Comp. Math. Vol:2, No:04 (2012), 345-357.
  • [7] E. Picard, Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl, Vol:6 No:4 (1890), 145-210.
  • [8] K. Dogan, Daha Hızlı Mann Sabit Nokta Yinelemesi U¨ zerine Bir C¸ alıs¸ma, Afyon Kocatepe U¨ niversitesi Fen ve Mu¨hendislik Bilimleri Dergisi, Vol:18, No:3 (2018), 852-860.
  • [9] K. Ullah and M. Arshad, On different results for the new three step iteration process in Banach spaces, SpringerPlus, Vol. 5, No.1 (2016) 1-15.
  • [10] M. Erturk, F. Gursoy, V. Karakaya, M. Başarır and A. Şahin, Some convergence and data dependence results by a simpler and faster iterative scheme Appl.Comput. Math. submitted, 2017.
  • [11] F. Gursoy, A Picard-S iterative method for approximating fixed point of weak-contraction mappings, Filomat, Vol:30 No:10 (2016), 2829-2845.
  • [12] D. Thakur, B. S. Thakur and M. Postolache, New iteration schme for numerical reckoning fixed points of nonexpansive mapping, J. Inequal. Appl. Vol. 2014, No. 1 (2014), 5 pages.
  • [13] V. Karakaya, Y. Atalan, K. Dogan, NEH. Bouzara, Convergence Analysis for a New Faster Iteration Method, Istanbul Commerce University Journal of Science, Vol:15 No:30 (2016) 35-53.
  • [14] M. Abbas and T.Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Math. Vesn. Vol:66, No:2 (2014), 223-234.
  • [15] D. R. Sahu, Applications of S iteration process to constrained minimization problems and split feasibility problems, Fixed Point Theory, Vol:12, No.1 (2011),187-204.
  • [16] N. Kadıoglu and I. Yıldırım, Approximating fixed points of nonexpansive mappings by a faster iteration process, J. Adv. Math. Stud. Vol:8, No. 2 (2015), 257-264.
  • [17] I. Karahan and M. O¨ zdemir, A general iterative method for approximation of fixed points and their applications, Adv. Fixed Point Theory, Vol.3, No.3 (2013) 510-526.
  • [18] X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. Vol:113, No: 3 (1991), 727-731.
  • [19] S. M. S¸ oltuz, T. Grosan, Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl. Vol:2008, No:1 (2008), 1-7.
  • [20] W. Pheungrattana and R.Suantai, Comparison of the Rate of Convergence of Various Iterative Methods for the Class of Weak Contractions in Banach Spaces, Thai J. Math. Vol:11, No:1 (2013), 217–226.
Yıl 2019, Cilt: 7 Sayı: 1, 97 - 106, 15.04.2019

Öz

Kaynakça

  • [1] R. P. Agarwal, D. O Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings. J. Nonlinear Convex Anal. Vol:8, No:1 (2007), 61-79.
  • [2] S. Ishikawa, Fixed Point By a New Iteration Method, Proc. Amer. Math. Soc. Vol:44 (1974), 147-150.
  • [3] W. R. Mann, Mean Value Methods in Iteration, Proc. Amer. Math. Soc., Vol:4 (1953), 506-510.
  • [4] M.A Noor, New Approximation Schemes for General Variational Inequalities, J. Math. Anal. Appl. Vol:251, (2000), 217-229.
  • [5] V. Karakaya, Y. Atalan, K. Dogan, NEH. Bouzara, Some Fixed Point Results for a new three steps iteration process in Banach spaces, Fixed Point Theory, Vol:18 No:2 (2017) 625-640.
  • [6] R.Chugh, V. Kumar, S. Kumar, Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces, Amer. J. Comp. Math. Vol:2, No:04 (2012), 345-357.
  • [7] E. Picard, Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl, Vol:6 No:4 (1890), 145-210.
  • [8] K. Dogan, Daha Hızlı Mann Sabit Nokta Yinelemesi U¨ zerine Bir C¸ alıs¸ma, Afyon Kocatepe U¨ niversitesi Fen ve Mu¨hendislik Bilimleri Dergisi, Vol:18, No:3 (2018), 852-860.
  • [9] K. Ullah and M. Arshad, On different results for the new three step iteration process in Banach spaces, SpringerPlus, Vol. 5, No.1 (2016) 1-15.
  • [10] M. Erturk, F. Gursoy, V. Karakaya, M. Başarır and A. Şahin, Some convergence and data dependence results by a simpler and faster iterative scheme Appl.Comput. Math. submitted, 2017.
  • [11] F. Gursoy, A Picard-S iterative method for approximating fixed point of weak-contraction mappings, Filomat, Vol:30 No:10 (2016), 2829-2845.
  • [12] D. Thakur, B. S. Thakur and M. Postolache, New iteration schme for numerical reckoning fixed points of nonexpansive mapping, J. Inequal. Appl. Vol. 2014, No. 1 (2014), 5 pages.
  • [13] V. Karakaya, Y. Atalan, K. Dogan, NEH. Bouzara, Convergence Analysis for a New Faster Iteration Method, Istanbul Commerce University Journal of Science, Vol:15 No:30 (2016) 35-53.
  • [14] M. Abbas and T.Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Math. Vesn. Vol:66, No:2 (2014), 223-234.
  • [15] D. R. Sahu, Applications of S iteration process to constrained minimization problems and split feasibility problems, Fixed Point Theory, Vol:12, No.1 (2011),187-204.
  • [16] N. Kadıoglu and I. Yıldırım, Approximating fixed points of nonexpansive mappings by a faster iteration process, J. Adv. Math. Stud. Vol:8, No. 2 (2015), 257-264.
  • [17] I. Karahan and M. O¨ zdemir, A general iterative method for approximation of fixed points and their applications, Adv. Fixed Point Theory, Vol.3, No.3 (2013) 510-526.
  • [18] X. Weng, Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc. Vol:113, No: 3 (1991), 727-731.
  • [19] S. M. S¸ oltuz, T. Grosan, Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl. Vol:2008, No:1 (2008), 1-7.
  • [20] W. Pheungrattana and R.Suantai, Comparison of the Rate of Convergence of Various Iterative Methods for the Class of Weak Contractions in Banach Spaces, Thai J. Math. Vol:11, No:1 (2013), 217–226.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Yunus Atalan 0000-0002-5912-7087

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 20 Kasım 2018
Kabul Tarihi 6 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

APA Atalan, Y. (2019). On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp Journal of Mathematics, 7(1), 97-106.
AMA Atalan Y. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp J. Math. Nisan 2019;7(1):97-106.
Chicago Atalan, Yunus. “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 97-106.
EndNote Atalan Y (01 Nisan 2019) On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp Journal of Mathematics 7 1 97–106.
IEEE Y. Atalan, “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”, Konuralp J. Math., c. 7, sy. 1, ss. 97–106, 2019.
ISNAD Atalan, Yunus. “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”. Konuralp Journal of Mathematics 7/1 (Nisan 2019), 97-106.
JAMA Atalan Y. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp J. Math. 2019;7:97–106.
MLA Atalan, Yunus. “On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 97-106.
Vancouver Atalan Y. On Numerical Approach to The Rate of Convergence and Data Dependence Results for a New Iterative Scheme. Konuralp J. Math. 2019;7(1):97-106.
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