Research Article
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Year 2020, Volume: 69 Issue: 1, 112 - 122, 30.06.2020
https://doi.org/10.31801/cfsuasmas.560471

Abstract

References

  • Misiak, A., n-inner product spaces, Math. Nachr., vol. 140, (1989), 299--319.
  • Gähler, S., Linear 2-normietre räume, Math. Nachr., vol. 28, (1965), 1--43.
  • Dutta, H., Some iterated convergence and fixed point theorems in real linear n-normed spaces, Miskolc Mathematical Notes, vol. 15, no. 2, (2014), 423-437.
  • Gunawan, H. and Mashadi, M., On n-normed spaces, Int. J. Math. Math. Sci., vol. 2, (2001), 631--639.
  • Chugh, R. and Sushma, L., On Generalized n-inner product spaces, Novi Sad J. Math., vol. 41, no. 2, (2011), 73-80.
  • Owojori, O. O. and Imoru, C. O., New iteration methods for pseudocontractive and accretive operators in arbitrary banach spaces, Kragujevac J. Math., vol. 25, (2003), 97--110.
  • Thianwan, S., Common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in a banach space, J. Comput. Appl. Math., vol. 224, (2009), 688--695.
  • Raphael, P. and Pulickakunnel, S., Fixed point theorems in normed linear spaces using a generalized Z-type condition, Kragujevac J. Math., vol. 36, no. 2, (2012), 207--214.
  • Khan, S.H., Approximating Fixed Points by a Two-Step Iterative Algorithm,World Academy of Science, Engineering and Technology International Journal of Mathematical, Computational, Physical and Quantum Engineering, vol. 8, no. 6, (2014), 939-941.
  • Bosede, A.O. and Rhoades, B.E., Stability of Picard and Mann iteration for a general class of functions, J. Adv. Math. Studies, vol. 3, no. 2, (2010), 23-25.
  • Weng, X., Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc., vol. 113, (1991), 727--731.
  • Soltuz, S. M. and Grosan, T., Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl., vol. 2008, (2008), 7 pages.
  • Urabe, M., Convergence of numerical iteration in solution of equations, Journal of Science of the Hiroshima University A, vol.19, (1956), 479--489.
  • Ostrowski, A. M., The round-off stability of iterations, Z. Angew. Math. Mech., vol. 47, (1967), 77-81.
  • Harder, A. M. and Hicks, T. L., Stability results for xed point iteration procedures, Math. Jap., vol. 33, no. 5, (1988), 693-706.
  • Bosede, A. O.,Stability of Noor Iteration for a General Class of Functions in Banach Spaces, Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Mathematica, vol. 51, no. 2, (2012), 19--25.
  • Khan, A. R., Kumar, V. and Hussain, N. Analytical and numerical treatment of Jungck-type iterative schemes, Appl. Math. Comput., vol. 231, (2014), 521-535.
  • Imoru, C. O. and Olatinwo, M. O., On the stability of Picard and Mann iteration processes, Carp. J. Math., vol. 19, no. 2, (2003), 155-160.
  • Gürsoy, F., Karakaya, V. and Rhoades, B. E., Some convergence and stability results for the Kirk multistep and Kirk-SP fixed point iterative algorithms, Abstr. Appl. Anal., vol. 2014, (2014), 12 pages.
  • Osilike, M. O., Stability of the Mann and Ishikawa iteration procedures for-strong pseudocontractions and nonlinearequations of the-strongly accretive type, J. Math. Anal. Appl., vol. 227, no. 2, (1998), 319-334.
  • Verinde, V. B., Summable almost stability of fixed point iteration procedures, Carpathian J. Math., vol. 19, (2003), 81-88.
  • Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., vol. 44, (1974), 147--150.
  • Mann, W. R., Mean value in iteration, Proc. Amer. Math. Soc., vol. 4, (1953), 506--510.
  • Agarwal, R. P., O' Regan, D. and Sahu, D. R., Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal., vol. 8, 2007, 61-79.
  • Gürsoy, F., Karakaya, V. and Rhoades, B.E., Data dependence results of new multi-step and S-iterative schemes for contractive-like operators, Fixed Point Theory Appl., vol. 76, (2013), 12 pages.

Some new results on convergence, stability and data dependence in n-normed spaces

Year 2020, Volume: 69 Issue: 1, 112 - 122, 30.06.2020
https://doi.org/10.31801/cfsuasmas.560471

Abstract

We introduce a new contractive condition and a new iterative
method in n0normed space setting. We employ both of these to
study convergence, stability, and data dependence. The results presented
here extend and improve some recent results announced in the existing
literature.

References

  • Misiak, A., n-inner product spaces, Math. Nachr., vol. 140, (1989), 299--319.
  • Gähler, S., Linear 2-normietre räume, Math. Nachr., vol. 28, (1965), 1--43.
  • Dutta, H., Some iterated convergence and fixed point theorems in real linear n-normed spaces, Miskolc Mathematical Notes, vol. 15, no. 2, (2014), 423-437.
  • Gunawan, H. and Mashadi, M., On n-normed spaces, Int. J. Math. Math. Sci., vol. 2, (2001), 631--639.
  • Chugh, R. and Sushma, L., On Generalized n-inner product spaces, Novi Sad J. Math., vol. 41, no. 2, (2011), 73-80.
  • Owojori, O. O. and Imoru, C. O., New iteration methods for pseudocontractive and accretive operators in arbitrary banach spaces, Kragujevac J. Math., vol. 25, (2003), 97--110.
  • Thianwan, S., Common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in a banach space, J. Comput. Appl. Math., vol. 224, (2009), 688--695.
  • Raphael, P. and Pulickakunnel, S., Fixed point theorems in normed linear spaces using a generalized Z-type condition, Kragujevac J. Math., vol. 36, no. 2, (2012), 207--214.
  • Khan, S.H., Approximating Fixed Points by a Two-Step Iterative Algorithm,World Academy of Science, Engineering and Technology International Journal of Mathematical, Computational, Physical and Quantum Engineering, vol. 8, no. 6, (2014), 939-941.
  • Bosede, A.O. and Rhoades, B.E., Stability of Picard and Mann iteration for a general class of functions, J. Adv. Math. Studies, vol. 3, no. 2, (2010), 23-25.
  • Weng, X., Fixed point iteration for local strictly pseudocontractive mapping, Proc. Amer. Math. Soc., vol. 113, (1991), 727--731.
  • Soltuz, S. M. and Grosan, T., Data dependence for Ishikawa iteration when dealing with contractive like operators, Fixed Point Theory Appl., vol. 2008, (2008), 7 pages.
  • Urabe, M., Convergence of numerical iteration in solution of equations, Journal of Science of the Hiroshima University A, vol.19, (1956), 479--489.
  • Ostrowski, A. M., The round-off stability of iterations, Z. Angew. Math. Mech., vol. 47, (1967), 77-81.
  • Harder, A. M. and Hicks, T. L., Stability results for xed point iteration procedures, Math. Jap., vol. 33, no. 5, (1988), 693-706.
  • Bosede, A. O.,Stability of Noor Iteration for a General Class of Functions in Banach Spaces, Acta Univ. Palacki. Olomuc., Fac. Rer. Nat., Mathematica, vol. 51, no. 2, (2012), 19--25.
  • Khan, A. R., Kumar, V. and Hussain, N. Analytical and numerical treatment of Jungck-type iterative schemes, Appl. Math. Comput., vol. 231, (2014), 521-535.
  • Imoru, C. O. and Olatinwo, M. O., On the stability of Picard and Mann iteration processes, Carp. J. Math., vol. 19, no. 2, (2003), 155-160.
  • Gürsoy, F., Karakaya, V. and Rhoades, B. E., Some convergence and stability results for the Kirk multistep and Kirk-SP fixed point iterative algorithms, Abstr. Appl. Anal., vol. 2014, (2014), 12 pages.
  • Osilike, M. O., Stability of the Mann and Ishikawa iteration procedures for-strong pseudocontractions and nonlinearequations of the-strongly accretive type, J. Math. Anal. Appl., vol. 227, no. 2, (1998), 319-334.
  • Verinde, V. B., Summable almost stability of fixed point iteration procedures, Carpathian J. Math., vol. 19, (2003), 81-88.
  • Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., vol. 44, (1974), 147--150.
  • Mann, W. R., Mean value in iteration, Proc. Amer. Math. Soc., vol. 4, (1953), 506--510.
  • Agarwal, R. P., O' Regan, D. and Sahu, D. R., Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal., vol. 8, 2007, 61-79.
  • Gürsoy, F., Karakaya, V. and Rhoades, B.E., Data dependence results of new multi-step and S-iterative schemes for contractive-like operators, Fixed Point Theory Appl., vol. 76, (2013), 12 pages.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Kadri Doğan

Faik Gürsoy 0000-0002-7118-9088

Vatan Karakaya 0000-0003-4637-3139

Safeer Hussain Khan This is me 0000-0003-2978-1974

Publication Date June 30, 2020
Submission Date May 10, 2019
Acceptance Date August 21, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Doğan, K., Gürsoy, F., Karakaya, V., Khan, S. H. (2020). Some new results on convergence, stability and data dependence in n-normed spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 112-122. https://doi.org/10.31801/cfsuasmas.560471
AMA Doğan K, Gürsoy F, Karakaya V, Khan SH. Some new results on convergence, stability and data dependence in n-normed spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):112-122. doi:10.31801/cfsuasmas.560471
Chicago Doğan, Kadri, Faik Gürsoy, Vatan Karakaya, and Safeer Hussain Khan. “Some New Results on Convergence, Stability and Data Dependence in N-Normed Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 112-22. https://doi.org/10.31801/cfsuasmas.560471.
EndNote Doğan K, Gürsoy F, Karakaya V, Khan SH (June 1, 2020) Some new results on convergence, stability and data dependence in n-normed spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 112–122.
IEEE K. Doğan, F. Gürsoy, V. Karakaya, and S. H. Khan, “Some new results on convergence, stability and data dependence in n-normed spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 112–122, 2020, doi: 10.31801/cfsuasmas.560471.
ISNAD Doğan, Kadri et al. “Some New Results on Convergence, Stability and Data Dependence in N-Normed Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 112-122. https://doi.org/10.31801/cfsuasmas.560471.
JAMA Doğan K, Gürsoy F, Karakaya V, Khan SH. Some new results on convergence, stability and data dependence in n-normed spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:112–122.
MLA Doğan, Kadri et al. “Some New Results on Convergence, Stability and Data Dependence in N-Normed Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 112-2, doi:10.31801/cfsuasmas.560471.
Vancouver Doğan K, Gürsoy F, Karakaya V, Khan SH. Some new results on convergence, stability and data dependence in n-normed spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):112-2.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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