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ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE

Year 2015, Volume: 64 Issue: 2, 77 - 87, 01.08.2015
https://doi.org/10.1501/Commua1_0000000735

Abstract

The purpose of this paper is to prove the strong and 4-convergencetheorems of the new multi-step iteration process for multi-valued quasi-nonexpansivemappings in a complete geodesic space. Our results extend and improve someresults in the literature

References

  • Ba¸sarır, M. and ¸Sahin, A., On the strong and 4-convergence of new multi-step and S-iteration processes in a CAT(0) space, J. Inequal. Appl. 2013, Article ID 482, 13 pages.
  • Bridson, M. and Hae*iger, A., Metric Spaces of Non-Positive Curvature, Springer, Berlin, 1999.
  • Espinola, R. and Fernandez-Leon, A., CAT( )-spaces, weak convergence and …xed points, J. Math. Anal. Appl. 353 (2009), 410-427.
  • 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. 2013, Article ID 76, 12 pages.
  • He, J. S., Fang, D. H., López, G. and Li, C., Mann’s algorithm for nonexpansive mappings in CAT( ) spaces, Nonlinear Anal. 75 (2012), 445-452.
  • Khan, S. H., Fukhar-ud-din, H. and Kalsoom, A., Common …xed points of two multivalued nonexpansive maps by a one-step implicit algorithm in hyperbolic spaces, Matematiµcki Vesnik 66(4) (2014), 397-409.
  • Kimura, Y. and Nakagawa, K., Another type of Mann iterative scheme for two mappings in a complete geodesic space, J. Inequal. Appl. 2014, Article ID 72, 9 pages.
  • Kimura, Y., Saejung, S. and Yotkaew, P., The Mann algorithm in a complete geodesic space with curvature bounded above, Fixed Point Theory Appl. 2013, Article ID 336, 13 pages.
  • Kimura, Y. and Satô, K., Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one, Fixed Point Theory Appl. 2013, Article ID 7, 14 pages.
  • Kirk, W. A. and Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), 3689-3696.
  • Panyanak, B., On the Ishikawa iteration processes for multivalued mappings in some CAT( ) spaces, Fixed Point Theory Appl. 2014, Article ID 1, 9 pages.
  • Phuengrattana, W. and Suantai, S., On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math. 235 (2011), 3006-3014.
  • Puttasontiphot, T., Mann and Ishikawa iteration schemes for multi-valued mappings in CAT(0) spaces, Appl. Math. Sci. 4 (2010), 3005-3018.
  • Salahifard, H., Vaezpour, S. M. and Dhompongsa, S., Fixed point theorems for some general- ized nonexpansive mappings in CAT(0) spaces, J. Nonlinear Anal. Optim. 4 (2013), 241-248. [15] Shabanian, S. and Vaezpour, S. M., A minimax inequality and its applications to …xed point theorems in CAT(0) spaces, Fixed Point Theory Appl. 2011, Article ID 61, 9 pages.
  • Shahzad, N. and Zegeye, H., On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71 (2009), 838-844.
  • Song, Y. and Cho, Y. J., Some notes on Ishikawa iteration for multi-valued mappings, Bull. Korean Math. Soc. 48(3) (2011), 575-584.
  • Thianwan, S., Common …xed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space, J. Comput. Appl. Math. 224 (2009), 688-695.
  • Current address : Aynur SAH·IN, Department of Mathematics, Faculty of Sciences and Arts, Sakarya University, Sakarya, 54050, Turkey.
Year 2015, Volume: 64 Issue: 2, 77 - 87, 01.08.2015
https://doi.org/10.1501/Commua1_0000000735

Abstract

References

  • Ba¸sarır, M. and ¸Sahin, A., On the strong and 4-convergence of new multi-step and S-iteration processes in a CAT(0) space, J. Inequal. Appl. 2013, Article ID 482, 13 pages.
  • Bridson, M. and Hae*iger, A., Metric Spaces of Non-Positive Curvature, Springer, Berlin, 1999.
  • Espinola, R. and Fernandez-Leon, A., CAT( )-spaces, weak convergence and …xed points, J. Math. Anal. Appl. 353 (2009), 410-427.
  • 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. 2013, Article ID 76, 12 pages.
  • He, J. S., Fang, D. H., López, G. and Li, C., Mann’s algorithm for nonexpansive mappings in CAT( ) spaces, Nonlinear Anal. 75 (2012), 445-452.
  • Khan, S. H., Fukhar-ud-din, H. and Kalsoom, A., Common …xed points of two multivalued nonexpansive maps by a one-step implicit algorithm in hyperbolic spaces, Matematiµcki Vesnik 66(4) (2014), 397-409.
  • Kimura, Y. and Nakagawa, K., Another type of Mann iterative scheme for two mappings in a complete geodesic space, J. Inequal. Appl. 2014, Article ID 72, 9 pages.
  • Kimura, Y., Saejung, S. and Yotkaew, P., The Mann algorithm in a complete geodesic space with curvature bounded above, Fixed Point Theory Appl. 2013, Article ID 336, 13 pages.
  • Kimura, Y. and Satô, K., Halpern iteration for strongly quasinonexpansive mappings on a geodesic space with curvature bounded above by one, Fixed Point Theory Appl. 2013, Article ID 7, 14 pages.
  • Kirk, W. A. and Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. 68 (2008), 3689-3696.
  • Panyanak, B., On the Ishikawa iteration processes for multivalued mappings in some CAT( ) spaces, Fixed Point Theory Appl. 2014, Article ID 1, 9 pages.
  • Phuengrattana, W. and Suantai, S., On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, J. Comput. Appl. Math. 235 (2011), 3006-3014.
  • Puttasontiphot, T., Mann and Ishikawa iteration schemes for multi-valued mappings in CAT(0) spaces, Appl. Math. Sci. 4 (2010), 3005-3018.
  • Salahifard, H., Vaezpour, S. M. and Dhompongsa, S., Fixed point theorems for some general- ized nonexpansive mappings in CAT(0) spaces, J. Nonlinear Anal. Optim. 4 (2013), 241-248. [15] Shabanian, S. and Vaezpour, S. M., A minimax inequality and its applications to …xed point theorems in CAT(0) spaces, Fixed Point Theory Appl. 2011, Article ID 61, 9 pages.
  • Shahzad, N. and Zegeye, H., On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces, Nonlinear Anal. 71 (2009), 838-844.
  • Song, Y. and Cho, Y. J., Some notes on Ishikawa iteration for multi-valued mappings, Bull. Korean Math. Soc. 48(3) (2011), 575-584.
  • Thianwan, S., Common …xed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space, J. Comput. Appl. Math. 224 (2009), 688-695.
  • Current address : Aynur SAH·IN, Department of Mathematics, Faculty of Sciences and Arts, Sakarya University, Sakarya, 54050, Turkey.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Aynur Şahin This is me

Metin Başarır This is me

Publication Date August 1, 2015
Published in Issue Year 2015 Volume: 64 Issue: 2

Cite

APA Şahin, A., & Başarır, M. (2015). ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(2), 77-87. https://doi.org/10.1501/Commua1_0000000735
AMA Şahin A, Başarır M. ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2015;64(2):77-87. doi:10.1501/Commua1_0000000735
Chicago Şahin, Aynur, and Metin Başarır. “ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64, no. 2 (August 2015): 77-87. https://doi.org/10.1501/Commua1_0000000735.
EndNote Şahin A, Başarır M (August 1, 2015) ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64 2 77–87.
IEEE A. Şahin and M. Başarır, “ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 64, no. 2, pp. 77–87, 2015, doi: 10.1501/Commua1_0000000735.
ISNAD Şahin, Aynur - Başarır, Metin. “ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64/2 (August 2015), 77-87. https://doi.org/10.1501/Commua1_0000000735.
JAMA Şahin A, Başarır M. ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64:77–87.
MLA Şahin, Aynur and Metin Başarır. “ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 64, no. 2, 2015, pp. 77-87, doi:10.1501/Commua1_0000000735.
Vancouver Şahin A, Başarır M. ON THE NEW MULTI-STEP ITERATION PROCESS FOR MULTI-VALUED MAPPINGS IN A COMPLETE GEODESIC SPACE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64(2):77-8.

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

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