Research Article
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Year 2018, Volume: 47 Issue: 6, 1595 - 1604, 12.12.2018

İzhar Uddin , Mohammad Imdad

Abstract

References

  • Agarwal, R. P., O'Regan, D., Sahu, D. R., Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex. Anal. 8 (1), 61-79, 2007.
  • Berinde, V., Iterative Approximation of Fixed Points, Lecture Notes Math., vol. 1912, Springer, Berlin, 2007.
  • Bridson, M., Haefliger, A., Metric Spaces of Nonpositive Curvature, Springer-Verlag, Berlin, 1999.
  • Brown, K. S., Buildings, Springer-Verlag, New York, 1989.
  • Bruhat, F., Tits, J., Groupes reductifs sur un corps local, I. Donnees radicielles valuees Inst Hautes Etudes Sci Publ Math. 41, 1972.
  • Burago, D., Burago, Y., Ivanov, S., A Course in Metric Geometry, in: Graduate Studies in Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001.
  • Dhompongsa, S., Kirk, W. A., Panyanak, B., Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8, 35-45, 2007.
  • Dhompongsa, S., Kirk, W. A., Sims, B., Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. 65, 762-772, 2006.
  • Dhompongsa, S., Panyanak, B., On $\Delta$-convergence theorems in CAT(0) space, Comput. Math. Appl. 56, 2572-2579, 2008. Goebel, K., Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, Inc., New York, 1984.
  • Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44, 147-150, 1974.
  • Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc., 59, 65-71, 1976.
  • Kirk, W. A., Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. 68, 3689-3696, 2008.
  • Lim, T. C., Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60, 179-182, 1976.
  • Mann, W. R., Mean value methods in iterations, Proc. Amer. Math. Soc., 4, 506-510, 1953.
  • Phuengrattana, W., 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, 3006-3014, 2011.
  • Razani, A., Salahifrd, H., Approximating fixed points of generalized non-expansive mappings, Bull. Iranian Math. Soc. 37 (1), 235-246, 2011.
  • Reich, S., Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67, 274-276, 1979.
  • Şahin, A., Başarır, M., On the strong and $\Delta$-convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 311, 10pp., 2013.
  • Senter, H. F., Dotson, W. G., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44, 375-380, 1974.
  • Suzuki, T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340, 1088-1095, 2008.
  • Tan, K. K., Xu, H. K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178, 301-308, 1993.
  • Thianwan, S., Common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in a Banach space, J. Comput. Appl. Math. 224, 688-695, 2009.
  • Uddin, I., Imdad, M., On certain convergence of S-iteration scheme in CAT(0) spaces Kuwait J. Sci. 42 (2), 93-106, 2015.
  • Uddin, I., Imdad, M., Some convergence theorems for a hybrid pair of generalized nonexpansive mappings in CAT (0) spaces, J. Nonlinear Convex Anal. 16 (3), 447-457, 2015.
  • Uddin, I., Imdad, M., Ali, J., Convergence Theorems for a Hybrid Pair of Generalized Nonexpansive Mappings in Banach Spaces, Bull. Malays. Math. Sci. Soc., 38 (2), 695-705, 2015.
  • Wangkeeree, R., Preechasilp, P., $\Delta$-Convergence for Generalized Hybrid Mappings in CAT(0) Spaces, Bull. Malays. Math. Sci. Soc., 38 (3), 1127-1141, 2015.
  • Xu, B., Noor, M. A., Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267, 444-453, 2002.

Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space

Year 2018, Volume: 47 Issue: 6, 1595 - 1604, 12.12.2018

İzhar Uddin , Mohammad Imdad

Abstract

In this paper, we study the convergence of  SP-iteration scheme for a class of mappings satisfying the condition (C) and prove $\Delta$-convergence as well as strong convergence theorems in Hadamard spaces. Our results generalize and improve several relevant results of the existing literature.

Keywords

Hadamard spaces $\Delta$-convergence

References

  • Agarwal, R. P., O'Regan, D., Sahu, D. R., Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex. Anal. 8 (1), 61-79, 2007.
  • Berinde, V., Iterative Approximation of Fixed Points, Lecture Notes Math., vol. 1912, Springer, Berlin, 2007.
  • Bridson, M., Haefliger, A., Metric Spaces of Nonpositive Curvature, Springer-Verlag, Berlin, 1999.
  • Brown, K. S., Buildings, Springer-Verlag, New York, 1989.
  • Bruhat, F., Tits, J., Groupes reductifs sur un corps local, I. Donnees radicielles valuees Inst Hautes Etudes Sci Publ Math. 41, 1972.
  • Burago, D., Burago, Y., Ivanov, S., A Course in Metric Geometry, in: Graduate Studies in Math., vol. 33, Amer. Math. Soc., Providence, RI, 2001.
  • Dhompongsa, S., Kirk, W. A., Panyanak, B., Nonexpansive set-valued mappings in metric and Banach spaces, J. Nonlinear Convex Anal. 8, 35-45, 2007.
  • Dhompongsa, S., Kirk, W. A., Sims, B., Fixed points of uniformly lipschitzian mappings, Nonlinear Anal. 65, 762-772, 2006.
  • Dhompongsa, S., Panyanak, B., On $\Delta$-convergence theorems in CAT(0) space, Comput. Math. Appl. 56, 2572-2579, 2008. Goebel, K., Reich, S., Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, Inc., New York, 1984.
  • Ishikawa, S., Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44, 147-150, 1974.
  • Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc., 59, 65-71, 1976.
  • Kirk, W. A., Panyanak, B., A concept of convergence in geodesic spaces, Nonlinear Anal. 68, 3689-3696, 2008.
  • Lim, T. C., Remarks on some fixed point theorems, Proc. Amer. Math. Soc. 60, 179-182, 1976.
  • Mann, W. R., Mean value methods in iterations, Proc. Amer. Math. Soc., 4, 506-510, 1953.
  • Phuengrattana, W., 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, 3006-3014, 2011.
  • Razani, A., Salahifrd, H., Approximating fixed points of generalized non-expansive mappings, Bull. Iranian Math. Soc. 37 (1), 235-246, 2011.
  • Reich, S., Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 67, 274-276, 1979.
  • Şahin, A., Başarır, M., On the strong and $\Delta$-convergence of SP-iteration on CAT(0) space, J. Inequal. Appl., 311, 10pp., 2013.
  • Senter, H. F., Dotson, W. G., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 44, 375-380, 1974.
  • Suzuki, T., Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340, 1088-1095, 2008.
  • Tan, K. K., Xu, H. K., Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178, 301-308, 1993.
  • Thianwan, S., Common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in a Banach space, J. Comput. Appl. Math. 224, 688-695, 2009.
  • Uddin, I., Imdad, M., On certain convergence of S-iteration scheme in CAT(0) spaces Kuwait J. Sci. 42 (2), 93-106, 2015.
  • Uddin, I., Imdad, M., Some convergence theorems for a hybrid pair of generalized nonexpansive mappings in CAT (0) spaces, J. Nonlinear Convex Anal. 16 (3), 447-457, 2015.
  • Uddin, I., Imdad, M., Ali, J., Convergence Theorems for a Hybrid Pair of Generalized Nonexpansive Mappings in Banach Spaces, Bull. Malays. Math. Sci. Soc., 38 (2), 695-705, 2015.
  • Wangkeeree, R., Preechasilp, P., $\Delta$-Convergence for Generalized Hybrid Mappings in CAT(0) Spaces, Bull. Malays. Math. Sci. Soc., 38 (3), 1127-1141, 2015.
  • Xu, B., Noor, M. A., Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267, 444-453, 2002.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

İzhar Uddin

Mohammad Imdad

Publication Date December 12, 2018
Published in Issue Year 2018 Volume: 47 Issue: 6

Cite

APA Uddin, İ., & Imdad, M. (2018). Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space. Hacettepe Journal of Mathematics and Statistics, 47(6), 1595-1604.
AMA Uddin İ, Imdad M. Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space. Hacettepe Journal of Mathematics and Statistics. December 2018;47(6):1595-1604.
Chicago Uddin, İzhar, and Mohammad Imdad. “Convergence of SP-Iteration for Generalized Nonexpansive Mapping in Hadamard Space”. Hacettepe Journal of Mathematics and Statistics 47, no. 6 (December 2018): 1595-1604.
EndNote Uddin İ, Imdad M (December 1, 2018) Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space. Hacettepe Journal of Mathematics and Statistics 47 6 1595–1604.
IEEE İ. Uddin and M. Imdad, “Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1595–1604, 2018.
ISNAD Uddin, İzhar - Imdad, Mohammad. “Convergence of SP-Iteration for Generalized Nonexpansive Mapping in Hadamard Space”. Hacettepe Journal of Mathematics and Statistics 47/6 (December 2018), 1595-1604.
JAMA Uddin İ, Imdad M. Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space. Hacettepe Journal of Mathematics and Statistics. 2018;47:1595–1604.
MLA Uddin, İzhar and Mohammad Imdad. “Convergence of SP-Iteration for Generalized Nonexpansive Mapping in Hadamard Space”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018, pp. 1595-04.
Vancouver Uddin İ, Imdad M. Convergence of SP-iteration for generalized nonexpansive mapping in Hadamard space. Hacettepe Journal of Mathematics and Statistics. 2018;47(6):1595-604.

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