본문 바로가기
KERD
논문KCI 등재

Strong and $\Delta $-convergence of a faster iteration process in hyperbolic space

Birol Gunduz|Sezgin Akbulut
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회논문집 (Communications of the KMS)|제30권 제3호|pp. 209-219

1

조회

0

다운로드

1

인용

0

참고문헌

키워드

iterative processcommon fixed pointsemi-compactnessnonexpansive maphyperbolic space$\Delta $-convergencecondition (A)
주제분류수학

초록

In this article, we first give metric version of an iteration scheme of Agarwal et al.~\cite{Agarwal} and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

Abstract

In this article, we first give metric version of an iteration scheme of Agarwal et al.~\cite{Agarwal} and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

참고문헌 (25)

  1. R. P. Agarwal, "Iterative construction of fixed points of nearly asymptotically nonexpansive mappings", J. Nonlinear Convex Anal, 8(1), pp.61~79 (2007)
  2. H. H. Bauschke, "Convex Analysis and Monotone Operator Theory in Hilbert Spaces" (2011), Springer-Verlag
  3. G. Das, "Fixed points of quasi-nonexpansive mappings", Indian J. Pure Appl. Math, 17(11), pp.1263~1269 (1986)
  4. S. Dhompongsa, "On -convergence theorems in CAT(0)-spaces", Com-put. Math. Appl, 56(10), pp.2572~2579 (2008)
  5. H. Fukhar-ud-din, "Approximating common fixed points in hyperbolic spaces", Fixed Point Theory Appl, 2014(113), pp.15~ (2014)
  6. K. Goebel, "Topological Methods in Nonlinear Functional Analysis", pp.115~123 (1983), Amer. Math. Soc.
  7. K. Goebel, "Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings" (1984), Marcel Dekker
  8. B. Gunduz, "Strong and -convergence theorems in hyperbolic spaces", Miskolc Math. Notes, 14(3), pp.915~925 (2013)
  9. A. R. Khan, "An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces", Fixed Point Theory Appl, 2012, pp.12~ (2012)
  10. S. H. Khan, "Strong and -convergence of some iterative schemes in CAT(0) spaces", Comput. Math. Appl, 61(1), pp.109~116 (2011)
  11. S. H. Khan, "Convergence to common fixed points by a modified iteration process", J. Appl. Math. Comput, 35(1-2), pp.607~616 (2011)
  12. S. H. Khan, "Weak and strong convergence of a scheme with errors for two nonexpansive mappings", Nonlinear Anal, 61(8), pp.1295~1301 (2005)
  13. S. H. Khan, "Approximating common fixed points of two asymptotically nonexpansive mappings", Sci. Math. Jpn, 53(1), pp.143~148 (2001)
  14. W. A. Kirk, "Krasnosel’ski iteration process in hyperbolic spaces", Numer. Funct. Anal. Optim, 4(4), pp.371~381 (1982)
  15. W. A. Kirk, "Approximate fixed points for nonexpansive mappings in uniformly convex spaces", Ann. Polon. Math, 51, pp.189~193 (1990)
  16. U. Kohlenbach, "Some logical metatheorems with applications in functional analysis", Trans. Amer. Math. Soc, 357(1), pp.89~128 (2005)
  17. L. Leustean, "Non-linear Analysis and Optimization I: Nonlinear Analysis", pp.193~209 (2010), Amer. Math. Soc
  18. T. C. Lim, "Remarks on some fixed point theorems", Proc. Amer. Math. Soc, 60, pp.179~182 (1976)
  19. S. Reich, "Nonexpansive iterations in hyperbolic spaces", Nonlinear Anal, 15(6), pp.537~558 (1990)
  20. A. Sahin, "Some convergence results for modified SP-iteration scheme in hyperbolic spaces", Fixed Point Theory Appl, 2014, pp.113~ (2014)
  21. H. F. Senter, "Approximating fixed points of nonexpansive mappings", Proc. Amer. Math. Soc, 44(2), pp.375~380 (1974)
  22. T. Shimizu, "Fixed points of multivalued mappings in certain convex metric spaces", Topol. Methods Nonlinear Anal, 8(1), pp.197~203 (1996)
  23. W. Takahashi, "A convexity in metric spaces and nonexpansive mappings", Kodai Math. Sem. Rep, 22, pp.142~149 (1970)
  24. W. Takahashi, "Iterative methods for approximation of fixed points and their applications", J. Oper. Res. Soc. Japan, 43(1), pp.87~108 (2000)
  25. W. Takahashi, "Limit theorems of operators by convex combinations of nonexpansive retractions in Banach spaces", J. Approx. Theory, 91(3), pp.386~397 (1997)

관련 논문AI추천

Common fixed point of generalized asymptotic pointwise (quasi-) nonexpansive mappings in hyperbolic spacesHafiz Fukhar-ud-din, Khairul Saleh강원경기수학회 · 한국수학논문집2020 · 제28권 제4호Two general iteration schemes for multi-valued maps in hyperbolic spacesAynur \c{S}ah{\.{I}}n, Met{\.{I}}n Ba\c{s}ar\i r대한수학회 · 대한수학회논문집2016 · 제31권 제4호Two Kinds of Convergences in Hyperbolic Spaces in Three-step Iterative Schemes강미광, 김승현한국수학교육학회 · 이론수학과 교직수학2021 · 제28권 제1호S-iteration process for asymptotic pointwise nonexpansive mappings in complete hyperbolic metric spacesAutchara Prasong, Prasit Cholamjiak, Suparat Kesornprom, Thikamporn Atsathi대한수학회 · 대한수학회논문집2016 · 제31권 제3호Some results of the new iterative scheme in hyperbolic spaceAynur Sahin, Metin Basarir대한수학회 · 대한수학회논문집2017 · 제32권 제4호Investigation of some fixed point theorems in hyperbolic spaces for a three step iteration processVatan Karakaya, Yunus Atalan강원경기수학회 · 한국수학논문집2019 · 제27권 제4호

이 간행물의 다른 논문 (16건)

Hesitant fuzzy bi-ideals in semigroups송석준, 이경자, 전영배pp. 143-154Filters of residuated lattices based on soft set theory노은환, 박철환, 전영배, 이경자pp. 155-168Numerical range and SOT-convergencyAbdolaziz Abdollahi, Mohammad Taghi Heydaripp. 169-176Convergence theorems for a pair of asymptotically and multivalued nonexpansive mapping in CAT(0) spacesNaknimit Akkasriworn, Kritsana Sokhumapp. 177-189Certain new generating relations for products of two Laguerre polynomials최준상, Arjun Kumar Rathiepp. 191-200
원문 보기