본문 바로가기
KERD
논문KCI 등재

Convergence of a new multistep iteration in convex cone metric spaces

Birol Gunduz
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회논문집 (Communications of the KMS)|제32권 제1호|pp. 39-46

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

strong convergencecommon fixed pointconvex metric spacescone metric spacesasymptotically quasi-nonexpansive mappings
주제분류수학

초록

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee \cite{lee} from the closed convex subset of a convex cone metric space to whole space.

Abstract

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee \cite{lee} from the closed convex subset of a convex cone metric space to whole space.

참고문헌 (11)

  1. B. Gunduz, "A new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces", J. Nonlinear Sci. Appl, 9(3), pp.1365~1372 (2016)
  2. L. G. Huang, "Cone metric spaces and fixed point theorems of contractive mappings", J. Math. Anal. Appl, 322(2), pp.1468~1476 (2007)
  3. A. R. Khan, "Convergence of a general iterative scheme for a fi-nite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications", Comput. Math. Appl, 59(8), pp.2990~2995 (2010)
  4. B. S. Lee, "Approximating common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex cone metric spaces", Univ. J. Appl. Math, 1(3), pp.166~171 (2013)
  5. 이병수, "STRONG CONVERGENCE IN NOOR-TYPE ITERATIVE SCHEMES IN CONVEX CONE METRIC SPACES", 순수 및 응용수학, 22(2), pp.185~197 (2015), 한국수학교육학회
  6. Q. Liu, "Iterative sequence for asymptotically quasi-nonexpansive mappings with errors member", J. Math. Anal. Appl, 259(1), pp.18~24 (2001)
  7. S. Suantai, "Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings", J. Math. Anal. Appl, 311(2), pp.506~517 (2005)
  8. W. Takahashi, "A convexity in metric space and nonexpansive mappings", Kodai. Math. Sem. Rep, 22, pp.142~149 (1970)
  9. L. A. Talman, "Fixed points for condensing multifunctions in metric spaces with convex structure", Kodai Math. Sem. Rep, 29(1-2), pp.62~70 (1977)
  10. B. L. Xu, "Fixed point iterations for asymptotically nonexpansive map-pings in Banach spaces", J. Math. Anal. Appl, 267(2), pp.444~453 (2002)
  11. L. Yang, "Modified multistep iterative process for some common fixed point of a finite family of nonself asymptotically nonexpansive mappings", Math. Comput. Modelling, 45(9-10), pp.1157~1169 (2007)

관련 논문AI추천

STRONG CONVERGENCE IN NOOR-TYPE ITERATIVE SCHEMES IN CONVEX CONE METRIC SPACES이병수한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제2호Convergence of modified multi-step iterative for a finite family of asymptotically quasi-nonexpansive mappingsJuan Xiao, Lei Deng, Ming-ge Yang대한수학회 · 대한수학회논문집2014 · 제29권 제1호COMMON FIXED POINTS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS BY ONE-STEP ITERATION PROCESS IN CONVEX METRIC SPACES김종규, Mujahid Abbas, Safeer Hussain Khan영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호Convergence theorems of a finite family of asymptotically quasi-nonexpansive type mappings in Banach spacesGurucharan Singh Saluja영남수학회 · East Asian Mathematical Journal2011 · 제27권 제1호Two 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 제3호

이 간행물의 다른 논문 (21건)

Galois irreducible polynomials권미연, 이지은, 이기석pp. 1-6Extended zero-divisor graphs of idealizationsJilali Mikram, Fouad Taraza, Driss Bennispp. 7-17Invo-clean unital ringsPeter V. Danchevpp. 19-27Certain integrals associated with generalized Mittag-Leffler functionShilpi Jain, Praveen Agarwal, 최준상, Mohammad Mehdi Rashidipp. 29-38Certain unified integral formulas involving the generalized modified k-Bessel function of first kindKottakkaran Sooppy Nisar, Saiful Rahman Mondalpp. 47-53
원문 보기