期刊信息

  • 刊名: 河北师范大学学报(自然科学版)Journal of Hebei Normal University (Natural Science)
  • 主办: 河北师范大学
  • ISSN: 1000-5854
  • CN: 13-1061/N
  • 中国科技核心期刊
  • 中国期刊方阵入选期刊
  • 中国高校优秀科技期刊
  • 华北优秀期刊
  • 河北省优秀科技期刊

双曲空间中混合型迭代的强收敛定理及应用

  • 宜宾学院 数学研究所, 四川 宜宾 644007
  • DOI: 10.11826/j.issn.1000-5854.2014.04.005

Strong Convergence Theorem for Mixed Type in Hyperbolic Spaces with Applications

摘要/Abstract

摘要:

在双曲空间中,讨论了一有限簇全渐近非扩张非自映象与另一有限簇全渐近非扩张映象公共不动点的问题,引入了一个混合型迭代序列.并在适当的条件下,证明了一个强收敛定理.所得结果推广和改进了已有结果.

Abstract:

The problem on the common fixed points of two finite family of total asymptotically nonexpansive nonself mappings in Hyperbolic spaces is discussed.Under suitable conditions,some strong convergence theorems are obtained,which extend and improve some of the latest results.

参考文献 17

  • [1] CHANG S S,WANG L,LEE H W J,CHAN C K.Strong and Δ-Convergence for Mixed Type Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces[J/OL].[2013-03-14].http://www.fixedpointtheoryandapplications
  • [2] AGARWAL R P,O'REGAN D,SAHU,D R.Iterative Construction of Fixed Points of Nearly Asymptotically Nonexpansive Mappings[J].J.Nonlinear Convex Anal,2007,8(1):61-79.
  • [3] SAHIN A,BASARIR M.On the Strong Convergence of Modified S-iteration Process for Asymptotically Quasi-non-expansive Mappings in CAT(0) Space[J/OL].[2014-06-14].http://www.fixedpointtheoryandapplications
  • [4] DHOMPONGSA S,PANYANAK B.On Δ-convergence Theorems in CAT(0) Spaces[J].Comput Math Appl,2008,56(10):2572-2579.
  • [5] LEUSTEAN L.A Quadratic Rate of Asymptotic Regularity for CAT(0)-spaces[J].J Math Anal Appl,2007,325:386-399.
  • [6] ESPINOLA R,FERNANDEZ L A.CAT(k)-spaces,Weak Convergence and Fixed Points[J].J Math Anal Appl,2009, 353(1):410-427.
  • [7] SHAHZAD N.Invariant Approximations in CAT(0) Spaces[J].Nonlinear Anal Theory Methods Appl,2009,70(12):4338-4340.
  • [8] NANJARAS B,PANYANAK B,PHUENGRATTANA W.Fixed Point Theorems and Convergence Theorems for Suzuki-generalizedNonexpansive Mappings in CAT(0) Spaces[J].Nonlinear Anal Hybrid Syst,2010,4(1):25-31.
  • [9] LEUSTEAN L.A Quadratic Rate of Asymptotic Regularity for CAT(0)-spaces[J].J Math Anal Appl,2007,325(1):386-399.
  • [10] 雷贤才.全渐近非扩张映象在CAT(0)空间的新迭代算法[J].四川师范大学学报:自然科学版,2013,36(6):876-880.
  • [11] KOHLENBACH U:Some logical Metatheorems with Applications in Functional Analysis[J].Trans Am Math Soc.2005,357:89-128.
  • [12] GOEBEL K,REICH S.Uniform Convexity,Hyperbolic Geometry,and Nonexpansive Mappings[M].New York:Marcel Dekker,1984:189-201.
  • [13] RIDSON M,HAEIGER A.Metric Spaces of Non-Positive Curvature[M].Berlin:Springer-verlag,1999,207-211.
  • [14] TAKAHASHI W.A Convexity in Metric Spaces and Nonexpansive Mappings[J].Kodai Math Sem Rep,1970,22:142-149.
  • [15] SHIMIZU T,TAKAHASHI W.Fixed Points of Multivalued Mappings in Certain Convex Metric Spaces[J].Topol Methods Non-linear Anal,1996,8:197-203.
  • [16] KNAN A R,FUKHARUDDIN H,Khan A A.An Implicit algorithm for two Finite Families of Nonexpansive Maps in Hyperbolic s-paces[J/OL].[2014-08-19].http://www.fixedpointtheoryandapplications
  • [17] LEUSTEAN L.Nonexpansive Iterations in Uniformly Convex W-hyperbolic Spaces[J/OL].[2008-10-22]http://www.arxiv.org/abs/0810.417