Banach空间中两个多值非扩张映射不动点的迭代逼近问题
|
摘要
研究了两个多值非扩张映射的公共不动点的迭代逼近问题.利用Hausdoff度量,引入了一类新的Ischikawa型迭代,在一致凸的Banach空间里,证明了在某些条件下,此迭代序列强收敛到多值非扩张映射的公共不动点.改进和推广了文献的相关结果.
The purpose of this paper is the use of Hausdoff metric to study the common fixed points of two multivalued mappings.we construct a new class of Ishikawa iterative schemes to approximate common fixed points of two multivalued mappings in a real uniformly convex Banach space and establish strong convergence theorems under some conditions.These improve and extend some corresponding results in.
The purpose of this paper is the use of Hausdoff metric to study the common fixed points of two multivalued mappings.we construct a new class of Ishikawa iterative schemes to approximate common fixed points of two multivalued mappings in a real uniformly convex Banach space and establish strong convergence theorems under some conditions.These improve and extend some corresponding results in.
引文
[1]J.Markin.A fixed point theorem for set valued mappings[J].Bull Amer Math Soc,1968,74:639-640.
[2]Nadler S B Jr.Multivalued contraction mappings[J].Pacific J Math,1969,30:475-488.
[3]Sastry K P R,Babu G V R.Convergence of Ishikawa iterates for multivalued mapping with a fixed point[J].Czechoslovak Math J,2005,55:817-826.
[4]Yisheng Song.Convergence of iterative algorithms for multivalued mappings in Banach spaces[J].Nonl Anal,2009,70:1547-1556.
[5]Abkar A,Eslamian M.Fixed point theorems for Suzuki multivalued nonexpansive mappings in Banach space[J].Fixed point theory Appl,2010,01:1155-1163.
[6]Hu T,Huang J C.A general principle for Ishikawa iterations for multivalued mappings[J].Appl Math,1997,28:1091-1098.
[7]Mujahid Abbas,Safeer H Khan.Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme[J].Appl Math Lett,2011,24:97-102.
[8]Xu H K.Inequalities in Banach space with applications[J].Nonl Anal,1991,16:1127-1138.
[9]Moha Esla,Ali Abkar.One-step iterative process for a finite family of multivalued mappings[J].Math and Comp Mode,2011,54:105-111.
[10]Dhompongsa S,Kaewkhao A,Panyanak B.On Kirk strong convergence theorem for multivalued nonexpansive mapping on CAT(O)spaces[J].Non Ana,2012,75:459-468.
[11]Hu T,Huang J C,Rhoades B E.A general principle for Ishikawa iterations for multivalued mappings[J].Indian J Pure Appl Math,1997,28:1091-1098.
[12]Wittmann R,Appoximation of fixed points of nanexpansive mapping[J].Arch Math,1992,58:486-491.
[13]Jean philippe,Chancelier,Iterative schemes for computing fixed point of nanexpansive mappings in Banach space[J].Jour Comp Appl Math,2009,353:141-153.
[14]Sahu D R.Strong convergence theorems for nonexpansive type and non-self multivalued mappings[J].Nonl Anal,1999,37:401-407.
[15]Naoki Shioji,Wataru Takahashi.Strong convergence of approximated sequences for nonexpansive mappings in Banach space[J].Amer Math Soci,1997,125:3641-3645.
[16]Khan S H,abbas M,Rhoades B E.A new One-step iterative process for approximating Common fixed points of two multivalued nonexpansive mappings[J].Rend Circ Mat,2010,59:149-157.
[17]Aoynama K,Kimura Y,Takahashi W,Toyoda M.Approximation of commom fixed points of countable family of nonexpansive mappings in a Banach spaces[J].Nonl Anal,2007,67:2350-2360.
[2]Nadler S B Jr.Multivalued contraction mappings[J].Pacific J Math,1969,30:475-488.
[3]Sastry K P R,Babu G V R.Convergence of Ishikawa iterates for multivalued mapping with a fixed point[J].Czechoslovak Math J,2005,55:817-826.
[4]Yisheng Song.Convergence of iterative algorithms for multivalued mappings in Banach spaces[J].Nonl Anal,2009,70:1547-1556.
[5]Abkar A,Eslamian M.Fixed point theorems for Suzuki multivalued nonexpansive mappings in Banach space[J].Fixed point theory Appl,2010,01:1155-1163.
[6]Hu T,Huang J C.A general principle for Ishikawa iterations for multivalued mappings[J].Appl Math,1997,28:1091-1098.
[7]Mujahid Abbas,Safeer H Khan.Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme[J].Appl Math Lett,2011,24:97-102.
[8]Xu H K.Inequalities in Banach space with applications[J].Nonl Anal,1991,16:1127-1138.
[9]Moha Esla,Ali Abkar.One-step iterative process for a finite family of multivalued mappings[J].Math and Comp Mode,2011,54:105-111.
[10]Dhompongsa S,Kaewkhao A,Panyanak B.On Kirk strong convergence theorem for multivalued nonexpansive mapping on CAT(O)spaces[J].Non Ana,2012,75:459-468.
[11]Hu T,Huang J C,Rhoades B E.A general principle for Ishikawa iterations for multivalued mappings[J].Indian J Pure Appl Math,1997,28:1091-1098.
[12]Wittmann R,Appoximation of fixed points of nanexpansive mapping[J].Arch Math,1992,58:486-491.
[13]Jean philippe,Chancelier,Iterative schemes for computing fixed point of nanexpansive mappings in Banach space[J].Jour Comp Appl Math,2009,353:141-153.
[14]Sahu D R.Strong convergence theorems for nonexpansive type and non-self multivalued mappings[J].Nonl Anal,1999,37:401-407.
[15]Naoki Shioji,Wataru Takahashi.Strong convergence of approximated sequences for nonexpansive mappings in Banach space[J].Amer Math Soci,1997,125:3641-3645.
[16]Khan S H,abbas M,Rhoades B E.A new One-step iterative process for approximating Common fixed points of two multivalued nonexpansive mappings[J].Rend Circ Mat,2010,59:149-157.
[17]Aoynama K,Kimura Y,Takahashi W,Toyoda M.Approximation of commom fixed points of countable family of nonexpansive mappings in a Banach spaces[J].Nonl Anal,2007,67:2350-2360.