We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-st...We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.展开更多
Let C be a nonempty closed convex subset of a real Banach space E. Let S ： C→ C be a quasi-nonexpansive mapping, let T ： C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F ：= ...Let C be a nonempty closed convex subset of a real Banach space E. Let S ： C→ C be a quasi-nonexpansive mapping, let T ： C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F ：= {x ∈C ： Sx = x and Tx = x}≠Ф Let {xn}n≥0 be the sequence generated irom an arbitrary x0∈Cby xn＋i=（1-cn）Sxn＋cnT^nxn, n≥0.We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F. These extend and improve the recent results of Moore and Nnoli.展开更多
本文在去掉lim inf||x_n||<∞,sum from n=0 to ∞(k_n-1)<∞条件下,并用α_n→0(n→∞)取代sum from n=0 to ∞α_n^2<∞,使用新的分析技巧,在赋范线性空间中建立了一致Lipschitz的渐近拟伪压缩型映象公共不动点的修改的广义I...本文在去掉lim inf||x_n||<∞,sum from n=0 to ∞(k_n-1)<∞条件下,并用α_n→0(n→∞)取代sum from n=0 to ∞α_n^2<∞,使用新的分析技巧,在赋范线性空间中建立了一致Lipschitz的渐近拟伪压缩型映象公共不动点的修改的广义Ishikawa迭代序列的强收敛定理,从而本质改进和推广了唐玉超,刘理蔚新近的结果.展开更多
文摘We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.
基金the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,Chinathe Dawn Program Foundation in Shanghai and partially supported by grant from the National Science Council of Taiwan
文摘Let C be a nonempty closed convex subset of a real Banach space E. Let S ： C→ C be a quasi-nonexpansive mapping, let T ： C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F ：= {x ∈C ： Sx = x and Tx = x}≠Ф Let {xn}n≥0 be the sequence generated irom an arbitrary x0∈Cby xn＋i=（1-cn）Sxn＋cnT^nxn, n≥0.We prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F. These extend and improve the recent results of Moore and Nnoli.
文摘本文在去掉lim inf||x_n||<∞,sum from n=0 to ∞(k_n-1)<∞条件下,并用α_n→0(n→∞)取代sum from n=0 to ∞α_n^2<∞,使用新的分析技巧,在赋范线性空间中建立了一致Lipschitz的渐近拟伪压缩型映象公共不动点的修改的广义Ishikawa迭代序列的强收敛定理,从而本质改进和推广了唐玉超,刘理蔚新近的结果.
