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
A Convergence Theorem for Monotone Increasing and Continuous Functions by Picard Iteration Sequence
摘要/Abstract
摘要:
证明了若f:[a,b]→[a,b]为单调增加的连续函数,∀λ∈(0,1),定义Fλ:[a,b]→[a,b],Fλx=(1-λ)x+λf(x),∀x1∈[a,b],xn+1=Fλxn=Fλx1n,n≥1,则{xn}单调地收敛于f的1个不动点.
Abstract:
Let f:[a,b]→[a,b] be a monotone increasing and continuous function,∀λ∈(0,1),Fλ:[a,b]→[a,b],Fλx=(1-λ)x+λf(x),∀x1∈[a,b],xn+1=Fλxn=Fλx1n,n≥1 is defined.Then {xn} monotonically converges to a fixed point of the function f.