论文标题
非固定ϕ收缩和相关分形
Non-stationary ϕ-contractions and associated fractals
论文作者
论文摘要
在这项研究中，我们提供了BANACH收缩原理的几种重要概括，其中Lipschitz常数被实现的控制函数取代，这是一个比较函数。我们研究定点的非平稳变体。特别是，本文研究了由功能系统定义的地图的轨迹，这些轨迹被认为是传统迭代功能系统的概括。分析了映射的一般序列的前向和向后轨迹的重要性。这些轨迹的收敛特征确定了传统固定点理论的非平稳变体。与在各种尺度上具有自相似性的正常分形不同，这些图轨迹的吸引子由功能系统定义的地图轨迹的吸引子，这些函数系统可能在各种尺度上具有各种结构。在本文中，我们还研究了在完整的度量空间上具有一些广义收缩的可数IF的顺序。
In this study we provide several significant generalisations of Banach contraction principle where the Lipschitz constant is substituted by real-valued control function that is a comparison function. We study non-stationary variants of fixed-point. In particular, this article looks into trajectories of maps defined by function systems which are regarded as generalizations of traditional iterated function system. The importance of forward and backward trajectories of general sequences of mappings is analyzed. The convergence characteristics of these trajectories determined a non-stationary variant of the traditional fixed point theory. Unlike the normal fractals which have self-similarity at various scales, the attractors of these trajectories of maps which defined by function systems that may have various structures at various scales. In this literature we also study the sequence of countable IFS having some generalized contractions on a complete metric space.
