φ-度量模块空间中的定点定理和迭代函数系统

Fixed Point Theory and Applications Pub Date : 2024-03-04 DOI:10.1186/s13663-024-00761-6

Bikramjit Acharjee, Guru Prem Prasad M

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引用次数: 0

摘要

我们介绍并研究了φ-metric 模块空间的概念，然后定义了其上φ-α-Meir-Keeler 收缩并探讨了其固定点。此外，我们还定义了所考虑空间的两个非空紧凑子集之间的豪斯多夫距离。我们还探讨了φ-metric 模块空间的一些拓扑性质。此外，我们还证明了由φ-α-Meir-Keeler收缩组成的IFS吸引子（分形）的存在性。

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Fixed point theorem and iterated function system in φ-metric modular space

We introduce and study the concept of φ-metric modular space and, then define φ-α-Meir-Keeler contraction on it and explore its fixed point. Further, we define the Hausdorff distance between two non-empty compact subsets of the considered space. Some topological properties of φ-metric modular space are also explored. Additionally, we prove the existence of the attractor (fractal) of the IFS consisting of φ-α-Meir-Keeler contractions.

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.