分形域中二次可微映射的加权参数化不等式及其应用

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-22 DOI:10.1142/s0218348x23500925

Yunxiu Zhou, Jiagen Liao, T. Du

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引用次数: 0

摘要

本文首先提出了两个加权参数化分形恒等式，其中所涉及的映射是二阶局部分数可微的。在此基础上，推导了一系列与分形凸映射相关的加权参数化不等式。此外，利用有界性和[公式:见文本]-Lipschitzian映射，也获得了一些误差估计。最后，分别根据随机变量和加权公式给出了一定的分形结果作为应用。

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THE WEIGHTED PARAMETERIZED INEQUALITIES IN RELATION TO TWICE DIFFERENTIABLE MAPPINGS IN THE FRACTAL DOMAINS ALONG WITH SOME APPLICATIONS

In this paper, two weighted parameterized fractal identities are first proposed, wherein the mappings involved are second-order local fractional differentiable. Based upon these equalities, a series of the weighted parameterized inequalities, which are related to the fractal convex mappings, are then deduced. Moreover, making use of boundedness and [Formula: see text]-Lipschitzian mappings, some error estimates are attained as well. Finally, certain fractal outcomes in accordance to random variable and the weighted formula, respectively, are presented as applications.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.