PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-11-11 DOI:10.1142/s0218348x23501347

XIAOHUA ZHANG, YUNXIU ZHOU, TINGSONG DU

引用次数: 0

Abstract

The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.

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分形(m,h)-预倒凸映射的性质和2α α -分形加权参数不等式

首先提出了分形[公式:见文]-预凸映射，并对其性质进行了研究。同时，推广了关于[公式:见文]-preinvexity的一些分形hermite - hadamard型([公式:见文])和fej - hermite - hadamard型([公式:见文])不等式。然后，提出了两个加权参数化[公式:见文]-分形恒等式，它们涉及两次局部分数阶可微映射。基于这些恒等式，利用分形[公式:见文]-预凸映射和[公式:见文]-Lipschitzian映射，推导出分形域的误差估计范围。最后，给出了与加权公式和随机变量相关的若干分形不等式作为应用。

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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.