Luciano Stefanini , Manuel Arana-Jiménez , Laerte Sorini
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引用次数: 0
摘要
在这项工作中,我们以广义的赫库哈拉 gH 差分为基础,扩展了多变量区间值函数(IV-函数)的可微性概念。在此背景下,我们引入了一个新的 gH 线性概念,并描述了一类 gH 线性 IV 函数的特征,这对于一阶弗雷谢特型和盖陶型 gH 微分的一般方法至关重要。此外,我们还考虑了向量 IV 函数,并概述了 gH-Jacobian 的定义;通过用中点半径符号表示区间和 IV 函数,我们建立了点微分、弗雷谢特微分和盖陶微分之间的性质和关系。最后,我们还考虑了高阶可微性和 gH-Hessian 矩阵。这些直观的概念在数学上和计算上都易于操作。
Fréchet and Gateaux gH-differentiability for interval valued functions of multiple variables
In this work we extend concepts of differentiability for Interval-Valued functions (IV-functions) of multiple variables, based on generalized Hukuhara gH-difference. In this context, we introduce a new concept of gH-linearity and characterize the class of gH-linear IV-functions, which are fundamental for a general approach to Fréchet-type and Gateaux-type gH-differentiability of the first order. We moreover consider vector IV-functions and outline the definition of the gH-Jacobian; by representing intervals and IV-functions in midpoint-radius notation, we establish properties and relations between pointwise, Fréchet and Gateaux gH-differentiability. Finally, higher-order differentiability and gH-Hessian matrix are considered. These intuitive concepts are mathematically and computationally easy to work with.
期刊介绍:
Informatics and Computer Science Intelligent Systems Applications is an esteemed international journal that focuses on publishing original and creative research findings in the field of information sciences. We also feature a limited number of timely tutorial and surveying contributions.
Our journal aims to cater to a diverse audience, including researchers, developers, managers, strategic planners, graduate students, and anyone interested in staying up-to-date with cutting-edge research in information science, knowledge engineering, and intelligent systems. While readers are expected to share a common interest in information science, they come from varying backgrounds such as engineering, mathematics, statistics, physics, computer science, cell biology, molecular biology, management science, cognitive science, neurobiology, behavioral sciences, and biochemistry.