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An overview to analyticity of dual functions
(Ankara Univ, Fac Sci, 2022) Durmaz, Olgun; Keçilioğlu, Osman; Aktaş, Büşra
In this paper, the analyticity conditions of dual functions are clearly examined and the properties of the concept derivative are given in detail. Then, using the dual order relation, the dual analytic regions of dual analytic functions are constructed such that a collection of these regions forms a basis on Dn. Finally, the equivalent of the inverse function theorem in dual space is given by a theorem and proved.
The inequalities on dual numbers and their topological structures
(Tubitak Scientific & Technological Research Council Turkey, 2023) Aktaş, Büşra; Durmaz, Olgun; Gündoğan, Halit
Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings.