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引用次数: 0
摘要
在本文中,我们提出了有界、普林斯海姆意义上的收敛、普林斯海姆意义上的无效、正则、正则无效和绝对可 p 求和的双复数双序列的概念。我们还引入了双复数双序列重复极限的概念。我们已经确定,每个双复数的 P 收敛双序列并不总是有界的,但双复数的正则收敛双序列是有界的。研究表明,引入的双复数双序列类是线性空间。借助定义在双复数上的欧氏规范,证明在这些类中,有界类是巴拿赫空间。我们建立了它们的一些代数和拓扑性质,如实体性、单调性、对称性和无收敛性。我们还讨论了一些合适的例子,以支持序列类的引入和那些不成立的性质。
In this paper we present the notion of bounded, convergent in Pringsheim sense, null in Pringsheim sense, regular, regular null and absolutely p-sumable double sequences of bi-complex numbers. We have also introduced the concept of repeated limit of the double sequences of bi-complex numbers. We have established that every P-convergent double sequence of bi-complex numbers is not always bounded but regular convergent double sequences of bi-complex numbers is bounded. It is shown that the introduced classes of double sequences of bi-complex numbers are linear spaces. With the help of the Euclidean norm defined on bi-complex numbers, it is shown that among these classes, the bounded classes are Banach spaces. We have established some of their algebraic and topological properties like solidity, monotonic, symmetric and convergence free. Suitable examples have been discussed to support the introduction of the classes of sequences and the properties, those fail to hold.