Recent zbMATH articles in MSC 46A35https://zbmath.org/atom/cc/46A352021-07-26T21:45:41.944397ZWerkzeugSpace of coefficients in a intionistic metric space. A basic criterionhttps://zbmath.org/1463.460052021-07-26T21:45:41.944397Z"Gulieva, F. A."https://zbmath.org/authors/?q=ai:gulieva.f-a(no abstract)On the space of coefficients in the intuitionistic fuzzy normed spaceshttps://zbmath.org/1463.460062021-07-26T21:45:41.944397Z"Guliyeva, F. A."https://zbmath.org/authors/?q=ai:gulieva.f-a|guliyeva.fatima-aSummary: Intuitionistic fuzzy normed space is defined using the concepts of \(t\)-norm and \(t\)-conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity and fuzzy space of coefficients are introduced. Weak completeness of fuzzy space of coefficients with regard to fuzzy norm and weak basicity of canonical system in this space are proved. Weak basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.Domain of the double band matrix defined by Fibonacci numbers in the Maddox's space \(\ell(p)\)https://zbmath.org/1463.460112021-07-26T21:45:41.944397Z"Çapan, Hüsamettin"https://zbmath.org/authors/?q=ai:capan.husamettin"Başar, Feyzi"https://zbmath.org/authors/?q=ai:basar.feyziSummary: In the present paper, some algebraic and topological properties of the domain \(\ell(F,p)\) of the double band matrix \(F\) defined by a sequence of Fibonacci numbers in the sequence space \(\ell(p)\) are studied, where \(\ell(p)\) denotes the space of all sequences \(x=(x_k)\) such that \(\sum_k|x_k|p^k<\infty\) and was defined by \textit{I. J. Maddox} in [Q. J. Math., Oxf. II. Ser. 18, 345--355 (1967; Zbl 0156.06602)]. Furthermore, the alpha-, beta- and gamma-duals of the space \(\ell(F,p)\) are determined, and the Schauder basis is given. The classes of matrix transformations from the space \(\ell(F,p)\) to the spaces \(\ell_\infty\), \(c\) and \(c_0\) are characterized. Additionally, the characterizations of some other matrix transformations from the space \(\ell(F,p)\) to the Euler, Riesz, difference, etc., sequence spaces are obtained from the main results of the paper.