Double sequence spaces over $n$-normed spaces
نویسندگان
چکیده
منابع مشابه
DOUBLE SEQUENCE SPACES OVER n-NORMED SPACES
In this paper, we define some classes of double sequences over n-normed spaces by means of an Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relations among the classes are also examined.
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*Correspondence: [email protected] 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India Full list of author information is available at the end of the article Abstract In the present paper we introduce double sequence spacem2(M,A,φ ,p,‖·, . . . , ·‖) defined by a sequence of Orlicz functions over n-normed space. We examine some of its topological properties and estab...
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The concept of 2-normed spaces was initially developed by Gähler[5] in the mid of 1960’s, while that of n-normed spaces one can see in Misiak[15]. Since then, many others have studied this concept and obtained various results, see Gunawan ([7,8]) and Gunawan and Mashadi [9] and references therein. Let n ∈ N and X be a linear space over the field K, where K is field of real or complex numbers of...
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Given ann-normed space withn≥ 2, we offer a simple way to derive an (n−1)norm from the n-norm and realize that any n-normed space is an (n−1)-normed space. We also show that, in certain cases, the (n−1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n− 1)-norm. Using this fact, we prove a fixed point t...
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ژورنال
عنوان ژورنال: Archivum Mathematicum
سال: 2014
ISSN: 0044-8753,1212-5059
DOI: 10.5817/am2014-2-65