Published September 30, 2015
| Version v1
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The Generalized Non-absolute type of sequence spaces
Creators
- 1. SASTRA University
- 2. CT Group Of Institutions
- 3. Rajamangala University of Technology Srivijaya
Description
In this paper we introduce the notion of $\lambda_{mn}-\chi^{2}$ and $\Lambda^{2}$ sequences. Further, we introduce the spaces $\left[\chi^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)}$ and $\left[\Lambda^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)},$ which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces $\chi^{2}$ and $\Lambda^{2},$ respectively. Moreover, we establish some inclusion relations between these spaces.
Translated Descriptions
⚠️
This is an automatic machine translation with an accuracy of 90-95%
Translated Description (Arabic)
نقدم في هذه الورقة فكرة تسلسل $\lambda _{ mn }-\chi^{ 2 }$ و $\Lambda^{ 2 }$. علاوة على ذلك، نقدم المسافات $\left[\chi^{ 2q\lambda }_{ f\mu },\left \|\ left(d\left(x _{ 1}, 0\right),\ cdots, d\left(x _{ n -1}, 0\right)\right)\right \|_{ p}\ right ]^{\ textit {I}\ left(F\right )}$ and $\ left [\ Lambda^{ 2q\ lambda }_{ f\ mu },\ left \|\ left (d\left(x _{ 1}, 0\right),d\left(x _{ 2}, 0\right)\cdots, d\left(x _{ n -1}, 0\right)\ right \|_{ p}\ right ]^{\ textit {I}\ left(F\right)},$ وهي من النوع غير المطلق، ونحن نثبت أن هذه المساحات هي مساحات خطية الشكل بالنسبة لـ ${ 2} و $ Lambda^{ 2} على التوالي. علاوة على ذلك، نقيم بعض علاقات الإدماج بين هذه المساحات.Translated Description (French)
Dans cet article, nous introduisons la notion de séquences $ \lambda_{mn}-\chi^{2}$ et $ \Lambda^{2}$ . En outre, nous introduisons les espaces $ \left[\chi^{2q\lambda}_{f\mu },\left\ |\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\ right\|_{p}\right]^{\textit{I}\left(F\right)}$ et $ \left[\Lambda^{2q\lambda}_{f\mu },\ left\ |\left(d\ left (x_{1},0\right),d\left(x_{2},0\right),\ cdots, d\left(x_{n-1},0\right)\right\|_{p}\right]^{\textit{I}\left(F\right)},$ qui sont de type non absolu et nous prouvons que ces espaces sont linéairement isomorphiques des espaces $ \chi^{2}$ et $ \Lambda^{2},$ respectivement. De plus, nous établissons des relations d'inclusion entre ces espaces.Translated Description (Spanish)
En este artículo presentamos la noción de secuencias $\lambda_{mn}-\chi^{2}$ y $\Lambda^{2}$. Además, presentamos los espacios $\left[\chi^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right\|_{p}\right]^{\ textit{I}\ left(F\right)}$ y $\left[\ Lambda^{2q\lambda}_{f\mu },\ left\ |\ left (d\left(x_{1},0\right),d\left(x_{2},0\right),\ cdots, d\left(x_{n-1},0\ right)\right)\right\right\|_{p}\right]^{\textit{I}\left(F\right)},$ que son de tipo no absoluto y demostramos que estos espacios son linealmente isomórficos a los espacios $\chi^{2} y $\Lambda^{2}, respectivamente $. Además, establecemos algunas relaciones de inclusión entre estos espacios.Files
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Additional details
Additional titles
- Translated title (Arabic)
- النوع المعمم غير المطلق لمسافات التسلسل
- Translated title (French)
- Le type Généralisé Non-absolu des espaces de séquence
- Translated title (Spanish)
- El tipo de espacios de secuencia no absolutos generalizados
Identifiers
- Other
- https://openalex.org/W2286780145
- DOI
- 10.5269/bspm.v34i1.25674
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