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Sequential $\Diamond$ Henstock Integral for Locally Convex Space Valued Function on Time Scale | ||
Caspian Journal of Mathematical Sciences | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 خرداد 1404 | ||
نوع مقاله: Review Article | ||
شناسه دیجیتال (DOI): 10.22080/cjms.2025.26691.1680 | ||
نویسندگان | ||
Victor Odalochi Iluebe* 1؛ David Adebisi Afariogun2؛ Christiana Iluno3؛ Joshua Olugbenga Ajilore3 | ||
1Department of Mathematics and Computing, Maranatha University, Lagos, Nigeria. | ||
2Mathematics Department, Faculty of Science, Ajayi Crowther University, Oyo, Nigeria | ||
3Mathematics Department, School of Pure and Applied Sciences, Lagos State University of Science and Technology, lkorodu, Nigeria | ||
تاریخ دریافت: 20 بهمن 1402، تاریخ بازنگری: 29 اردیبهشت 1404، تاریخ پذیرش: 10 خرداد 1404 | ||
چکیده | ||
Let $X$ be a Hausdorff locally convex topological vector space with $\Omega $ and $X^{*}$ as its topology and Topological dual respectively. Suppose $f:[0,1]\rightarrow X$ is a function defined on $X$ and $\rho(X)$, a family of $\rho$-continuous seminorms on $X$ such that the topology is generated by $\rho(X)$. Is f Sequential Mcshane(SMcS) and Sequential Henstock(SH) integrable with respect to the semi-norm on time scale? Do these integrals coincide and relate to other integrals such as Pettis and Bochner for which the Sequential Henstock lemma holds for the characterization of locally Convex space on time scale? It is the purpose of this paper to give affirmative answers to these questions. | ||
کلیدواژهها | ||
Hausdorff Topological vector Space؛ Guages؛ Topological dual؛ Semi-norms؛ Time scale | ||
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