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Iluebe, Victor, Afariogun, David, Iluno, Christiana, Ajilore, Joshua. (1404). Sequential $\Diamond$ Henstock Integral for Locally Convex Space Valued Function on Time Scale. پژوهشنامه مدیریت اجرایی, 14(2), 185-201. doi: 10.22080/cjms.2025.26691.1680
Victor Odalochi Iluebe; David Adebisi Afariogun; Christiana Iluno; Joshua Olugbenga Ajilore. "Sequential $\Diamond$ Henstock Integral for Locally Convex Space Valued Function on Time Scale". پژوهشنامه مدیریت اجرایی, 14, 2, 1404, 185-201. doi: 10.22080/cjms.2025.26691.1680
Iluebe, Victor, Afariogun, David, Iluno, Christiana, Ajilore, Joshua. (1404). 'Sequential $\Diamond$ Henstock Integral for Locally Convex Space Valued Function on Time Scale', پژوهشنامه مدیریت اجرایی, 14(2), pp. 185-201. doi: 10.22080/cjms.2025.26691.1680
Iluebe, Victor, Afariogun, David, Iluno, Christiana, Ajilore, Joshua. Sequential $\Diamond$ Henstock Integral for Locally Convex Space Valued Function on Time Scale. پژوهشنامه مدیریت اجرایی, 1404; 14(2): 185-201. doi: 10.22080/cjms.2025.26691.1680

Sequential $\Diamond$ Henstock Integral for Locally Convex Space Valued Function on Time Scale

Caspian Journal of Mathematical Sciences
دوره 14، شماره 2 - شماره پیاپی 26، مهر 2025، صفحه 185-201    اصل مقاله (166.93 K)
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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