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

Let X be a Hausdorff locally convex topological vector space with \Omega and X^{*} as its topology and Topological dual respectively. Suppose f:[۰,۱]\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.

کلیدواژه ها:

Hausdorff Topological vector Space ، guages ، Topological dual ، Semi-norms ، time scale