Paper's Title:

Harnack Extension of C[a, B]-valued Functions

Author(s):

Andrew Felix IV Suarez Cunanan

Davao Del Sur State College
E-mail: andrewfelixiv.cunanan@dssc.edu.ph

Abstract:

In this paper, a version of Harnack extension of Henstock-Kurzweil integral of C[a,b]-valued functions was introduced. Moreover, some conditions were presented such that the said function is closed under Harnack extension.

Paper's Title:

Lebesgue Absolutely Continuous Functions Taking Values on C[a,b]

Author(s):

Andrew Felix IV Suarez Cunanan

North Eastern Mindanao State University
E-mail: afccunanan@nemsu.edu.ph

Abstract:

In this paper a version of absolutely continuous function using Lebesgue partition instead of Riemann partition over the field of C[a,b] will be introduced and we call this function as Lebesgue absolutely continuous function on [f,g]. Moreover, some properties of Lebesgue absolutely continuous function on [f,g] will be presented together with its relationship with the other continuous functions.

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