Summary
In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.
Recently Kiryakova and several other ones have investigated so-called
multiindex Mittag-Leffler functions associated with fractional calculus.
Here, in this paper, we aim at establishing a new fractional integration
formula (of pathway type) involving the generalized multiindex Mittag-Leffler
function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result
are also considered and shown to be connected with certain known ones.
In this paper the author introduces a general integral operator and
determines conditions for the univalence of this integral operator. Also, the
significant relationships and relevance with other results are also given.
The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space
