**Milan Tvrdy**

## Linear Integral Equations in The Space of Regulated Functions

**abstract:**

In this paper, we investigate the existence of solutions to a wide class of
systems of linear integral equations with solutions which can have in the closed
interval [0,1] only discontinuities of the first kind and are left--continuous
on the corresponding open interval (0,1). The results cower, e.g., the results
knownfor systems of linear generalized differential equations as well as systems
of Stieltjes Integral equations. Some possible applications to functional
differential equationsare discussed as well.

**Mathematics Subject Classification:**
} 45A05, 47G10, 26A39, 26A42.

**Key words and phrases:**
Regulated function, Fredholm--Stieltjes integral
equation, Voltera--Stieltjes integral equation, compact operator,
Perron--Stieltjes integral, Kurzweil integral.