Introduction to the Stieltjes extension of Dunford and Pettis-type integrals on time scales
Abstract
Abstract. In this manuscript, we introduce the Reimann-Stieltjes-Dunford, Reimann-Stieltjes-
Pettis and Reimann-Stieltjes-Gelfand integrals. Scalarly Reimann-Stieltjes integral, weak
Reimann-Stieltjes integral and weak∗ scalarly Reimann-Stieltjes integral definitions are put
forward; and few relations between these integrals with the above mentioned integrals are
established. Uniform convergence of a sequence of functions which are either Reimann-Stieltjes-
Dunford integral, Reimann-Stieltjes-Pettis integral or Reimann-Stieltjes-Gelfand integral is also
formulated.
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