*-Boundedness and *-Continuity of Non-Newtonian Superposition Operators on L∞,α and L1,β

Abstract

Sagir and Erdogan [13] have defined non-Newtonian superposition operators S-N(phi) where phi : N x R-alpha -> R-beta by S-N(phi)(x) = (phi(m, x(m)))(m=1)(infinity) for all alpha-sequences (x(m)). In this study, we get the conditions for the *-boundedness, *-locally boundedness and *-uniform continuity of the non-Newtonian superposition operator S-N(phi) : l(infinity,alpha) -> l(1,beta).