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Spaces defined by the level function and their duals

100%

Sinnamon G.

nr 1

19-52

The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of $L^p$. These domains are shown to be Banach spaces which, although closely tied to $L^p$ spaces, are not reflexive. A related construction is given which characterizes their dual spaces.

Generalization of different type integral inequalities for generalized (s, m)-preinvex Godunova-Levin functions

63%

Kashuri A. , Liko R.

tom Vol. 24, nr 2

211--221

In the present paper, the notion of generalized (s, m)-preinvex Godunova-Levin function of second kind is introduced, and some new integral inequalities involving generalized (s, m)-preinvex Godunova-Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite-Hadamard, Ostrowski and Simpson type inequalities for generalized (s, m)-preinvex Godunova-Levin functions of second kind via Riemann-Liouville fractional integral are established.

On the zeros of an analytic function

63%

Jain V.

2014

tom Vol. 37

51--58