Abstract
A variant of Jessen’s type inequality for a semigroup of positive linear operators, defined on a Banach lattice algebra, is obtained. The corresponding mean value theorems lead to a new family of mean-operators.
Highlights
The idea behind the main contents of this article is not very unusual but has been an active area of research in the present decade [1–4]
In the past few years, the generalization of known inequalities to the operators has become the topic of active research in the field of applied analysis
There has been considerable interest in the generalization of “functional-inequalities” and “type-inequalities” to the semigroups of operators defined on a Banach space [5,6]
Summary
The idea behind the main contents of this article is not very unusual but has been an active area of research in the present decade [1–4]. Let {S(t)}t≥0 be the strongly continuous positive semigroup, defined on a Banach lattice E. Let Dc(E) denote the set of all differentiable convex operators φ : E → E. (Jessen’s Type Inequality) Let {S(t)}t≥0 be the positive C0-semigroup on E such that it satisfies (2).
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