Abstract
Hermite–Hadamard’s-type inequality is derived using superquadratic maps for positive operator semigroups. A methodical procedure was adopted to obtain the corresponding mean operators.
Highlights
Matloob Anwar is an assistant professor of Mathematics in the Department of Mathemaics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan
In this note, a Hermite-Hadamard type inequality has been proved for a positive C0-semigroup and a superquadratic mapping defined on a Banach lattice algebra
A methodic way has been adopted to prove the corresponding mean value theorems, which enabled us to define a new set of mean operators
Summary
This research is devoted to Cauchy-type mean Operators defined on superquadratic mappings and operator semigroups. Gul I Hina Aslam and Matloob Anwar have been generalizing the theory of inequalities for operator semigroups. The set of all positive linear mappings forms a convex cone in the space L( ) and defines the natural ordering in it. Definition 1.1 A family of bounded linear operators { (s)}s≥0 on a Banach space is called a (one parameter) C0-semigroup (or strongly continuous semigroup), if it satisfies (i) (s) (t) = (s + t) for all s, t ∈ R+.
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