Abstract
Schuster introduced the notion of Blaschke-Minkowski homomorphism and considered its Shephard problems. Wang gave the definition of Blaschke-Minkowski homomorphisms and considered its Shephard problems for volume. In this paper, we obtain its Shephard type inequalities for the affine surface area and two monotonicity inequalities for Blaschke-Minkowski homomorphisms are established. MSC:52A20, 52A40.
Highlights
Let Kn denote the set of convex bodies in Euclidean space Rn
We continuously study the Lp Blaschke-Minkowski homomorphisms
Ωpn = {N ∈ Fen : there exists Z ∈ Zpn with fp(N, ·) = h(Z, ·)–(n+p)}, where fp(N, ·) is the p-curvature function of N, Fen denotes the set of convex bodies in Ken with positive continuous curvature function and Zpn denotes the set of Lp Blaschke-Minkowski homomorphisms
Summary
Let Kn denote the set of convex bodies (compact, convex subsets with nonempty interiors) in Euclidean space Rn. Schuster in [ ] gave the definition of Blaschke-Minkowski homomorphism as follows:. Let p > , a map p : Ken → Ken satisfying the following properties (a), (b) and (c) is called an Lp Blaschke-Minkowski homomorphism. Theorem .B Let p : Ken → Ken is an Lp Blaschke-Minkowski homomorphism, K ∈ Ken, L ∈ pKen and p is not an even integer. Comparing with Theorem .B, we give the Lp-affine surface area of Shephard type inequalities for the Lp Blaschke-Minkowski homomorphisms. Ωpn = {N ∈ Fen : there exists Z ∈ Zpn with fp(N, ·) = h(Z, ·)–(n+p)}, where fp(N, ·) is the p-curvature function of N , Fen denotes the set of convex bodies in Ken with positive continuous curvature function and Zpn denotes the set of Lp Blaschke-Minkowski homomorphisms.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
