A NOTE ON THE M ∗ - LIMITING CONVOLUTION BODY 3 Proof

A Note on the M * -limiting Convolution Body

We introduce the mixed convolution bodies of two convex symmetric bodies. We prove that if the boundary of a body K is smooth enough then as δ tends to 1 the δ-M∗-convolution body of K with itself tends to a multiple of the Euclidean ball after proper normalization. On the other hand we show that the δ-M∗-convolution body of the n-dimensional cube is homothetic to the unit ball of `1 .

A note on the comparison between Laplace and Sumudu transforms

A SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS

In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.

A Note on the Descent Property Theorem for the Hybrid Conjugate Gradient Algorithm CCOMB Proposed by Andrei

In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...

The Volume of the Intersection of a Convex Body with its Translates

It is proved that for a symmetric convex body K in R, if for some τ > 0, |K ∩ (x + τK)| depends on ‖x‖K only, then K is an ellipsoid. As a part of the proof, smoothness properties of convolution bodies are studied.