a consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable hilbert space. it is proved, through a kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the hilbert space. as an application, this will naturally accomplish the work of kante...

We establish some common fixed point theorems for Kannan fuzzy mappings on closed balls in a complete metric space. Our investigation is based on the fact that fuzzy fixed point results can be obtained simply from the fixed point theorem of multivalued mappings with closed values. In real world problems there are various mathematical models in which the mappings are contractive on the subset of...

In recent years the stability of the isoperimetric and related inequalities has been the object of many investigations. Roughly speaking, given the well known isoperimetric property of balls, the question is how far a set E ⊂ R is from the unit ball B1 if |E| = |B1| and its perimeter P (E) is close to the perimeter of B1. The first results in this direction where obtained for planar sets by Ber...

We give Schwarz lemma at the boundary for holomorphic mappings between $p$-unit ball $B_{p}^{n} \subset \mathbb{C}^{n}$ and $B_{p}^{N} \mathbb{C}^{N}$, where $p \geq 2$. When = 2$, this result reduces to that of Liu, Chen Pan [21] Euclidean unit balls, our method is new. By generalizing pluriharmonic Gauthier [5] from 2$ we obtain balls.

Example 3. How many ways are there to put m balls into n bins. Assume m ≤ n. 1. Balls are distinct and bins are distinct. Every ball has n choices. Hence n. Exercise 2. Why is the answer not m by looking at the opposite argument. 2. Balls are not distinct but bins are distinct. Take m identical balls and n− 1 identical sticks and permute them. Every permutation gives a different arrangement. So...