... Publishing as Pearson Addison-Wesley
function header
function body
Function Definition
Provides the same information as the declaration
Describes how the function does its task
Example:
double ... you
Write a function declaration and a function definition
for a function that takes three arguments, all of type
int, and that returns the sum of its three arguments?
Describe the call-by -value ... mechanism?
Write a function declaration and a function definition
for a function that takes one argument of type int and
one argument of type double, and that returns a value
of type double...
... convex functions taking the infinity value
Passing from sets to functions
A common device to construct convex functions on IR
n
is to construct a
convex set F in IR
n+1
and then take the function ... sets and convex functions taking the infinity value
Quasi-convex functions
However if the sublevel sets are convex, the function f is not necessarily
convex. See the figure below.
A function satisfying ... Chapter 1 Convex sets and convex functions taking the infinity value
Example. The indicator function
Let S be a nonempty subset of IR
n
. The indicator function of S is defined
by
δ
S
: IR
n
→...
... bandlimited function
using very coarsely quantized data:
A family of stable sigma -delta
modulators of arbitrary order
By Ingrid Daubechies and Ron DeVore
APPROXIMATING A BANDLIMITED FUNCTION ... APPROXIMATING A BANDLIMITED FUNCTION 685
Proposition 2.3. For f ∈C
1
,λ>1, define the sequence q
λ
through
the recurrence (8), with u
0
chosen arbitrarily in (−1, 1).Letg beafunction
satisfying (6). ... single-loop sigma -delta modulator
with dc input, IEEE Trans. on Commun. COM-37 (1989), 588–599.
[6]
R. M. Gray, W. Chou, and P. W. Wong, Quantization noise in single-loop sigma -delta
modulation...
... co-ordinated convex functions by using Lemma 1 and to establish some new
Hadamard-type inequalities for co-ordinated s-convex functions by using Lemma 2.
2. Inequalities for co-ordinated convex functions
To ... Maligranda, L: Some remarks on s-convex functions. Aequationes Math. 48, 100–
111 (1994)
[3] Dragomir, SS, Fitzpatrick, S: The Hadamard’s inequality for s-convex functions in the second
sense. Demonstratio ... Hadamard-type inequalities for s-convex
functions. Appl. Math. Comput. 193, 26–35 (2007)
[5] Burai, P, H´azy, A, Juh´asz, T: Bernstein-Doetsch type results for s-convex functions. Publ.
Math. Debrecen....
... Generalized Hyers-Ulam-Rassias stability of functional inequalities and functional
equations. J Math Inequal. 3(1), 63–77 (2009)
14. Moghimi, M, Najati, A, Park, C: A functional inequality in restricted ... F: Stability of a quadratic functional equation in quasi Banach spaces. Bull Korean Math Soc. 45,
587–600 (2008)
18. Najati, A, Lee, J, Park, C: On a Cauchy- Jensen functional inequality. Bull ... Hyers-Ulam stability of functional equa-
tion (b) and functional inequality (c) has been presented in [ 13]. We remark that there
are some interesting papers concerning the stability of functional inequalities...
... Yang, CC, Hua, X: Uniqueness and value sharing of meromorphic functions. Ann Acad Sci Fenn Math. 22, 395–406
(1997)
5. Fang, ML: Uniqueness and value sharing of entire functions. Math Appl. 44, 828–831 ... Meromorphic Functions. Clarendon Press, Oxford (1964)
2. Yang, L: Value Distribution Theory. Springer/Science Press, Berlin/Beijing (1993)
3. Yang, CC, Yi, HX: Uniqueness Theory of Meromorphic Functions. ... sharing the same value. Int J Pure Appl Math. 48,
41–56 (2008)
7. Lahiri, I, Sahoo, P: Uniqueness of meromorphic functions when two non-linear differential polynomials share a small
function. Arch...
... periodic boundary value problem s with
sign-changing Green’s function. Boundary Value Problems 2011 2011:8.
Zhong and An Boundary Value Problems 2011, 2011:8
http://www.boundaryvalueproblems.com/content/2011/1/8
Page ... boundary value problem with vanishing Green’s function. Appl Math Lett. 21,
176–180 (2008). doi:10.1016/j.aml.2007.02.019
6. Webb, TRL: Boundary value problems with vanishing Green’s function. ... case of posi-
tive Green’s function, vanishing Green’s function and sign-changing Green’sfunction,
respectively.
4 An example
Let 0 ≠ q<1 be a constant, h be the function:
h(x)=
1, x ≥ 0,
0,...
... Corporation
Boundary Value Problems
Volume 2010, Article ID 973731, 22 pages
doi:10.1155/2010/973731
Research Article
Solutions and Green’s Functions for
Boundary Value Problems of Second-Order
Four-Point Functional ... Green’s functions and the existence of positive solutions for a second-order
functional difference equation with four-point boundary conditions.
1. Introduction
In recent years, boundary value problems ... and multiplicity of the boundary value problems to a
class of second-order functional difference equations
Lu
n
f
n, u
n1
,u
n
,u
n−1
1.1
with boundary value conditions
Δu
0
A, u
k1
...