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Inequalities for monotonic series

✍ Scribed by R.P Boas Jr.


Book ID
107798664
Publisher
Elsevier Science
Year
1960
Tongue
English
Weight
223 KB
Volume
1
Category
Article
ISSN
0022-247X

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Some integral inequalities for generalized monotone functions of one variable and an integral inequality for monotone functions of several variables are proved. Some applications are presented and discussed.

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Weighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi-linear operators on monotone functions. Several properties of the classes B@, n) and C(p, n) introduced by NEUGEBAUER in [I31 are given. In particular, we characterize the weight pairs w, v for

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Let L L N denote the class of functions defined by ## Ε½ . Ε½ . For N Βͺ Ο± we write f g L L. Functions in L L are called completely monotonic on Ε½ . 0, Ο± . We derive several inequalities involving completely monotonic functions. In particular, we prove that the implication is true for 0 F N F 7, bu