Inequalities for differences and their applications

This paper deals with various weighted inequalities for the forward difference operator acting on products of compositions and convolutions of functions on . A discrete version of Saitoh's inequality in the Sobolev space and some generalizations of discrete Opial-type inequalities are considere...

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Bibliographic Details
Published in:Journal of difference equations and applications 2014-09, Vol.20 (9), p.1319-1343
Main Authors: Vi Nhan, Nguyen Du, Duc, Dinh Thanh, Tuan, Vu Kim, Huy Vu, Nguyen Du
Format: Article
Language:English
Subjects:
Convolution
convolutions
Difference equations
difference operators
Differential equations
Inequalities
inequalities for sums and series
Mathematical functions
Mathematics
Operators
Riemann zeta function
Sobolev space
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Summary:This paper deals with various weighted inequalities for the forward difference operator acting on products of compositions and convolutions of functions on . A discrete version of Saitoh's inequality in the Sobolev space and some generalizations of discrete Opial-type inequalities are considered. Several applications to the zeta functions and difference equations are also given.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2014.916285