General Opial type inequality

In this paper our goal is to give a general Opial type inequality. We consider two functions, convex and concave and prove a new general inequality on a measure space (Ω,Σ, μ ). The obtained inequalities are not direct generalizations of the Opial inequality but are of Opial type because the integra...

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Published inAequationes mathematicae Vol. 89; no. 3; pp. 641 - 655
Main Authors Barbir, Ana, Himmelreich, Kristina Krulić, Pečarić, Josip
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.06.2015
Springer Nature B.V
Subjects
Analysis
Combinatorics
Mathematical functions
Mathematics
Mathematics and Statistics
Polynomials
Symmetry
jensen inequality
green function
Opial inequality
hermite interpolating polynomial
Secondary 26A51
Primary 26D15
lidstone polynomial
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ISSN0001-9054
1420-8903
DOI10.1007/s00010-013-0252-4

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Summary:In this paper our goal is to give a general Opial type inequality. We consider two functions, convex and concave and prove a new general inequality on a measure space (Ω,Σ, μ ). The obtained inequalities are not direct generalizations of the Opial inequality but are of Opial type because the integrals contain a function and its integral representation. We apply our result to numerous symmetric functions and obtain new results that involve Green’s functions, Lidstone series and the Hermite’s interpolating polynomials.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-013-0252-4