A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity

We utilize a new definition for the fractional delta operator and prove that it is equivalent by translation to the more commonly used operator. By means of the convolution operation we demonstrate that this new operator is strongly connected to the positivity, monotonicity, and convexity of the fun...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 236; no. 2; pp. 533 - 589
Main Authors Goodrich, Christopher, Lizama, Carlos
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.03.2020
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Convexity
Convolution
Group Theory and Generalizations
Linear operators
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Theoretical
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Summary:We utilize a new definition for the fractional delta operator and prove that it is equivalent by translation to the more commonly used operator. By means of the convolution operation we demonstrate that this new operator is strongly connected to the positivity, monotonicity, and convexity of the functions on which it operates. We also analyze the case of compositions of discrete fractional operators. Finally, since the operator we study here is translationally related to the more commonly used discrete fractional operators, we are able to establish many new results for all types of discrete fractional differences, and we explicitly demonstrate that our results improve all known existing results in the literature.
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ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-020-1991-2