Hahn Difference Operator and Associated Jackson–Nörlund Integrals

M. H. Annaby (), A. E. Hamza () and K. A. Aldwoah ()
Additional contact information
M. H. Annaby: Qatar University
A. E. Hamza: Cairo University
K. A. Aldwoah: Jazan University

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 9, 133-153

Abstract: Abstract This paper is devoted for a rigorous investigation of Hahn’s difference operator and the associated calculus. Hahn’s difference operator generalizes both the difference operator and Jackson’s q-difference operator. Unlike these two operators, the calculus associated with Hahn’s difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to establish a calculus of differences based on Hahn’s difference operator. We construct a right inverse of Hahn’s operator and study some of its properties. This inverse also generalizes both Nörlund sums and the Jackson q-integrals. We also define families of corresponding exponential and trigonometric functions which satisfy first and second order difference equations, respectively.

Keywords: Hahn’s operator; Difference equations; q-Difference equations; Nörlund sums; Jackson q-integral (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-012-9987-7

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