Leibniz’s Rule and Fubini’s Theorem Associated with a General Quantum Difference Operator

Alaa E. Hamza (), Enas M. Shehata () and Praveen Agarwal ()
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Alaa E. Hamza: Faculty of Science
Enas M. Shehata: Menoufia University
Praveen Agarwal: Anand International College of Engineering

A chapter in Computational Mathematics and Variational Analysis, 2020, pp 121-134 from Springer

Abstract: Abstract In this paper, we derive Leibniz’s rule and Fubini’s theorem associated with a general quantum difference operator D β which is defined by D β f ( t ) = f ( β ( t ) ) − f ( t ) β ( t ) − t $$D_\beta f(t)=\frac {f(\beta (t))-f(t)}{\beta (t)-t}$$ , β(t) ≠ t. Here β is a strictly increasing continuous function defined on a set I ⊆ ℝ $$I\subseteq \mathbb R$$ that has only one fixed point s 0 ∈ I and satisfies the inequality (t − s 0)(β(t) − t) ≤ 0 for all t ∈ I.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-44625-3_7

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DOI: 10.1007/978-3-030-44625-3_7

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