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The power quantum calculus and variational problems
Quantum variational problems n q-power difference operator generalized Norlund sum
2011/8/23
Abstract: We introduce the power difference calculus based on the operator $D_{n,q} f(t) = \frac{f(qt^n)-f(t)}{qt^n -t}$, where $n$ is an odd positive integer and $0at...
D-polynomials and Taylor formula in quantum calculus
quantum calculus Taylor formula difference operator
2011/1/21
Quantum calculus based on the right invertible divided difference operator D is proposed here in context of algebraic analysis [9].
L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
L'Hopital-Type Rules Quantum Calculus
2010/11/24
We prove new l'Hopital rules for monotonicity valid on an arbitrary time scale. Both delta and nabla monotonic l'Hopital rules are obtained. As an example of application, we give some new upper and lo...
ON A PALEY-WIENER THEOREM FOR A THIRD OPERATOR IN QUANTUM CALCULUS
q-Analysis q-Fourier transform q-translation
2008/11/26
In this paper, a q-version of the Paley Wiener theorem related to the q-3-cosine
Fourier transform is given for 0 < q < 1.