On the fundamental theorem of $(p,q)$-calculus and some $(p,q)$-Taylor formulas

By P. N. Sadjang. 2013

204 citations recorded by the source corpus.

In this paper, the $(p,q)$-derivative and the $(p,q)$-integration are investigated. Two suitable polynomials bases for the $(p,q)$-derivative are provided and various properties of these bases are given. As application, two $(p,q)$-Taylor formulas for polynomials are given, the fundamental theorem of $(p,q)$-calculus is included and the formula of $(p,q)$-integration by part is proved.

Subfields: Algebra and Number Theory, Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/facc272362bb71ee46c13a03244b4c3c989ed0d2

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In Algebra and Number Theory

In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

$$\left( p,q\right) $$p,q-Hermite–Hadamard inequalities and $$\left( p,q\right) $$p,q-estimates for midpoint type inequalities via convex and quasi-convex functions (2018, background): “1), then 0Dp,q f (t) = Dp,q f (t), where Dp,q f (t) is familiar (p, q)-derivative of f at t ∈ [a, b] defined by the expression (see [5,13]) Dp,q f (t) = f (pt) − f (qt) (p − q) t , t = 0.”
On a Kantorovich Variant of (p,q) -Szász-Mirakjan Operators (2015, unknown): “ﬁned by Z a 0 f(x)dp,qx= (q−p)a X∞ k=0 pk qk+1 f pk qk+1 a , when p q <1, and Z a 0 f(x)dp,qx= (p−q)a X∞ k=0 qk pk+1 f qk pk+1 a , when p q >1. Details on (p,q)-calculus can be found in [5, 8, 17]. For p= 1, all the notions of (p,q)-calculus are reduced to q-calculus. 2. Operators and esti”