Symmetric Quantum Calculus

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Simpson and Newton type inequalities for convex functions via newly defined quantum integrals (2020, methodology): “Then, using the expression (1) for the first quantum integral in (7), we find that”
Basic and fractional q-calculus and associated Fekete-Szegő problem for p-valently q-starlike functions and p-valently q-convex functions of complex order (2019, background): “INTRODUCTION, DEFINITIONS AND PRELIMINARIES The theory of the basic and the fractional quantum calculus (that is, the basic qcalculus and the fractional q-calculus) plays important roles in many diverse areas of the mathematical, physical and engineering sciences (see, for example, [5, 9, 16] and [2”
The H-Laplace and Q-Laplace Transforms (2010, background): “Let us use the notation from [13], in particular [α] = [α]q = q α − 1 q − 1 , α ∈ R, [n]! = n ∏ k=1 [k], [ n m ] = [n]! [m]![n − m]! , m,n ∈ N0, (t − s)q = n−1 ∏ k=0 ( t − qks), t, s ∈ T, n ∈ N0, with [0]! = 1 and (t − s)0 q = 1.”