The history of q-calculus and a new method

By Thomas Ernst. 2000

307 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/895b4f8b059dc7ad18807f5aabdf09f2158d0c66

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Citations in the corpus

Statistical approximation properties of q-Baskakov-Kantorovich operators (2009, methodology): “In what follows we mention some basic definitions and notations used in q-calculus, details can be found in [14] and [ 12 ].”
Nontrivial solutions for fractional q-difference boundary value problems (2010, background): “It is rich in history and in applications as the reader can confirm in the paper [6].”
A generalization of starlike functions of order alpha (2014, unknown): “The q-theory has important role in special functions and quantum physics (see for instance [4, 11, 12, 19, 20, 30]).”
On a Sequence of Linear and Positive Operators (2009, methodology): “where x ∈ [0, 1 ], q ∈ (0, 1), C being a positive constant which does not depend on n and q .F orq = qn → 1 we obtain for all n 0 ≤ (L � q”
Fractional q-Calculus on a time scale (2007, background): “Eloe [10], McAnally ([22], [23]), Ernst [12], and Koornwinder [20], [21] and books by Andrews, Askey, Verma [6] and Carlson [9] for current and excellent accounts of q-special functions.”
Generalized q-Baskakov operators (2011, methodology): “By using above equality in q-Taylor formula given in [9], we get Bn,q(f, x) = ∞ ∑”
A Method for q-Calculus (2003, methodology): “We have used the following definition from [41]:”
Simpson and Newton type inequalities for convex functions via newly defined quantum integrals (2020, methodology): “Should we multiply both sides of the resulting equality by (b−a) after substituting the equalities (8)-(10) in (6), then we obtain the required identity which finishes the proof.”
Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, background): “In addition, since q-calculus has a tremendous potential for applications [16], we find it pertinent to investigate such a demand.”