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Zbl 1087.33009
Rajković, Predrag M.; Marinković, Sladjana D.; Stanković, Miomir S.
Finding the zeros of the functions treated by $q$-calculus. (English)
[A] Mladenov, Iva\"ilo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3--10, 2004. Sofia: Bulgarian Academy of Sciences. 284-286 (2005). ISBN 954-84952-9-5/pbk

The authors prove a $q$-analogue of the Taylor formula for functions of several variables and develop some new methods for solving equations and systems of equations. They apply their methods in solving equations where the function involved is defined by some $q$-integral. The convergence and accuracy of the introduced methods are discussed and several examples are given.
[Stamatis Koumandos (Nicosia)]

MSC 2000:: *33D45 Basic hypergeometric functions and integrals in several variables
05A30 q-calculus and related topics
33D90 Appl. of basic hypergeometric functions
33D60 Basic hypergeometric integrals and functions defined by them

Keywords: Partial $q$-derivatives; $q$-Taylor formula; $q$-Newton method; zeros of functions defined by $q$-integrals

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