FACTA UNIVERSITATIS (NI ˇ S) Ser.Math.Inform. Vol. 28, No 4 (2013), 379–392 THE q–ITERATIVE METHODS IN NUMERICAL SOLVING OF SOME EQUATIONS WITH INFINITE PRODUCTS ∗ Sladjana D. Marinkovi´ c, Predrag M. Rajkovi´ c, Miomir S. Stankovi´ c (Dedicated to prof. dr Ljiljana Petkovi´ c for her 60th birthday) Abstract. We consider a few modifications of the well known methods for numerical solving of a equation or a system of equations. Especially, we included Newton’s, the Newton-Kantorovich and gradient method. The purpose was to adapt them to cases when the functions are given in the form of infinite products. The examples comprehend the infinite q-power products and prove that the methods are pretty suitable for them. 1. Introduction A lot of papers were written about the iterative methods for solving of a non- linear equation F(x) = 0, where F(x) is a continuous operator defined on a nonempty subset of a Banach space. In a few papers were considered some unusual functions such as continuous but non-differentiable functions [7] or noncontinuous functions. Another perspective branch of mathematics is q–calculus. It appears as a con- nection between mathematics and physics (see [2], [5], [10]). It has a lot of ap- plications in different mathematical areas, such as: number theory, combinatorics, orthogonal polynomials, basic hyper geometric functions and other sciences: quan- tum theory, mechanics and theory of relativity. Let q  1. A q–complex number [a] q is defined by [a] q = 1 - q a 1 - q , a ∈ C. Received November 21, 2013. 2000 Mathematics Subject Classification. Primary 65H10; Secondary 26A24, 33D15 ∗ The authors were supported in part by the Ministry of Science and Technological Development of the Republic Serbia, projects No 174011 and No 44006. 379