Mean value theorems in q-calculus

Abstract

In this paper, some properties of continuous functions in q-analysis are investigated. The behavior of q-derivative in a neighborhood of a local extreme point is described. Two theorems are proved which are q-analogons of the fundamental theorems of the differential calculus. Also, two q-integral mean value theorems are proved and applied to estimating remainder term in ́-Taylor formula. Finally, the previous results are used in considering some new iterative methods for equation solving. q-calculus.