Mean value theorems in q-calculus

Authors

  • Predrag M. Rajković Faculty of Mechanical Engineering, University of Niš, 18000 Niš, Yugoslavia Author
  • Miomir S. Stanković Faculty of Occupational Safety, University of Niš, 18000 Niš, Yugoslavia Author
  • Sladjana D. Marinković Faculty of Electrical Engineering, University of Niš, 18000 Niš, Yugoslavia Author

Keywords:

q-calculus

Subjects:

26A99

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 q-Taylor formula. Finally, the previous results are used in considering some new iterative methods for equation solving.

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Published

2002-10-15