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

Issue

Vol. 54 No. 3–4 (2002): Vol. 54, Issue 3–4

Section

Articles

License

Copyright (c) 2002 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.