A Study on New q-Integral Inequalities

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DOI: 10.4236/am.2011.24059   PDF   HTML     8,286 Downloads   12,563 Views   Citations

Abstract

A q-analog, also called a q-extension or q-generalization is a mathematical expression parameterized by a quantity q that generalized a known expression and reduces to the known expression in the limit . There are q-analogs for the fractional, binomial coefficient, derivative, Integral, Fibonacci numbers and so on. In this paper, we give several results, some of them are new and others are generalizations of the main results of [1]. As well as we give a generalization to the key lemma ([2], lemma 1.3).

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W. Sulaiman, "A Study on New q-Integral Inequalities," Applied Mathematics, Vol. 2 No. 4, 2011, pp. 465-469. doi: 10.4236/am.2011.24059.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Y. Miao and F. Qi, “Several q-Integral Inequalities,” Journal of Mathematical Inequalities, Vol. 3, No. 1, 2009, pp. 115-121.
[2] K. Brahim, N. Bettaibi and M. Sellemi, “On Some Feng Qi Type q-Intagral Inequlities,” Pure Applied Mathematics, Vol. 9, No. 2, 2008, Art. 43.
[3] E. W. Weisstein, “q-Derivative,” Math World-A Wolfram Web Resource,” 2010. http://mathword. Wolfram .com/q-Derivative.html
[4] E. W. Weisstein, “q-Integral,” Math World-A Wolfram Web Resource,” 2010. http://mathword. Wolfram .com/q-integral.html
[5] F. H. Jackson, “On q-Definite Integrals,” Pure Applied Mathematics, Vol. 41, No. 15, 1910, pp. 193-203.
[6] V. Kac and P. Cheung, “Quantum Calculus,” Universitext, Springer-Verlag, New York, 2003.

  
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