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Certain Generalized Quantum Simpson's and Quantum Newton's type Inequalities for Convex Functions in Quantum Calculus
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  • Muhammad Aamir Ali,
  • Hüseyin BUDAK,
  • PRAVEEN AGARWAL,
  • Yuming Chu
Muhammad Aamir Ali
Nanjing Normal University School of Mathematical Sciences
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Hüseyin BUDAK
Düzce University
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PRAVEEN AGARWAL
Anand International College of Engineering
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Yuming Chu
Huzhou University
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Abstract

In this paper first we present some new identities by using the notions of quantum integrals and derivatives which allows us to obtain new quantum Simpson’s and quantum Newton’s type inequalities for differentiable convex functions by using the q_{x}-quantum integral and q^{y}-quantum integral. In particular, this paper generalises and extends previous results obtained by the various authors in the field of quantum and classical integral inequalities.