Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NEW QUANTUM VARIANTS OF SIMPSON-NEWTON TYPE INEQUALITIES VIA (α, m)-CONVEXITY

  • Saad Ihsan Butt (Department of Mathematics, COMSATS University Islamabad, Lahore Campus) ;
  • Qurat Ul Ain (Department of Mathematics, COMSATS University Islamabad, Lahore Campus) ;
  • Huseyin Budak (Faculty of Science and Arts, Duzce University)
  • Received : 2022.12.27
  • Accepted : 2023.04.27
  • Published : 2023.06.30
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Abstract

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q𝝔1-integral and q𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.

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References

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