Geodesic
Some Milne's rule type inequalities in quantum calculus
Filomat, Tome 37 (2023) no. 27, p. 9119

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DOI

The main goal of the current study is to establish some new Milne's rule type inequalities for single-time differentiable convex functions in the setting of quantum calculus. For this, we establish a quantum integral identity and then we prove some new inequalities of Milne's rule type for quantum differentiable convex functions. These inequalities are very important in Open-Newton's Cotes formulas because, with the help of these inequalities, we can find the bounds of Milne's rule for differentiable convex functions in classical or quantum calculus. The method adopted in this work to prove these inequalities are very easy and less conditional compared to some existing results. Finally, we give some mathematical examples to show the validity of newly established inequalities.
DOI : 10.2298/FIL2327119S
Classification : 26D10, 26A51, 26D15
Keywords: Hermite–Hadamard inequality, Jensen-inequality, convex interval-valued functions 
Ifra Bashir Siala; Hüsein Budak; Muhammad Aamir Ali. Some Milne's rule type inequalities in quantum calculus. Filomat, Tome 37 (2023) no. 27, p. 9119 . doi: 10.2298/FIL2327119S
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     title = {Some {Milne's} rule type inequalities in quantum calculus},
     journal = {Filomat},
     pages = {9119 },
     year = {2023},
     volume = {37},
     number = {27},
     doi = {10.2298/FIL2327119S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2327119S/}
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