Geodesic
On some error bounds of Maclaurin’s formula for convex functions in q-calculus
Filomat, Tome 37 (2023) no. 18, p. 5883

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DOI

The main goal of this paper is to establish some error bounds for Maclaurin’s formula which is three point quadrature formula using the notions of q-calculus. For this, we first prove a q-integral identity involving fist time q-differentiable functions. Then, by using the new established identity we find the error bounds for maclaurin’s formula by using the convexity of fist time q-differentiable functions. It is also shown that the newly established inequalities are extension of some existing inequalities inside the literature.
DOI : 10.2298/FIL2318883S
Classification : 26D10, 26A51, 26D15
Keywords: Maclaurin’s formula, convex functions, q-calculus 
Thanin Sitthiwirattham; Muhammad Aamir Ali; Jarunee Soontharanon. On some error bounds of Maclaurin’s formula for convex functions in q-calculus. Filomat, Tome 37 (2023) no. 18, p. 5883 . doi: 10.2298/FIL2318883S
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     title = {On some error bounds of {Maclaurin{\textquoteright}s} formula for convex functions in q-calculus},
     journal = {Filomat},
     pages = {5883 },
     year = {2023},
     volume = {37},
     number = {18},
     doi = {10.2298/FIL2318883S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2318883S/}
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