Geodesic
New parameterized inequalities for twice differentiable functions
Filomat, Tome 37 (2023) no. 12, p. 3737

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DOI

The present paper first establishes that an identity involving generalized fractional integrals is proved for twice differentiable functions by using a parameter. By using this equality, we obtain some parameterized inequalities for the functions whose second derivatives in absolute value are convex. Finally, we show that our main results reduce to trapezoid, midpoint Simpson and Bullen-type inequalities which are proved in earlier published papers.
DOI : 10.2298/FIL2312737B
Classification : 26D07, 26D10, 26D15, 26A33
Keywords: Trapezoid inequalities, Midpoint inequalities, Simpson type inequalities, Bullen-type inequalities, generalized fractional integrals, twice differentiable functions 
Hüsein Budak; Hasan Kara; Fatih Hezenci; Mehmet Zeki Sarıkaya. New parameterized inequalities for twice differentiable functions. Filomat, Tome 37 (2023) no. 12, p. 3737 . doi: 10.2298/FIL2312737B
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     title = {New parameterized inequalities for twice differentiable functions},
     journal = {Filomat},
     pages = {3737 },
     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312737B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312737B/}
}
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