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A study on error bounds for Newton-type inequalities in conformable fractional integrals
(Walter De Gruyter Gmbh, 2024) Budak, Huseyin; Unal, Cihan; Hezenci, Fatih
The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the H & ouml;lder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation.
Conformable fractional Newton-type inequalities with respect to differentiable convex functions
(Springer, 2023) Unal, Cihan; Hezenci, Fatih; Budak, Huseyin
The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Holder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.