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Some remarks on parameterized inequalities involving conformable fractional operators
(Tubitak Scientific & Technological Research Council Turkey, 2023) Unal, Cihan; Hezenci, Fatih; Budak, Hueseyin
In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems.
A study on error bounds for Newton-type inequalities in conformable fractional integrals
(Walter De Gruyter Gmbh, 2024) Budak, Hüseyin; 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.