TY - JOUR
T1 - Remarks On Inequalities With Parameter By Conformable Fractional Integrals
AU - Hezenci, Fatih
AU - Vivas-Cortez, Miguel
AU - Budak, Hüseyin
N1 - Publisher Copyright:
© 2024 The Author(s).
PY - 2024
Y1 - 2024
N2 - We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established by using the conformable fractional integrals. Namely, we show that our main inequalities reduce to Ostrowski-, Hermite-Hadamard-, Simpson-, and Bullen-type inequalities which are proved in earlier published papers. More precisely, some inequalities are acquired by taking advantage of the convexity, the Hölder, and the power mean inequalities. Finally, examples are given to illustrate the investigated results.
AB - We prove that an equation holds for differentiable convex functions, and this result has been derived using conformable integrals. With the help of this equality, several parameterized inequalities are established by using the conformable fractional integrals. Namely, we show that our main inequalities reduce to Ostrowski-, Hermite-Hadamard-, Simpson-, and Bullen-type inequalities which are proved in earlier published papers. More precisely, some inequalities are acquired by taking advantage of the convexity, the Hölder, and the power mean inequalities. Finally, examples are given to illustrate the investigated results.
KW - Bullen-Type Inequality
KW - Convex Function
KW - Fractional Calculus
KW - Fractional Conformable Integrals
KW - Hermite-Hadamard-Type Inequality
KW - Ostrowski-Type Inequality
KW - Simpson-Type Inequality
UR - http://www.scopus.com/inward/record.url?scp=85207936409&partnerID=8YFLogxK
U2 - 10.1142/S0218348X24501378
DO - 10.1142/S0218348X24501378
M3 - Article
AN - SCOPUS:85207936409
SN - 0218-348X
JO - Fractals
JF - Fractals
M1 - 2450137
ER -