TY - JOUR
T1 - Multiplicative tempered fractional Newton-type inequalities for twice *differentiable multiplicatively inverse cosine convex functions with applications
AU - Samraiz, Muhammad
AU - Ashraf, Muhammad Abu Bakar
AU - Naheed, Saima
AU - Vivas-Cortez, Miguel
N1 - Publisher Copyright:
© The Author(s) 2025.
PY - 2025/12
Y1 - 2025/12
N2 - In this paper, an integral identity is developed using the framework of multiplicative tempered Riemann-Liouville fractional integrals. By utilizing the identity several Newton-type inequalities are established for twice *differentiable multiplicatively inverse cosine convex functions. The appeal of generalized convex functions stems from their applicability to a broader function class than ordinary convex functions. This helps in finding the best possible lower and upper bounds more effectively. In addition, we establish some more refined results via Hölder and power-mean inequalities. The obtained results are verified through graphs. Finally, some applications are given in the context of quadrature formulae.
AB - In this paper, an integral identity is developed using the framework of multiplicative tempered Riemann-Liouville fractional integrals. By utilizing the identity several Newton-type inequalities are established for twice *differentiable multiplicatively inverse cosine convex functions. The appeal of generalized convex functions stems from their applicability to a broader function class than ordinary convex functions. This helps in finding the best possible lower and upper bounds more effectively. In addition, we establish some more refined results via Hölder and power-mean inequalities. The obtained results are verified through graphs. Finally, some applications are given in the context of quadrature formulae.
KW - Inverse Cosine convex functions
KW - Multiplicative calculus
KW - Newton formula
KW - Newton-type inequalities
KW - Tempered fractional integrals
UR - https://www.scopus.com/pages/publications/105025366428
U2 - 10.1186/s13660-025-03399-z
DO - 10.1186/s13660-025-03399-z
M3 - Article
AN - SCOPUS:105025366428
SN - 1025-5834
VL - 2025
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
IS - 1
M1 - 156
ER -