Article
Mathematics, Applied
Miguel Vivas-Cortez, Muhammad Aamir Ali, Artion Kashuri, Huseyin Budak
Summary: This paper establishes inequalities for convex functions using generalized fractional integrals, extending and refining Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. Special cases are discussed and new inequalities are presented for different fractional integrals such as Riemann-Liouville (RL), k-Riemann-Liouville (k-RL), conformable, and exponential kernel fractional integrals.
Article
Physics, Multidisciplinary
Ohud Bulayhan Almutairi
Summary: This article extends several integral inequalities involving (h-m)-convexity via quantum calculus, generalizes some quantum integral inequalities for q-differentiable (h-m)-convexity, and can serve as the refinement and unification of classical results in the literature by taking the limit q -> 1(-).
Article
Mathematics, Applied
Thanin Sitthiwirattham, Muhammad Aamir Ali, Huseyin Budak, Sotiris K. Ntouyas, Chanon Promsakon
Summary: In this paper, new Ostrowski type inequalities for differentiable harmonically convex functions are proved using generalized fractional integrals. Special cases of Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals are considered to establish these new inequalities. Finally, applications to special means of real numbers for the newly established inequalities are given.
Article
Mathematics, Applied
B. Meftah, M. Benssaad, W. Kaidouchi, S. Ghomrani
Summary: This paper establishes some conformable fractional Hermite-Hadamard type integral inequalities via harmonic s-convexity, and also considers estimates of the products of two harmonic s-convex functions.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics
Cihan Unal, Fatih Hezenci, Hueseyin Budak
Summary: In this paper, an identity for differentiable convex functions related to conformable fractional integrals is proven. Additionally, parameterized inequalities are established using conformable fractional integrals, exploiting the convexity, Holder inequality, and power mean inequality. Furthermore, previous and new results are presented based on special cases of the obtained theorems.
TURKISH JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Fangfang Ma
Summary: In this paper, we investigate further versions of generalized Hadamard type fractional integral inequality for k-fractional integrals using the definition of h-convex function. The presented results are applicable to variant types of convexities and fractional integrals.
Article
Mathematics, Applied
Huseyin Budak, Fatih Hezenci, Hasan Kara
Summary: This paper establishes an identity involving generalized fractional integrals for differentiable functions using two parameters. By utilizing this identity, several parameterized inequalities for convex functions with derivatives in absolute value are obtained. It is shown that the main inequalities reduce to previously proven Ostrowski type, Simpson type, and trapezoid type inequalities in earlier published papers.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Multidisciplinary Sciences
Miguel Vivas-Cortez, Asia Latif, Rashida Hussain
Summary: In this research, some new Hermite-Hadamard-Fejer-type inequalities for the class of v-convex functions are obtained using Raina fractional integrals. These inequalities are more comprehensive and inclusive than the corresponding ones present in the literature.
Article
Mathematics, Interdisciplinary Applications
Maja Andric
Summary: This article presents several fractional integral inequalities of the Hermite-Hadamard type for the class of (h,g;m)-convex functions. By using fractional integral operators with extended generalized Mittag-Leffler functions as their kernel, new inequalities are derived, extending and generalizing known results. As an application, upper bounds of fractional integral operators for (h,g;m)-convex functions are provided.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Hao Fu, Yu Peng, Tingsong Du
Summary: This paper introduces a class of the multiplicative tempered fractional integral operators and investigates related inequalities. The results generalize previous findings and provide examples to illustrate the simplicity of calculations.
Article
Mathematics, Interdisciplinary Applications
Dafang Zhao, Muhammad Aamir Ali, Chanon Promsakon, Thanin Sitthiwirattham
Summary: In this paper, we establish a generalized fractional integrals identity involving parameters and differentiable functions. We then prove various generalized fractional integrals inequalities for differentiable convex functions using this newly established identity. Finally, we demonstrate the applications of these inequalities in the context of quadrature formulas.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Kin Keung Lai, Jaya Bisht, Nidhi Sharma, Shashi Kant Mishra
Summary: This paper introduces a new class of interval-valued preinvex functions, termed as harmonically h-preinvex interval-valued functions. New inclusion of Hermite-Hadamard for harmonically h-preinvex interval-valued functions is established via interval-valued Riemann-Liouville fractional integrals. Furthermore, fractional Hermite-Hadamard-type inclusions for the product of two harmonically h-preinvex interval-valued functions are proven. These findings include several well-known results and newly obtained results of the existing literature as special cases. Additionally, applications of the main results are demonstrated by presenting some examples.
Article
Mathematics, Interdisciplinary Applications
Yongfang Qi, Guoping Li
Summary: In this paper, new Hermite-Hadamard-Fejer type inequalities are presented via Riemann-Liouville fractional integrals for specific types of functions, which yield classic inequalities in special cases, and applications of the results are provided at the end.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics, Interdisciplinary Applications
Yongfang Qi, Guoping Li, Shan Wang, Qing Zhi Wen
Summary: This paper establishes generalizations of Hermite-Hadamard-Fejer-type inequalities using Holder's inequality and Katugampola fractional integrals for studying estimations of integral averages of convex functions.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Hao Wang, Zhijuan Wu, Xiaohong Zhang, Shubo Chen
Summary: By applying exponential type m-convexity, the Hoelder inequality, and the power mean inequality, this paper concludes explicit bounds for fractional integrals with exponential kernel inequalities. The results provide generalizations of earlier works.
