Results 81 to 90 of about 250 (112)

Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 B.C.--2017) and another new proof

, 2018
In this article, we provide a comprehensive historical survey of 183 different proofs of famous Euclid's theorem on the infinitude of prime numbers.
Meštrović, Romeo
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Superquadratic functions and eigenvalue inequalities

, 2023
There exist two major subclasses in the class of superquadratic functions, one contains concave and decreasing functions and the other, contains convex and monotone increasing functions.
Kian, Mohsen
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Generalization of Hermite–Hadamard, trapezoid, and midpoint Mercer type inequalities for fractional integrals in multiplicative calculus

Boundary Value Problems
This study generalizes Hermite–Hadamard–Mercer type inequalities using Riemann–Liouville fractional integrals within the framework of multiplicative calculus.
Abdul Mateen, Zhiyue Zhang, Serap Özcan, Muhammad Aamir Ali   +3 more
doaj   +1 more source

Some Hermite–Hadamard-mercer Inequalities on the Coordinates on Post Quantum

Annals of Mathematics and Physics
In this paper, we develop new Hermite-Hadamard-Mercer type inequalities on coordinates via post-quantum calculus, also known as (p, q) - calculus. By introducing novel (p1, p2, q1, q2)-differentiable and (p1, p2, q1, q2)-integrable functions, we generalize classical results and extend previous inequalities under the setting of coordinate convexity ...
openaire   +1 more source

On fractional Bullen-type inequalities with applications [PDF]

Integral inequalities in mathematical interpretations are a substantial and ongoing body of research. Because fractional calculus techniques are widely used in science, a lot of research has recently been done on them.
Jongsuk Ro, Sabir Hussain, Sobia Rafeeq
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Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus [PDF]

The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval $ [\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re $, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its ...
Hossam A. Nabwey, Muhammad Nasim Aftab, Saad Ihsan Butt, Sina Etemad   +3 more
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New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

Fractal and Fractional
We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs).
Asfand Fahad, Zammad Ali, Shigeru Furuichi, Saad Ihsan Butt, Ayesha, Yuanheng Wang   +5 more
doaj   +1 more source

Fractional Hermite–Hadamard–Mercer-Type Inequalities for Interval-Valued Convex Stochastic Processes with Center-Radius Order and Their Related Applications in Entropy and Information Theory

Fractal and Fractional
We propose a new definition of the γ-convex stochastic processes (CSP) using center and radius (CR) order with the notion of interval valued functions (C.RI.V). By utilizing this definition and Mean-Square Fractional Integrals, we generalize fractional Hermite–Hadamard–Mercer-type inclusions for generalized C.RI.V versions of convex, tgs-convex, P ...
Ahsan Fareed Shah, Serap Özcan, Miguel Vivas–Cortez, Muhammad Shoaib Saleem, Artion Kashuri   +4 more
openaire   +2 more sources

Refinement of Jensen Mercer and Hermite–Hadamard-Mercer type inequalities for generalized convex functions on co-ordinates with their computational analysis

Annals of Mathematics and Physics
In the current study, the Jensen-Mercer inequality is extended to co-ordinated h-convex functions. Additionally, a novel inequality is employed to derive Hermite–Hadamard-Mercer type inequalities for h-convex functions defined on the co-ordinates of a rectangle in the plane.
Toseef Muhammad, Zhang Zhiyue, Mateen Abdul, Budak Hüseyin, Kashuri Artion   +4 more
openaire   +2 more sources

Some Generalizations of Mercer inequality and its operator extensions

We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators.
Kian, Mohsen, Mazraj, Zainab Peymani
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