Results 101 to 110 of about 250 (112)

Refinement of Jensen's Inequality for Analytical Convex (Concave) Functions [PDF]

Kórus Péter, Retkes Zoltán
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Some Hermite-Hadamard-Mercer Inequalities for General Fractional Convex on the Coordinates

Advances in Pure Mathematics
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Some new q-Hermite-Hadamard-Mercer inequalities and related estimates in quantum calculus

Journal of Nonlinear and Variational Analysis, 2023
Summary: In this paper, we establish a quantum version of the Hermite-Hadamard-Mercer inequalities using the well-known Jensen-Mercer inequality. Moreover, we derive some new \(q\)-midpoint and \(q\)-trapezoidal type inequalities for differentiable functions.
Ali, Muhammad Aamir, Köbis, Elisabeth
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On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus

Analysis, 2023
Abstract In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI.
Muhammad Aamir Ali, Christopher S. Goodrich   +1 more
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A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS

Fractals
In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite–Hadamard–Mercer-type inequalities for differentiable function.
THANIN SITTHIWIRATTHAM, MIGUEL VIVAS-CORTEZ, MUHAMMAD AAMIR ALI, HÜSEYIN BUDAK, İBRAHIM AVCI   +4 more
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Generalization of Hermite-Hadamard-Mercer]{Generalization of Hermite-Hadamard-Mercer and Trapezoid Formula Type Inequalities Involving Beta Function

In this work, we prove a generalized version of Hermite-Hadamard-Mercer type inequalities using the Beta function. Moreover, we prove some new trapezoidal type inequalities involving Beta functions for differentiable convex functions. The main advantage of these inequalities is that these can be converted into similar classical integral inequalities ...
Muhammad Aamir Ali, Zhiyue Zhang
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GENERALIZATION OF HERMITE–HADAMARD–MERCER AND TRAPEZOID FORMULA TYPE INEQUALITIES INVOLVING THE BETA FUNCTION

Rocky Mountain Journal of Mathematics
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Ali, Muhammad Aamir, Zhang, Zhiyue, Fečkan, Michal   +2 more
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On q-Hermite–Hadamard–Mercer and midpoint-Mercer inequalities for general convex functions with their computational analysis

International Journal of Geometric Methods in Modern Physics
This paper establishes some new inequalities of Hermite–Hadamard–Mercer type for [Formula: see text]-convex functions in the framework of [Formula: see text]-calculus and classical calculus. Some new [Formula: see text]-midpoint-Mercer type inequalities for the [Formula: see text]-differentiable [Formula: see text]-convex functions are also proved ...
Muhammad Toseef, Zhiyue Zhang, Muhammad Aamir Ali   +2 more
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STRENGTHENED VERSION OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR HARMONICALLY CONVEX FUNCTIONS BASED ON JENSEN–MERCER INEQUALITY

Fractals
This study is chiefly concerned with the application of the harmonically convexity condition to establish a series of novel fractional Hermite–Hadamard–Mercer inequalities via the Jensen–Mercer inequality. In both classical and fractional calculus, the existing Hermite–Hadamard–Mercer inequalities have provided certain bounds.
FANGFANG SHI, MUHAMMAD AMIR ALI, WEI LIU, DONGDONG GAO   +3 more
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On generalization of Hermite–Hadamard–Mercer inequalities for interval-valued functions with generalized geometric–arithmetic convexity

International Journal of Geometric Methods in Modern Physics
In this paper, we introduce a new convexity notion for inter-valued functions, known as Geometrically–Arithmetically Cr-[Formula: see text]-convex functions (abbreviated as GA-Cr-[Formula: see text]-CFs) and explore its properties. The family of GA-Cr-[Formula: see text]-CFs simultaneously covers the family of GA-CFs, GA-[Formula: see text]-CFs and GA-
Asfand Fahad, Youhua Qian, Zammad Ali, Awais Younus   +3 more
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