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On differentiable functions [PDF]

Bulletin of the American Mathematical Society, 1960
2. In this note, we intend to give a more detailed description of Eap. We prove the following THEOREM. The set Eap gives rise to a set of nonoverlapping and nonabutting open sub-intervals {/ 0 . Thus, each point of Eap is a limiting point of the set. I.e., EapQE'ap.
Fu Cheng Hsiang
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Algebras of differentiable functions [PDF]

Proceedings of the American Mathematical Society, 1954
1. Let M be a compact differentiable manifold of class Cr, 1
S. B. Myers
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Differentiable functions on 𝑐₀ [PDF]

Bulletin of the American Mathematical Society, 1969
John C. Wells
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A Quantum Calculus View of Hermite–Hadamard–Jensen–Mercer Inequalities with Applications

Symmetry, 2022
In this paper, we derive some new quantum estimates of generalized Hermite–Hadamard–Jensen–Mercer type of inequalities, essentially using q-differentiable convex functions. With the help of numerical examples, we check the validity of the results.
Bandar Bin-Mohsin, Mahreen Saba, Muhammad Zakria Javed, Muhammad Uzair Awan, Hüseyin Budak, Kamsing Nonlaopon   +5 more
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Some Improvements of the Hermite–Hadamard Integral Inequality

Symmetry, 2020
We propose several improvements of the Hermite−Hadamard inequality in the form of linear combination of its end-points and establish best possible constants.
Slavko Simić, Bandar Bin-Mohsin
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Continuous Regular Functions [PDF]

Logical Methods in Computer Science, 2020
Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function $f:[0,1] \to [0,1]$ is $r$-regular if there is a B\"{u}chi automaton that accepts precisely the set of base $r \in \mathbb{N}$ representations of elements of the graph of $f$.
Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan, Ruoyu Meng, Erik Walsberg, Zihe Wang, Ziqin Xiong, Hongru Yang   +7 more
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On some Simpson's and Newton's type of inequalities in multiplicative calculus with applications

AIMS Mathematics, 2023
In this paper, we establish an integral equality involving a multiplicative differentiable function for the multiplicative integral. Then, we use the newly established equality to prove some new Simpson's and Newton's inequalities for multiplicative ...
Saowaluck Chasreechai , Muhammad Aamir Ali, Surapol Naowarat, Thanin Sitthiwirattham, Kamsing Nonlaopon   +4 more
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A New Parameterless Filled Function Method for Global Optimization

Axioms, 2022
The filled function method is an effective way to solve global optimization problems. However, its effectiveness is greatly affected by the selection of parameters, and the non-continuous or non-differentiable properties of the constructed filled ...
Haiyan Liu, Siyan Xue, Yuan Cheng, Shouheng Tuo   +3 more
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Composite differentiable functions [PDF]

Duke Mathematical Journal, 1996
19 pages, hard copy available on request.
Bierstone, Edward, Milman, Pierre D., Pawłucki, Wiesław   +2 more
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On Hermite–Hadamard-Type Inequalities for Functions Satisfying Second-Order Differential Inequalities

Axioms, 2023
Hermite–Hadamard inequality is a double inequality that provides an upper and lower bounds of the mean (integral) of a convex function over a certain interval.
Ibtisam Aldawish, Mohamed Jleli, Bessem Samet   +2 more
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