scholarly journals Fractional Variational Calculus for Non-differentiable Functions

2011 ◽  
pp. 97-108 ◽  
Author(s):  
Agnieszka B. Malinowska
Keyword(s):  
Variational Calculus ◽  
Differentiable Functions

Differentiable Functions Have Sparse Graphs

1978 ◽  
Vol 4 (1) ◽  
pp. 91
Author(s):  
Laczkovich ◽  
Petruska
Keyword(s):  
Sparse Graphs ◽  
Differentiable Functions

scholarly journals Cosmic Analogues of Classic Variational Problems

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 71 ◽  
Author(s):  
Valerio Faraoni
Keyword(s):  
Relativistic Particle ◽  
Friedmann Equation ◽  
Variational Calculus ◽  
Variational Problems ◽  
Particle Mechanics ◽  
One Dimensional ◽  
Spatially Homogeneous

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Integral Inequality ◽  
Target Function ◽  
Convexity Property ◽  
Concave Functions ◽  
Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

scholarly journals Explicit, Determinantal, and Recurrent Formulas of Generalized Eulerian Polynomials

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 37
Author(s):  
Yan Wang ◽  
Muhammet Cihat Dağli ◽  
Xi-Min Liu ◽  
Feng Qi
Keyword(s):  
General Formula ◽  
Bell Polynomials ◽  
Eulerian Polynomials ◽  
Differentiable Functions ◽  
Faà Di Bruno Formula ◽  
Derivatives Of

In the paper, by virtue of the Faà di Bruno formula, with the aid of some properties of the Bell polynomials of the second kind, and by means of a general formula for derivatives of the ratio between two differentiable functions, the authors establish explicit, determinantal, and recurrent formulas for generalized Eulerian polynomials.

scholarly journals A new bound for the Jensen gap pertaining twice differentiable functions with applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahid Khan ◽  
Muhammad Adil Khan ◽  
Saad Ihsan Butt ◽  
Yu-Ming Chu
Keyword(s):  
Differentiable Functions

scholarly journals General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1288
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Norm Inequalities ◽  
Differentiable Functions ◽  
Fréchet Differentiable ◽  
General Norm

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

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