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A hierarchy in the family of real surjective functions

Mar Fenoy-Muñoz, José Luis Gámez-Merino, Gustavo A. Muñoz-Fernández, Eva Sáez-Maestro (2017)

Open Mathematics

This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...

A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications

Bianca Satco (2006)

Czechoslovak Mathematical Journal

This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.

A Marchaud type inequality

Jorge Bustamante (2022)

Commentationes Mathematicae Universitatis Carolinae

We present a new Marchaud type inequality in 𝕃 p spaces.

A new algorithm for approximating the least concave majorant

Martin Franců, Ron Kerman, Gord Sinnamon (2017)

Czechoslovak Mathematical Journal

The least concave majorant, F ^ , of a continuous function F on a closed interval, I , is defined by F ^ ( x ) = inf { G ( x ) : G ≥ F , G concave } , x ∈ I . We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on I . Given any function F ∈ 𝒞 4 ( I ) , it can be well-approximated on I by a clamped cubic spline S . We show that S ^ is then a good approximation to F ^ . We give two examples, one to illustrate, the other to apply our algorithm.

A new application of the homotopy analysis method in solving the fractional Volterra's population system

Mehdi Ghasemi, Mojtaba Fardi, Reza Khoshsiar Ghaziani (2014)

Applications of Mathematics

This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.

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