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Register a new userOn the differentiability of interval functions
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Authors
Walter F. Mascarenhas
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Two articles published by Information Science discuss the derivatives of interval functions, in the sense of Svetoslav Markov. The authors of these articles tried to characterize for which functions and points such derivatives exist. Unfortunately, their characterization is inaccurate. This article describes this inaccuracy and explains how it can be corrected.
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In this paper, some sufficient conditions for the differentiability of the $n$-variable real-valued function are obtained, which are given based on the differentiability of the $n-1$-variable real-valued function and are weaker than classical conditions.
We introduce and investigate the concept of harmonical $h$-convexity for interval-valued functions. Under this new concept, we prove some new Hermite-Hadamard type inequalities for the interval Riemann integral.
99 -
Xiao-Jun Yang (School of Mathematics
, China University of Mining andn Technology
, Xuzhou
2021
This article proves the products, behaviors and simple zeros for the classes of the entire functions associated with the Weierstrass-Hadamard product and the Taylor series.
For a function $fcolon [0,1]tomathbb R$, we consider the set $E(f)$ of points at which $f$ cuts the real axis. Given $fcolon [0,1]tomathbb R$ and a Cantor set $Dsubset [0,1]$ with ${0,1}subset D$, we obtain conditions equivalent to the conjunction $fin C[0,1]$ (or $fin C^infty [0,1]$) and $Dsubset E(f)$. This generalizes some ideas of Zabeti. We observe that, if $f$ is continuous, then $E(f)$ is a closed nowhere dense subset of $f^{-1}[{ 0}]$ where each $xin {0,1}cap E(f)$ is an accumulation point of $E(f)$. Our main result states that, for a closed nowhere dense set $Fsubset [0,1]$ with each $xin {0,1}cap E(f)$ being an accumulation point of $F$, there exists $fin C^infty [0,1]$ such that $F=E(f)$.
112 -
Xiao-Jun Yang (School of Mathematics
, China University of Mining andn Technology
, Xuzhou
2021
In this article an alternative infinite product for a special class of the entire functions are studied by using some results of the Laguerre-P{o}lya entire functions. The zeros for a class of the special even entire functions are discussed in detail. It is proved that the infinite product and series representations for the hyperbolic and trigonometric cosine functions, which are coming from Euler, are our special cases.
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