Related papers: Entire functions sharing simple $a$-points with th…

If $f$ is an entire function and $a$ is a complex number, $a$ is said to be an asymptotic value of $f$ if there exists a path $\gamma$ from $0$ to infinity such that $f(z) - a$ tends to $0$ as $z$ tends to infinity along $\gamma$. The…

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are \phi-convex, log-\phi-convex, and quasi-\phi-convex.

For every $m\in\mathbb{N}$, we establish the convergence of the averaged distributions of the zeros of the $m$-th order derivatives $(f^n)^{(m)}$ of the iterated polynomials $f^n$ of a polynomial $f\in\mathbb{C}[z]$ of degree $>1$ towards…

We prove that a function $f(x,y)$ of real variables defined on a rectangle, having square integrable partial derivatives $f"_{xx}$ and $f"_{yy}$, has almost everywhere mixed derivatives $f"_{xy}$ and $f"_{yx}$.

In this paper, we obtain new estimates on generalization of Hermite-Hadamard, Simpson and Ostrowski type inequalities for functions whose second derivatives is $\varphi$-convex via fractional integrals.

Recently a function was constructed that satisfies all known properties of a tree-level scattering of four massless scalars via the exchange of an infinite tower of particles with masses given by the non-trivial zeroes of the Riemann zeta…

We prove that any $q$-automatic completely multiplicative function $f:\mathbb{N}\to\mathbb{C}$ essentially coincides with a Dirichlet character. This answers a question of J. P. Allouche and L. Goldmakher and confirms a conjecture of J.…

In this paper, we seek to explore under what conditions the periodicity of an entire function $ f(z) $ follows from the periodicity of a differential polynomial in $ f(z) $. We improve and generalize some earlier results and we give other…

We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…

We prove that finite sets of mutual neighbor points in an affine scheme admit affine combinations, preserved by any map. Furthermore, such combination has a value which is neighbor point of all the original points.

The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

In this paper, we show the existence of a transcendental function $f\in\mathbb{Z}\{z\}$ with coefficients that are almost all bounded such that $f$ and all its derivatives assume algebraic values at algebraic points. Furthermore, we…

Let $f$ be a normalized, ordinary newform of weight $\ge 2$. For each prime $\mathfrak{p}$ of $F=\mathbb{Q}(a_n)_{n\in \mathbb{N}}$, there is an associated $\mathfrak{p}$-adic $L$-function $\mathcal{L}_\mathfrak{p}(f)\in \Lambda \otimes…

We study the sets of points where a L\'evy function and a translated L\'evy function share a given couple of H\''older exponents, and we investigate how their Hausdorff dimensions depend on the translation parameter.

In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those…

Two fractional Stefan problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0,1)$ such that in the limit case ($\alpha =1$) both problems coincide with the same classical Stefan problem. For the one…

Perfect nonlinear functions from a finite group $G$ to another one $H$ are those functions $f: G \rightarrow H$ such that for all nonzero $\alpha \in G$, the derivative $d_{\alpha}f: x \mapsto f(\alpha x) f(x)^{-1}$ is balanced. In the case…

Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…

Let $x,y\in(0,1]$ and let $A,B,C$ be disjoint nonempty subsets of a graph $G$, where every vertex in $A$ has at least $x|B|$ neighbours in $B$, and every vertex in $B$ has at least $y|C|$ neighbours in $C$. We denote by $\phi(x,y)$ the…