Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.

We show that the imaginary multiplicative chaos $\exp(i\beta \Gamma)$ determines gradient of underlying field $\Gamma$ for all log-correlated Gaussian fields with covariance form $-\log |x-y| + g(x,y)$ mild regularity conditions on $g$, $d \geq 2$ and $\beta \in (0,\sqrt{d})$. In particular, we 2D continuum zero boundary free is measurable w.r.t. its chaos.

Models of intermittent behaviour are usually formulated using a set of multiplicative random weights on a Cayley tree. However, inter-mittency in particle multiproduction from QCD jets is related to fragmentation of an additive quantum number, e.g. energy-momentum. We exhibit the non-trivial stochastic mapping between these additive and multiplicative cascading processes.

| To each number > 1 there corresponds a discrete countable set of numbers denoted by Z and named set of beta-integers. The set Z is precisely the set of real numbers which are polynomial in when they are written in \basis ", and Z = Zwhen 2 N. We prove here a list of arithmetic properties of Z : addition, multiplication, relation with integers, when is a quadratic Pisot-Vijayaraghavan unit (qu...

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...

In this paper, we introduce and study  a mapping from the collection of all  intermediate rings of $C(X)$ to the collection of all  realcompactifications of $X$ contained in $beta X$. By establishing the relations between this mapping and its converse,  we give a different approach to the main statements of De et. al. Using these, we provide different answers to the   four basic questions...

Write $$\mathrm {ord}_p(\cdot )$$ for the multiplicative order in $${\mathbb {F}}_p^{\times }$$ . Recently, Matthew Just and second author investigated problem of classifying pairs $$\alpha , \beta \in {\mathbb {Q}}^{\times }\setminus \{\pm 1\}$$ which {ord}_p(\alpha ) > \mathrm {ord}_p(\beta holds infinitely many primes p. They called such order-dominant. We describe an easily-checkable suffic...