Let $D$ be the open disk $|x|< R$ of a complete ultrametric algebraically closed field $\mathbb K$. We define growth order $\rho(f)$, type $\sigma(f)$ cotype $\psi(f)$ and another expression $\theta(f)$ an analytic function in we show relations between number zeros $f$ ``maximum modulus'' involving $\rho,\sigma,\psi$. Then $\rho(f)$ lies $[\theta(f)-1, \theta(f)]$. Moreover, if $0< \rho(f)< +\i...

Let (A; ) be a principally polarized abelian variety (ppav) of dimension g over the eld C of complex numbers. This means that is an ample divisor on A, well-determined up to translation, with h(A; ) := dimH(A; ) = 1. Let [ ] 2 H(A;Z) be the cohomology class of the theta divisor . Then the cohomology class [ ] e is divisible by (g e)!. The class [ ] g e (g e)! is not divisible and it is called t...

In this paper, we first introduce a new family of functions like an implicit function called ?-functions. Furthermore, concept ?-?F-fuzzy contractive mappings, which is weaker than the class fuzzy F-contractive mappings. Then, existence and uniqueness fixed point are established for type mappings in setting metric spaces. Moreover, some examples application to nonlinear fractional differential ...

A substantial body of empirical work documents the lack robustness in deep learning models to adversarial examples. Recent theoretical proved that examples are ubiquitous two-layers networks with sub-exponential width and ReLU or smooth activations, multi-layer width. We present a result same type, no restriction on for general locally Lipschitz continuous activations. More precisely, given neu...

The well-known Banach’s fixed point theorem asserts that if D = X, f is contractive and (X, d) is complete, then f has a unique fixed point in X. In nonlinear analysis, the study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been investigated deeply. The Banach contraction principle [1] is one of the initial and crucial results in thi...

In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f -MK -pair mappings and f -CJM-pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfie...

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, F {T h : h ≥ 0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f : K → K a fixed contractive mapping with contractive coefficient β ∈ 0, 1 . We prove that the following implicit and modified implicit viscosity iterative schemes {xn}...

Abstract Given $$E_0, E_1, E, F$$ E 0 , 1 F rearrangement invariant spaces, $$a, \mathrm {b}, {b}_0, {b}_1$$ a b slowly varying functions and $$0\le \theta _0&lt;...