Using Leray-Schauder degree theory we study the existence of at least one solution for boundary value problem type\[\left\{\begin{array}{lll}(\varphi(u' ))' = f(t,u,u') & \\u'(0)=u(0), \ u'(T)= bu'(0), \quad \end{array}\right.\] where $\varphi: \mathbb{R}\rightarrow \mathbb{R}$ is a homeomorphism such that $\varphi(0)=0$, $f:\left[0, T\right]\times \mathbb{R} \times $ continuous function, $...

It is known that it a very restrictive condition for frame $\{f_{k}\}^{\infty }_{k=1}$ to have representation $ \{T^n \varphi \}_{n=0}^\infty as the orbit of bounded operator $T$ under single generator $\varphi \in \mathcal H.$ We prove that,

Given a family $$\varphi = (\varphi_1, \ldots, \varphi_d)\in \mathbb{Z}[T]^d$$ of d distinct nonconstant polynomials, positive integer $$k\le d$$ and real parameter $$\rho$$ , we consider the mean value $$M_{k, \rho} (\varphi, N) \int_{{\rm x} \in [0,1]^k} \sup_{{\rm y} [0,1]^{d-k}} | S_{\varphi}({\rm x}, {\rm y}; |^\rho \,d{\rm $$ of exponential sums $$S_{\varphi}({\rm \sum_{n=1}^{N} \...

Abstract Kreisel’s conjecture is the statement: if, for all $n\in \mathbb {N}$ , $\mathop {\text {PA}} \nolimits \vdash _{k \text { steps}} \varphi (\overline {n})$ then \forall x.\varphi (x)$ . For a theory of arithmetic T given recursive function h $T _{\leq h} $ holds if there proof $\varphi in whose code at most $h(\#\varphi )$ This notion depends on underlying coding. ${P}^h_T(x)$ predicat...

Let f be an entire function, f(0) = 1, F(z) zf′ (z)/f(z), and Γm $$\bigcup_{j=1}^{m}\left\{z:\mathrm{arg}z={\psi }_{j}\right\},$$ 0 ≤ ψ1 < ψ2 ...< ψm 2π. An function is called a of improved regular growth if for some ρ ∈ (0;+∞) ρ2 (0; ρ), 2π-periodic ρ-trigonometrically convex h(φ) ≢ −∞, there exists set U ⊂ $${\mathbb{C}}$$ contained in the union disks with finite sum radii such that $$\begin{...

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...