Let $\mathcal{A}$ denote the class of functions $f$ which are analytic in open unit disk $\mathbb{U}$ and given by\[f(z)=z+\sum_{n=2}^{\infty }a_{n}z^{n}\qquad \left( z\in \mathbb{U}\right) .\]The coefficient functional $\phi _{\lambda }\left( f\right) =a_{3}-\lambda a_{2}^{2}$ on $f\in \mathcal{A}$ represents various geometric quantities. For example, _{1}\left( =a_{3}-a_{2}^{2}=S_{f}\left( 0\...

In this paper, We define a $\mathcal{F}$-functional and study $\mathcal{F}$-stability of $\lambda$-hypersurfaces, which extend result Colding-Minicozzi. Lower bound growth upper area for complete non-compact $\lambda$-hypersurfaces are studied.

We pursue two goals in this article. As our first goal, we construct a family $\mathcal{M}_G$ of Gibbs like measures on the set piecewise linear convex functions $g:\mathbb{R}^2\to\mathbb{R}$. It turns out that there is one-to-one correspondence between gradient such and $\textit{Laguerre tessellations}$. Each cell Laguerre tessellation polygon marked by vector $\rho\in\mathbb{R}^2$. measure $\...

Abstract In this paper we investigate the spectra and ergodic properties of multiplication operators convolution acting on Schwartz space $${\mathcal S}({\mathbb R})$$ S ( R ) rapidly decreasing functions, i.e., form $$M_h: {\mathcal R}...

Let $$z_0$$ and $$w_0$$ be given points in the open unit disk $$\mathbb {D}$$ with $$|w_0| < |z_0|$$ , $$\mathcal {H}_0$$ class of all analytic self-maps f normalized by $$f(0)=0$$ . In this paper, we establish third-order Dieudonné’s Lemma apply it to explicitly determine variability region $$\{f'''(z_0): f\in \mathcal {H}_0,f(z_0) =w_0, f'(z_0)=w_1\}$$ for $$z_0,w_0,w_1$$ give form extremal f...

This work is concerned to study the bouncing nature of universe for an isotropic configuration fluid $\mathcal{T}_{\alpha\beta}$ and Friedmann-Lema\^{i}tre-Robertson-Walker metric scheme. carried out under novel $f(\mathcal{G},\mathcal{T}_{\alpha \beta} \mathcal{T}^{\alpha \beta})$ gravitation by assuming a specific model i.e, $f(\mathcal{G},\mathcal{T}^2)=\mathcal{G}+\alpha \mathcal{G}^2+2\lam...

"Let $\mathcal{S}^*_e$ and $\mathcal{S}^*_B$ denote the class of analytic functions $f$ in open unit disc normalized by $f(0)=0=f'(0)-1$ satisfying, respectively, following subordination relations: $$ \frac{zf'(z)}{f(z)}\prec e^z\quad{\rm and}\quad\frac{zf'(z)}{f(z)}\prec e^{e^z-1}.$$ In this article, we investigate majorization problems for classes without acting upon any linear or nonlinear o...

In this article, we study the space $\mathcal B_\mu(B_X,Y)$ of $Y$-valued Bloch-type functions on unit ball $B_X$ an infinite dimensional Hilbert $X$ with $\mu$ is a normal weight and $Y$ Banach space. We also investigate characterizations $\mathcal{WB}_\mu(B_X)$ $Y$-valued, locally bounded, weakly holomorphic associated B_\mu(B_X)$ scalar-valued in sense that $f\in \mathcal{WB}_\mu(B_X)$ if $w...

‎We define hyperbolic harmonic $omega$-$alpha$-Bloch space‎ ‎$mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and‎ ‎characterize it in terms of‎ ‎$$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}‎},$$ where $0leq gammaleq 1$‎. ‎Similar results are extended to‎ ‎little $omega$-$alpha$-Bloch and Besov spaces‎. ‎These obtained‎...