Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. $\varphi$ $\theta$-psh function, let $f$ continuous function with bounded distributional laplacian respect to $\omega$ $\varphi \leq f. $ Then the non-pluripolar measure $\theta_\va...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...

in this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. meantime, an example is provided toillustrate this theorem. the main result shows that a self-mappingon a g-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. afterwards, some results inco...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

We study the spectrum of operators $$aT \in {\cal B}(H)$$ on a Hilbert space H where T is an isometry and belongs to commutative C*-subalgebra $$C(X) \cong A \subseteq such that formula L(a) = T*aT defines faithful transfer operator A. Based analysis C*-algebra C* (A, T) generated by aT, ∈ A, we give dynamical conditions implying σ(aT) invariant under rotation around zero, coincides with essent...

Let the function $$\varphi $$ be holomorphic in unit disk $${\mathbb {D}}$$ of complex plane {C}}$$ and let ({\mathbb {D}})\subset {\mathbb . We study level sets critical points hyperbolic derivative , $$\begin{aligned} |D_{\varphi }(z)|:=\frac{(1-|z|^2)|\varphi '(z)|}{1-|\varphi (z)|^2}. \end{aligned}$$ In particular, we show how Schwarzian reveals nature points.