we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

The purpose of this paper is to study the Schwarz–Pick type inequality and Lipschitz continuity for solutions nonhomogeneous biharmonic equation: $$\Delta (\Delta f)=g$$ , where g : $$\overline{{\mathbb D}}\rightarrow {\mathbb {C}}$$ a continuous function D}}$$ denotes closure unit disk $${\mathbb D}$$ in complex plane . In fact, we establish following properties these solutions: First, show th...

In this article we prove that there are no nontrivial solutions tothe Dirichlet problem for the fractional Laplacian$$ \displaylines{(-\Delta)^s u =f(u) \quad \text{in }\Omega,\\ u=0 } \mathbb{R}^N \backslash \Omega,}$$ where \(\Omega \subset \mathbb{R}^N\) (\(N\geq 1\)) is a bounded domain, and f locally Lipschitz with non-positive primitive \(F(t)= \int_0^t f(\tau)d\tau\).

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

Abstract The aim of this article is to present some Δ \Delta -convergence and strong convergence results for a countable family non-self mappings. More precisely, we employ Mann-Dotson’s algorithm approximate, common fixed points L n {...

in this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional brownian motion in a hilbert space. we establish the existence and uniqueness of mild solutions for these equations under non-lipschitz conditions with lipschitz conditions being considered as a special case. an example is provided to illustrate the theory

‎in this work we prove malliavin differentiability for the solution to an sde with locally lipschitz and semi-monotone drift‎. ‎to prove this formula‎, ‎we construct a sequence of sdes with globally lipschitz drifts and show that the $p$-moments of their malliavin derivatives are uniformly bounded‎.