The invertibility of Wiener-Hopf plus Hankel operators with essentially bounded Fourier symbols is characterized via certain factorization properties of the Fourier symbols. In addition, a Fredholm criterion for these operators is also obtained and the dimensions of the kernel and cokernel are described.

We examine the uniqueness of the bounded structure of semisimple and Mackey complete uniformly $A$-convex algebras. We also consider the particular locally $C^{\ast}$-case and the uniform one.

We study the connection between conjugations of a special kind of dynamical systems, called P-configurations, and solutions to homogeneous Cauchy type functional equations. We find that any two regular P-configurations are conjugate by a homeomorphism, but cannot be conjugate by a diffeomorphism. This leads us to the following conclusion (answering an open question posed by Paneah): there exist continuous nonlinear solutions to the functional equation: $$ f(t) = f\left(\frac{t+1}{2}\right) + f\left(\frac{t-1}{2}\right) \,\, , \,\, t \in [-1,1] . $$

The paper is devoted to the study of Hyers, Ulam and Rassias types of stability for a class of nonlinear Volterra integral equations. Both Hyers-Ulam-Rassias stability and Hyers-Ulam stability are obtained for such a class of Volterra integral equations when considered on a finite interval. In addition, for corresponding Volterra integral equations on infinite intervals the Hyers-Ulam-Rassias stability is also obtained.

In this paper we give some results on single-valuedness of set-valued maps satisfying linear inclusions.

We consider second order hyperbolic equations with unbounded operator's coefficients possessing time dependent domain of definition in a Hilbert space. Existence and uniqueness of the strong generalized solution are studied. The proofs rely on a generalization of the well known energy integral method. First, we derive a priori estimates for the strong generalized solutions with the help of Yosida operator approximation. Then, using previous results, we show that the range of the operators generated by the posed problem is dense.

By using a certain operator $S^n$, we introduce a class of holomorphic functions $S_n(\beta )$, and obtain some subordination results. We also show that the set $S_n(\beta )$ is convex and obtain some new differential subordinations related to certain integral operators.

We study the action and properties of a differential operator in the polydisk, extending some classical results from the unit disk. Using so called dyadic decomposition of the polydisk we find precise connections between quazinorms of holomorphic function in the polydisk with quazinorms on the subframe and the unit disk. All our results were previously well-known in the unit disk.

If $N\ge 2$, then there exist finitely many rotations of the sphere $\mathbb{S}^N$ such that the set of the corresponding rotation operators on $L^p(\mathbb{S}^N)$ determines the norm topology for $1 \leq p \leq\infty, p \neq 1$. For $N=1$ the situation is different: the norm topology of $L^2(\mathbb{S}^1)$ cannot be determined by the set of operators corresponding to the rotations by elements of any `thin' set of rotations of $\mathbb{S}^1$.

Let $\varphi$ be a holomorphic self-map of the open unit disk $D$ on the complex plane and $p,\ q>0.$ In this paper, the boundedness and compactness of composition operator $C_{\varphi}$ from generally weighted Bloch space $B^{p}_{\log}$ to $Q^{q}_{\log}$ are investigated.

A certain subclass of analytic functions in the open unit disc with negative coefficients is introduced. The new class is defined by means of multiplier transformations. By making use of the familiar concept of neighborhoods of analytic function, the author proves coefficient inequalities, distortion theorems and associated inclusion relations for the $(n,\delta)$-neighborhoods of functions belonging to the new class, which satisfy a certain nonhomogeneous Cauchy-Euler differential equation.

Let $\varphi$ be a holomorphic self-map and $g$ a fixed holomorphic function on the unit ball $B$. The boundedness and compactness of the Volterra composition operator $$T_{g,\varphi} f(z)= \int_0^1 f(\varphi(tz)) \Re g(tz)\frac{dt}{t}$$ on the logarithmic Bloch space and little logarithmic Bloch space are studied in this paper.

Let $A$ be a Banach algebra and let $\varphi$ and $\psi$ be continuous homomorphisms on $A$. We consider the following module actions on $A$, $$a\cdot x=\varphi(a)x , \hspace{0.7cm} x\cdot a=x\psi(a) \hspace{1.5cm} (a,x\in A).$$ We denote by $A_{(\varphi,\psi)}$ the above $A$-module. We call the Banach algebra $A$, $(\varphi,\psi)$-weakly amenable if every derivation from $A$ into $(A_{(\varphi,\psi)})^*$ is inner. In this paper among many other things we investigate the relations between weak amenability and $(\varphi,\psi)$-weak amenability of $A$. Some conditions can be imposed on $A$ such that the $(\varphi'',\psi'')$-weak amenability of $A^{**}$ implies the $(\varphi,\psi)$-weak amenability of $A$.

Let $X$ be an infinite dimensional complex vector space. We show that a non-constant endomorphism of $X$ has a proper hyperinvariant subspace if and only if its spectrum is non-void. As an application we show that each non-constant continuous endomorphism of the locally convex space $(s)$ of all complex sequences has a proper closed hyperinvariant subspace.