let $p$ be an analytic function defined on the open unit disc $mathbb{d}$ with $p(0)=1.$ the conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{c}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of bernoulli $|w^{2}-1...

We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form _ x = A(t)x+f(t) (), with f having precompact range, which will be then applied to nd new spectral criteria for the existence of almost periodic solutions with speciic spectral properties in the resonnant case where e isp(f) may intersect the spectrum of t...

The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...

We define the (w∗-) boundedness property and the (w∗-) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called (w∗-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of tw...

Let f be a bounded function on the real line IF!. One may characterize the structural properties off by the modulus of smoothness w(t,f) = sup{lf (4 -f( y)l; x, y E 08, I x y I < t>, and, if w(t) is a continuous nondecreasing function of t > 0 such that w(O) = 0, by the Lipschitz class Lip(w) which is the set of all continuous functions such that su~~<~<i w(t, f)/o(t) < 00. It is possible to ex...

and Applied Analysis 3 introducing a new inner product over the resolvent of Laplacian, we surmount this obstacle and obtain the estimate of the solution in the Sobolev space V0, which is weaker than V , see Lemma 4.2 in Section 4. Here some basic results about Dirichlet forms of Laplacian are used. For details on the Dirichlet forms of a negative definite and self-adjoint operator please refer...

where f(t,x,y) is bounded for bounded x andy and all t>0 , and the following conditions on a Lyapunov function V(x,y). 1) V(x,y) is positive definite and has continuous first partial derivatives. 2) V(X,Y)+WasIIxIZ+IIYll 3) V(X,Y) W(x)+h,( where i) W(x) is continuous and positive definite. ii) q(,y) is continuous. iii) jFlhi()ldt<co, i = 1,2. Theorem [Z]: If for the system (3) there exists a fu...

In this paper we provide a characterization of intrinsic Lipschitz graphs in the subRiemannian Heisenberg groups in terms of their distributional gradients. Moreover, we prove the equivalence of different notions of continuous weak solutions to the equation φy + [φ/2]t = w, where w is a bounded function.

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