Some Geometric Properties for a Certain Class of Meromorphic Univalent Functions by Differential Operator

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and neighborhoods.

Optimal Control of a Nonlinear PDE Governed by Fractional Laplacian

We consider an optimal control problem containing a control system described by a partial nonlinear differential equation with the fractional Dirichlet–Laplacian, associated to an integral cost. We investigate the existence of optimal solutions for such a problem. In our study we use Filippov’s approach combined with a lower closure theorem for orientor fields.

On q-analogue of Janowski-type starlike functions with respect to symmetric points

The main objective of the present paper is to define a class of q q -starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.

Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

Some Geometric Properties Of Multivalent Convex Function For Operator On Hilbert Space

By making use of the operator on Hilbert space, we introduce and study some properties of geometric of a subclass of multivalent convex functions with negative coefficients. Also, we obtain some geometric properties, such as coefficient inequality, growth and distortion theorem, extreme points, convex set, closure theorem, radius of close-to-convexity, weighted mean and inclusive properties.

Euclidean-valued group cohomology is always reduced

Let [Formula: see text] be a topological field and [Formula: see text] a countable discrete group. Then for any linear [Formula: see text]-action on a finite-dimensional vector space over [Formula: see text], the groups of coboundaries in the inhomogeneous bar resolution are closed in all degrees, and hence the cohomology is reduced in all degrees. This can be deduced from a more general automatic-closure theorem for continuous linear transformations between inverse limits of finite-dimensional vector spaces.

A DIRECT PROOF OF SCHWICHTENBERG’S BAR RECURSION CLOSURE THEOREM

In [12], Schwichtenberg showed that the System T definable functionals are closed under a rule-like version Spector’s bar recursion of lowest type levels 0 and 1. More precisely, if the functional Y which controls the stopping condition of Spector’s bar recursor is T-definable, then the corresponding bar recursion of type levels 0 and 1 is already T-definable. Schwichtenberg’s original proof, however, relies on a detour through Tait’s infinitary terms and the correspondence between ordinal recursion for $\alpha < {\varepsilon _0}$ and primitive recursion over finite types. This detour makes it hard to calculate on given concrete system T input, what the corresponding system T output would look like. In this paper we present an alternative (more direct) proof based on an explicit construction which we prove correct via a suitably defined logical relation. We show through an example how this gives a straightforward mechanism for converting bar recursive definitions into T-definitions under the conditions of Schwichtenberg’s theorem. Finally, with the explicit construction we can also easily state a sharper result: if Y is in the fragment Ti then terms built from $BR^{\mathbb{N},\sigma } $ for this particular Y are definable in the fragment ${T_{i + {\rm{max}}\left\{ {1,{\rm{level}}\left( \sigma \right)} \right\} + 2}}$.