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We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
The extremal functions \(f_0(z)\) realizing the maxima of some functionals (e.g. \(\max|a_3|\), and \(\max{arg f^{'}(z)}\)) within the so-called universal linearly invariant family \(U_\alpha\) (in the sense of Pommerenke [10]) have such a form that \(f_0^{'}(z)\) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition...
In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space \(E_1^4\).
We describe all \(\mathcal{F}^2\mathcal{M}_{m_1,m_2,n_1,n_2}\)-natural operators \(D\colon Q^{\tau}_{proj-proj} \rightsquigarrow QT^*\) transforming projectable-projectable classical torsion-free linear connections \(\nabla\) on fibred-fibred manifolds \(Y\) into classical linear connections \(D(\nabla)\) on cotangent bundles \(T^*Y\) of \(Y\). We show that this problem can be reduced to finding \(\mathcal{F}^2...
We obtain a representation of the mapping class group of genus 2 surface in terms of a coordinate system of the Teichmuller space defined by trace functions.
In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj–Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
Some results related to extremal problems with free poles on radial systems are generalized. They are obtained by applying the known methods of geometric function theory of complex variable. Sufficiently good numerical results for γ are obtained.
We consider a certain analog of Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical. We establish sufficient conditions for an existence of limiting values of this integral on the curve of integration.
For functions of the form \[f(z) = z^{p} + \sum_{n = 1}^{\infty} a_{p + n} z^{p + n}\] we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.
Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p-1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.
We present new inequalities of \(L_p\) norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in \(L_p(\mathbb{R})\).
Let \(\mathbb{D}\) denote the unit disk \(\{z:|z|<1\}\) in the complex plane \(\mathbb{C}\). In this paper, we study a family of polynomials \(P\) with only one zero lying outside \(\overline{\mathbb{D}}\). We establish criteria for \(P\) to satisfy implying that each of \(P\) and \(P'\) has exactly one critical point outside \(\overline{\mathbb{D}}\).
Let \(\mathcal{P}_n\) denote the class of analytic functions \(p(z)\) of the form \(p(z)=1+c_nz^n+c_{n+1}z^{n+1}+\dots\) in the open unit disc \(\mathbb{U}\). Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for \(p(z)\) concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned...
The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order \(\alpha\) and from the class \(\mathcal{CVH}(\beta)\) and also we estimate the first two coefficients for functions obtained by this operator...
In this work we consider the class of analytic functions \(\mathcal{G}(\alpha,\gamma)\), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Złotkiewicz in Gamma starlike functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 28 (1974), 53–58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass.
We point out certain flaws in two papers published in Ann. Univ. Mariae Curie-Skłodowska Sect. A, one in 2009 and the other in 2011. We discuss in detail the validity of the results in the two papers in question.
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