Recent zbMATH articles in MSC 30C80https://www.zbmath.org/atom/cc/30C802022-05-16T20:40:13.078697ZWerkzeugCertain estimates of normalized analytic functionshttps://www.zbmath.org/1483.300332022-05-16T20:40:13.078697Z"Anand, Swati"https://www.zbmath.org/authors/?q=ai:anand.swati"Jain, Naveen Kumar"https://www.zbmath.org/authors/?q=ai:jain.naveen-kumar"Kumar, Sushil"https://www.zbmath.org/authors/?q=ai:kumar.sushilSummary: Let \(\phi\) be a normalized convex function defined on open unit disk \(\mathbb{D}\). For a unified class of normalized analytic functions which satisfy the second order differential subordination \(f'(z)+\alpha zf''(z)\prec\varphi(z)\) for all \(z\in\mathbb{D}\), we investigate the distortion theorem and growth theorem. Further, the bounds on initial logarithmic coefficients, inverse coefficient and the second Hankel determinant involving the inverse coefficients are examined.A family of holomorphic functions defined by differential inequalityhttps://www.zbmath.org/1483.300422022-05-16T20:40:13.078697Z"Mohammed, Nafya Hameed"https://www.zbmath.org/authors/?q=ai:hameed-mohammed.nafya"Adegani, Ebrahim Analouei"https://www.zbmath.org/authors/?q=ai:adegani.ebrahim-analouei"Bulboacă, Teodor"https://www.zbmath.org/authors/?q=ai:bulboaca.teodor"Cho, Nak Eun"https://www.zbmath.org/authors/?q=ai:cho.nak-eunSummary: The aim of the present paper is to introduce and study a subfamily of holomorphic and normalized functions defined by a differential inequality. Some geometric properties of this family of holomorphic functions and different problems of a family of such functions are presented.Fekete-Szegö inequality for certain subclasses of analytic functions related with crescent-shaped domain and application of poison distribution serieshttps://www.zbmath.org/1483.300432022-05-16T20:40:13.078697Z"Murugusundaramoorthy, Gangadharan"https://www.zbmath.org/authors/?q=ai:murugusundaramoorthy.gangadharanSummary: The purpose of this paper is to define a new class of analytic, normalized functions in the open unit disk \(\mathbb{D}=\{ z:z\in \mathbb{C}\text{ and } \left\vert z\right\vert <1\}\) subordinating with crescent shaped regions, and to derive certain coefficient estimates \(a_2, a_3\) and Fekete-Szegö inequality for \(f\in\mathcal{M}_q(\alpha,\beta,\lambda)\). A similar result have been done for the function \(f^{-1}\). Further application of our results to certain functions defined by convolution products with a normalized analytic function is given, in particular we obtain Fekete-Szegö inequalities for certain subclasses of functions defined through Poisson distribution series.On an extension of Nunokawa's lemmahttps://www.zbmath.org/1483.300442022-05-16T20:40:13.078697Z"Nunokawa, Mamoru"https://www.zbmath.org/authors/?q=ai:nunokawa.mamoru"Sokół, Janusz"https://www.zbmath.org/authors/?q=ai:sokol.januszSummary: Jack's Lemma says that if \(f(z)\) is regular in the disc \(|z|\le r\), \(f(0)=0\), and \(|f(z)|\) assumes its maximum at \(z_0\) on the circle \(|z|=r\), then \(z_0f'(z)_0/f(z_0)\ge 1\). This Lemma was generalized in several directions. In this paper we consider an improvement of some first author's results of this type.Properties of functions with symmetric points involving subordinationhttps://www.zbmath.org/1483.300462022-05-16T20:40:13.078697Z"Raza, Malik Ali"https://www.zbmath.org/authors/?q=ai:raza.malik-ali"Bukhari, Syed Zakar Hussain"https://www.zbmath.org/authors/?q=ai:bukhari.syed-zakar-hussain"Ahmed, Imtiaz"https://www.zbmath.org/authors/?q=ai:ahmed.imtiaz"Ashfaq, Muhammad"https://www.zbmath.org/authors/?q=ai:ashfaq.muhammad"Nazir, Maryam"https://www.zbmath.org/authors/?q=ai:nazir.maryamSummary: We study a new subclass of functions with symmetric points and derive an equivalent formulation of these functions in term of subordination. Moreover, we find coefficient estimates and discuss characterizations for functions belonging to this new class. We also obtain distortion and growth results. We relate our results with the existing literature of the subject.On sufficient conditions for strongly starlikeness of order a and type \(\beta\)https://www.zbmath.org/1483.300472022-05-16T20:40:13.078697Z"Sharma, Vidyadhar"https://www.zbmath.org/authors/?q=ai:sharma.vidyadhar"Mathur, Nisha"https://www.zbmath.org/authors/?q=ai:mathur.nisha"Soni, Amit"https://www.zbmath.org/authors/?q=ai:soni.amitSummary: By making use of differential subordination technique, we derive certain conditions for \(p\)-valent strongly starlike functions of order \(\alpha\) and type \(\beta\). The results presented here are sharp.On the third and fourth Hankel determinants for a subclass of analytic functionshttps://www.zbmath.org/1483.300522022-05-16T20:40:13.078697Z"Wang, Zhi-Gang"https://www.zbmath.org/authors/?q=ai:wang.zhigang"Raza, Mohsan"https://www.zbmath.org/authors/?q=ai:raza.mohsan"Arif, Muhammad"https://www.zbmath.org/authors/?q=ai:arif.muhammad"Ahmad, Khurshid"https://www.zbmath.org/authors/?q=ai:ahmad.khurshidSummary: The objective of this paper is to investigate the third and fourth Hankel determinants for the class of functions with bounded turning associated with Bernoulli's lemniscate. The fourth Hankel determinants for 2-fold symmetric and 3-fold symmetric functions are also studied.Open-door lemma for functions with fixed second coefficientshttps://www.zbmath.org/1483.300572022-05-16T20:40:13.078697Z"Amani, M."https://www.zbmath.org/authors/?q=ai:amani.mostafa"Aghalary, R."https://www.zbmath.org/authors/?q=ai:aghalary.rasoul"Ebadian, A."https://www.zbmath.org/authors/?q=ai:ebadian.aliSummary: We extend the well-known open-door lemma by using the theory of differential subordination for functions with fixed initial coefficient and apply it to study some integral operators. Further, using an extension of Nunokawa lemma, we determine some sufficient conditions for the radii and order of starlike functions with fixed second coefficient. Our results improve and generalize some previously known results.Variability regions for the second derivative of bounded analytic functionshttps://www.zbmath.org/1483.300942022-05-16T20:40:13.078697Z"Chen, Gangqiang"https://www.zbmath.org/authors/?q=ai:chen.gangqiang"Yanagihara, Hiroshi"https://www.zbmath.org/authors/?q=ai:yanagihara.hiroshiSummary: Let \(z_0\) and \(w_0\) be given points in the open unit disk \({\mathbb{D}}\) with \(|w_0| < |z_0|\). Let \({\mathcal{H}}_0\) be the class of all analytic self-maps \(f\) of \({\mathbb{D}}\) normalized by \(f(0)=0\), and \({\mathcal{H}}_0 (z_0,w_0) = \{ f \in{\mathcal{H}}_0 : f(z_0) =w_0\} \). In this paper, we explicitly determine the variability region of \(f''(z_0)\) when \(f\) ranges over \({\mathcal{H}}_0 (z_0,w_0)\). Moreover, we approximate this region numerically in some special cases, to illustrate our main result.Asymptotic upper bound for tangential speed of parabolic semigroups of holomorphic self-maps in the unit dischttps://www.zbmath.org/1483.370572022-05-16T20:40:13.078697Z"Cordella, Davide"https://www.zbmath.org/authors/?q=ai:cordella.davideThe author studies continuous semigroups of holomorphic maps in the unit disc \((\Phi_t)_{t\ge 0}\). For a non-elliptic semigroup, \textit{F. Bracci} [Ann. Univ. Mariae Curie-Skłodowska, Sect. A 73, No. 2, 21--43 (2019; Zbl 1436.30007)] introduced and studied three kinds of speeds: the total speed, the orthogonal speed, and the tangential speed. The tangential speed \(v^T(t)\) is related to the slope of convergence of orbits to the Denjoy-Wolff point of the semigroup. In the present paper, the author proves a conjecture in [loc. cit.] claiming that \(\limsup_{t\to\infty}\left(v^T(t)-\frac 12\log t\right)<\infty\) holds for parabolic semigroups.
Reviewer: Barbara Drinovec Drnovsek (Ljubljana)