Recent zbMATH articles in MSC 30Chttps://zbmath.org/atom/cc/30C2022-09-13T20:28:31.338867ZWerkzeugBook review of: L. Lovász, Graphs and geometryhttps://zbmath.org/1491.000162022-09-13T20:28:31.338867Z"Meunier, Frédéric"https://zbmath.org/authors/?q=ai:meunier.fredericReview of [Zbl 1425.05001].Lucas polynomials and applications to an unified class of bi-univalent functions equipped with \((p, q)\)-derivative operatorhttps://zbmath.org/1491.050112022-09-13T20:28:31.338867Z"Altinkaya, Ş."https://zbmath.org/authors/?q=ai:altinkaya.sahsene"Yalcin, S."https://zbmath.org/authors/?q=ai:yalcin.sibelSummary: We want to remark explicitly that, by using the \(L_n(x)\) functions (essentially linked to Lucas polynomials of the second kind), our methodology builds a bridge, to our knowledge not previously well known, between the Theory of Geometric Functions and that of Special Functions, which are usually considered as very different fields. Thus, also making use of the differential operator \(\mathbf{I}^k_{p,q}\), we introduce a new class of analytic bi-univalent functions. Coefficient estimates, Fekete-Szegö inequalities and several special consequences of the results are obtained.On radiuses of convergence of \(q\)-metallic numbers and related \(q\)-rational numbershttps://zbmath.org/1491.050342022-09-13T20:28:31.338867Z"Ren, Xin"https://zbmath.org/authors/?q=ai:ren.xinSummary: The \(q\)-rational numbers and the \(q\)-irrational numbers were introduced by \textit{S. Morier-Genoud} and \textit{V. Ovsienko} [Forum Math. Sigma 8, Paper No. e13, 55 p. (2020; Zbl 1434.05023)]. In this paper, we focus on \(q\)-real quadratic irrational numbers, especially \(q\)-metallic numbers and \(q\)-rational sequences which converge to \(q\)-metallic numbers, and consider the radiuses of convergence of them when we assume that \(q\) is a complex number. We construct two sequences given by recurrence formula as a generalization of the \(q\)-deformation of the Fibonacci and Pell numbers which are introduced by Morier-Genoud and Ovsienko [loc. cit.]. For these two sequences, we prove a conjecture of \textit{L. Leclere} et al. [``On radius of convergence of \(q\)-deformed real numbers'', Preprint, \url{arXiv:2102.00891}] concerning the expected lower bound of the radiuses of convergence. In addition, we obtain a relationship between the radius of convergence of these two sequences in two special cases.Coefficient estimates for a subclass of bi-univalent functions associated with symmetric q-derivative operator by means of the Gegenbauer polynomialshttps://zbmath.org/1491.300012022-09-13T20:28:31.338867Z"Amourah, Ala"https://zbmath.org/authors/?q=ai:amourah.ala-ali"Frasin, Basem Aref"https://zbmath.org/authors/?q=ai:frasin.basem-aref"Al-Hawary, Tariq"https://zbmath.org/authors/?q=ai:al-hawary.tariqSummary: In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric \(q\)-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.Uniformly close-to-convex functions with respect to conjugate pointshttps://zbmath.org/1491.300022022-09-13T20:28:31.338867Z"Bukhari, Syed Zakar Hussain"https://zbmath.org/authors/?q=ai:bukhari.syed-zakar-hussain"Salahuddin, Taimoor"https://zbmath.org/authors/?q=ai:salahuddin.taimoor"Ahmad, Imtiaz"https://zbmath.org/authors/?q=ai:ahmad.imtiaz"Ishaq, Muhammad"https://zbmath.org/authors/?q=ai:ishaq.muhammad"Muhammad, Shah"https://zbmath.org/authors/?q=ai:muhammad.shahSummary: In this paper, we introduce a new subclass of k-uniformly close-to-convex functions with respect to conjugate points. We study characterization, coefficient estimates, distortion bounds, extreme points and radii problems for this class. We also discuss integral means inequality with the extremal functions. Our findings may be related with the previously known results.The coefficient estimates for a class defined by Hohlov operator using conic domainshttps://zbmath.org/1491.300032022-09-13T20:28:31.338867Z"Çaglar, Murat"https://zbmath.org/authors/?q=ai:caglar.murat"Gurusamy, Palpandy"https://zbmath.org/authors/?q=ai:gurusamy.palpandy"Orhan, Halit"https://zbmath.org/authors/?q=ai:orhan.halitSummary: Exploiting this article, we provide the coefficient estimate with \(m\)-th root transform for a class defined by Hohlov operator using quasi-subordination for conic domains. The authors sincerely hope this article will revive this concept and encourage the other researchers to work in this quasi subordination in the near future in the area of complex function theory.Coefficients bounds for a family of bi-univalent functions defined by Horadam polynomialshttps://zbmath.org/1491.300042022-09-13T20:28:31.338867Z"Frasin, Basem A."https://zbmath.org/authors/?q=ai:frasin.basem-aref"Sailaja, Yerragunta"https://zbmath.org/authors/?q=ai:sailaja.yerragunta"Swamy, Sondekola R."https://zbmath.org/authors/?q=ai:swamy.sondekola-rudra"Wanas, Abbas Kareem"https://zbmath.org/authors/?q=ai:wanas.abbas-kareemSummary: In the present paper, we determine upper bounds for the first two Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\) for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete-Szegö problem of functions belonging to this family. Further, we point out several special cases of our results.On strongly Ozaki \(\lambda\)-pseudo bi-close-to-convex functionshttps://zbmath.org/1491.300052022-09-13T20:28:31.338867Z"Güney, H. Özlem"https://zbmath.org/authors/?q=ai:guney.hatun-ozlem"Owa, Shigeyoshi"https://zbmath.org/authors/?q=ai:owa.shigeyoshiSummary: In the current article, we introduce and investigate two new families of strongly Ozaki \(\lambda\)-pseudo bi-close-to-convex functions in the open unit disk. We determine upper bounds for the second and third coefficients of functions belonging to these new subclasses. Also, we point out several certain special cases for our results.Harmonic univalent functions related to \(q\)-derivative based on basic hypergeometric functionhttps://zbmath.org/1491.300062022-09-13T20:28:31.338867Z"Najafzadeh, Shahram"https://zbmath.org/authors/?q=ai:najafzadeh.shahram"Dehdast, Zeynab"https://zbmath.org/authors/?q=ai:dehdast.zeynab"Foroutan, Mohammad Reza"https://zbmath.org/authors/?q=ai:foroutan.mohammadrezaSummary: We study a family of harmonic univalent functions using an operator involving \(q\)-derivative and hypergeometric function. We then obtain a necessary and sufficient condition for functions in this family. Extreme points and convexity of such functions are also introduced.Characterizations of mono-components: the Blaschke and starlike typeshttps://zbmath.org/1491.300072022-09-13T20:28:31.338867Z"Qian, Tao"https://zbmath.org/authors/?q=ai:qian.tao"Tan, Lihui"https://zbmath.org/authors/?q=ai:tan.lihuiSummary: Since the last decade, motivated by attempts of positive frequency decomposition of signals, complex periodic functions \(s(e^{it})=\rho (t)e^{i\theta (t)}\) satisfying the conditions
\[
H(\rho (t)\cos \theta (t))=\rho (t)\sin \theta (t), \quad \rho (t)\geq 0,\;\theta'(t)\geq 0,\text{ a.e.},
\]
have been sought, where \(H\) is the circular Hilbert transform and the phase derivative \(\theta '(t)\) is suitably defined and interpreted as instantaneous frequency of the signal \(\rho (t)\cos \theta (t)\). Functions satisfying the above conditions are called mono-components. Mono-components have been found to form a large pool and used to decompose and analyze signals. This note in a great extent concludes the study of seeking for mono-components through characterizing two classes of mono-components of which one is phrased as the Blaschke type and the other the starlike type. The Blaschke type mono-components are of the form \(\rho (t)\cos \theta (t)\), where \(\rho (t)\) is a real-valued (generalized) amplitude functions and \(e^{i\theta (t)}\) is the boundary limit of a finite or infinite Blaschke product. For the starlike type mono-components, we assume the condition \(\int_{0}^{2\pi }\theta'(t)dt=n\pi \), where \(n\) is a positive integer. It shows that such class of mono-components is identical with the class consisting of products between \(p\)-starlike and boundary \((n-2p) \)-starlike functions. The results of this paper explore connections between harmonic analysis, complex analysis, and signal analysis.Unified approach to starlike and convex functions Involving Poisson distribution serieshttps://zbmath.org/1491.300082022-09-13T20:28:31.338867Z"Shrigan, Mallikarjun"https://zbmath.org/authors/?q=ai:shrigan.mallikarjun"Yalcin, Sibel"https://zbmath.org/authors/?q=ai:yalcin.sibel"Altinkaya, Sahsene"https://zbmath.org/authors/?q=ai:altinkaya.sahseneSummary: The motivation behind present paper is to establish connection between analytic univalent functions \(\mathcal{T}S_p(\zeta,\gamma,\delta)\) and \(UC\mathcal{T}(\zeta,\gamma,\delta)\) by applying Hadamard product involving Poisson distribution series. We likewise consider an integral operator connection with this series.On the difference of inverse coefficients of convex functionshttps://zbmath.org/1491.300092022-09-13T20:28:31.338867Z"Sim, Young Jae"https://zbmath.org/authors/?q=ai:sim.youngjae"Thomas, Derek K."https://zbmath.org/authors/?q=ai:thomas.derek-keithSummary: Let \(f\) be analytic in the unit disk \(\mathbb{D}=\{z\in \mathbb{C}:|z|<1 \}\), and \(\mathcal{S}\) be the subclass of normalised univalent functions given by \(f(z)=z+\sum_{n=2}^{\infty}a_n z^n\) for \(z\in \mathbb{D}\). Let \(F\) be the inverse function of \(f\) defined in some set \(|\omega |\leq r_0(f)\), and be given by \(F(\omega)=\omega +\sum_{n=2}^{\infty}A_n \omega^n\). We prove the sharp inequalities \(-1/3 \leq |A_4|-|A_3| \leq 1/4\) for the class \(\mathcal{K}\subset \mathcal{S}\) of convex functions, thus providing an analogue to the known sharp inequalities \(-1/3 \leq |a_4|-|a_3| \leq 1/4\), and giving another example of an invariance property amongst coefficient functionals of convex functions.Erratum to: ``Harmonic quasiconformal mappings between \(\mathcal{C}^1\) smooth Jordan domains''https://zbmath.org/1491.300102022-09-13T20:28:31.338867Z"Kalaj, David"https://zbmath.org/authors/?q=ai:kalaj.davidErratum to the author's paper [ibid. 38, No. 1, 95--111 (2022; Zbl 1486.30065)].Analysis of the inverse Born series: an approach through geometric function theoryhttps://zbmath.org/1491.354592022-09-13T20:28:31.338867Z"Hoskins, Jeremy G."https://zbmath.org/authors/?q=ai:hoskins.jeremy-g"Schotland, John C."https://zbmath.org/authors/?q=ai:schotland.john-cAn extension of several essential numerical radius inequalities of \(2\times 2\) off-diagonal operator matriceshttps://zbmath.org/1491.470032022-09-13T20:28:31.338867Z"Al-Dolat, Mohammed"https://zbmath.org/authors/?q=ai:al-dolat.mohammed"Jaradat, Imad"https://zbmath.org/authors/?q=ai:jaradat.imad"Baleanu, Dumitru"https://zbmath.org/authors/?q=ai:baleanu.dumitru-iSummary: In this work, we provide upper and lower bounds for the numerical radius of an \(n\times n\) off-diagonal operator matrix, which extends some results by \textit{A. Abu-Omar} and \textit{F. Kittaneh} [Stud. Math. 216, No. 1, 69--75 (2013; Zbl 1279.47015); Linear Algebra Appl. 468, 18--26 (2015; Zbl 1316.47005); Rocky Mt. J. Math. 45, No. 4, 1055--1064 (2015; Zbl 1339.47007)], and \textit{K. Paul} and \textit{S. Bag} [Appl. Math. Comput. 222, 231--243 (2013; Zbl 1339.30003)].The effects of potential shape on inhomogeneous inflationhttps://zbmath.org/1491.830452022-09-13T20:28:31.338867Z"Aurrekoetxea, Josu C."https://zbmath.org/authors/?q=ai:aurrekoetxea.josu-c"Clough, Katy"https://zbmath.org/authors/?q=ai:clough.katy"Flauger, Raphael"https://zbmath.org/authors/?q=ai:flauger.raphael"Lim, Eugene A."https://zbmath.org/authors/?q=ai:lim.eugene-a(no abstract)