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This paper is mainly intended as a survey of the recent work of a number of authors concerning certain infinite group actions on spheres and to raise some as yet unanswered questions. The main thrust of the current research in this area has been to decide what topological and geometrical properties characterise the infinite conformal or Möbius groups. One should then obtain reasonable topological or geometrical restrictions on a subgroup G of the homeomorphism group of a sphere which will imply...

Infinite products over visible lattice points.

Campbell, Geoffrey B. (1994)

International Journal of Mathematics and Mathematical Sciences

Infinite-dimensional bicomplex Hilbert spaces.

Gervais Lavoie, Raphaël, Marchildon, Louis, Rochon, Dominic (2010)

Annals of Functional Analysis (AFA) [electronic only]

Infinitely many asymptotic values of locally univalent meromorphic functions.

Barth, Karl F., Rippon, Philip J. (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

Infinitesimal geometry of quasilinear mappings.

Gutlyanskij, V.Ya., Martio, O., Ryazanov, V.I., Vuorinen, M. (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

Jeff Cheeger, Bruce Kleiner, Andrea Schioppa (2016)

Analysis and Geometry in Metric Spaces

We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.

Initial coefficients for generalized subclasses of bi-univalent functions defined with subordination

Gagandeep Singh, Gurcharanjit Singh, Gurmeet Singh (2022)

Archivum Mathematicum

This paper is concerned with certain generalized subclasses of bi-univalent functions defined with subordination in the open unit disc $E = \}z : ∣ z ∣ < 1\{$ . The bounds for the initial coefficients for the functions in these classes are studied. The earlier known results follow as special cases.

Initial Maclaurin coefficient estimates for $λ$ -pseudo-starlike bi-univalent functions associated with Sakaguchi-type functions

Abbas Kareem Wanas, Basem Aref Frasin (2022)

Mathematica Bohemica

We introduce and study two certain classes of holomorphic and bi-univalent functions associating $λ$ -pseudo-starlike functions with Sakaguchi-type functions. We determine upper bounds for the Taylor–Maclaurin coefficients $| a_{2} |$ and $| a_{3} |$ for functions belonging to these classes. Further we point out certain special cases for our results.

Injectivity of local quasi-isometries.

F.W. Gehring (1982)

Commentarii mathematici Helvetici

Injectivity of sections of convex harmonic mappings and convolution theorems

Liulan Li, Saminathan Ponnusamy (2016)

Czechoslovak Mathematical Journal

We consider the class $ℋ_{0}$ of sense-preserving harmonic functions $f = h + \bar{g}$ defined in the unit disk $| z | < 1$ and normalized so that $h (0) = 0 = h^{'} (0) - 1$ and $g (0) = 0 = g^{'} (0)$ , where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $𝒫_{H}^{0} (α)$ and $𝒢_{H}^{0} (β)$ of functions from $ℋ_{0}$ and show that if $f \in 𝒫_{H}^{0} (α)$ and $F \in 𝒢_{H}^{0} (β)$ , then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters $α$ and $β$ are satisfied. In the second part we study the harmonic sections (partial...

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Inequalities for zeros of entire functions.

Inequalities in the complex plane.

Inequalities involving a class of analytic functions

Inequalities involving multipliers for multivalent harmonic functions.

Inequalities of Grunsky-Nehari type for pairs of vector functions

Inequalities of Littlewood-Paley type, multipliers and radial growth of the derivative and analytic functions.

Inextremization and Boundedness on Open Riemann Surfaces.

Infinite group actions on spheres.