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Smooth univalent universal functions
Mathematical Proceedings of the Royal Irish Academy, 2007Let \(\Omega\) be a Jordan domain in the complex plane. In this paper, universal functions in \(H(\Omega)\) having additional univalence and smoothness properties are studied. The authors consider the space \(A^\infty (\Omega)\) of all functions in \(H(\Omega)\) having the property that all derivatives extend continuously to \(\overline{\Omega}\) with ...
Costakis, G. +2 more
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New Criteria for Univalent Functions
Proceedings of the American Mathematical Society, 1975The classes K n {K_n} of functions f ( z ) f(z) regular in the unit disc U \mathfrak {U} with f ( 0 ) = 0 , f ′ ( 0 )
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On univalent harmonic functions
2002In Ann. Acad. Sci. Fenn., Ser. A I 9, 3--25 (1984; Zbl 0506.30007) \textit{J. Clunie} and \textit{T. Sheil-Small } introduced and studied the class \(S_H\) of complex valued, harmonic, orientation preserving, univalent functions \(f\) in the unit disk normalized by \(f(0)=0\), \(f'_z(0)-1=0\). Such functions have representation \[ f(z)=h(z)+\overline{g}
Yalçın Tokgöz, Sibel, Öztürk, Metin
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A New Comprehensive Subclass of Analytic Bi-Univalent Functions Related to Gegenbauer Polynomials
Symmetry, 2023Tariq Al-Hawary +2 more
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A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions
Axioms, 2023Ala Ali, Abdullah Alsoboh, Osama Ogilat
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