Nehari found sufficient conditions implying univalence of analytic functions, expressed in terms of the Schwarzian derivative. His theorem had been used by us to generate additional families of conditions for univalence, depending on parameters. Recently, Aliaga and Tuneski used the method of selecting parameters to find a new criterion for univalence of analytic functions. However, they presented determining specific suitable values of the parameters and their precise domain of admissibility for this family as an open question.

In what follows we obtain additional information about the exact domain of possible parameters in the family of criteria studied by Aliaga and Tuneski. Particular cases, open problems, and questions will be also mentioned. Publisher Springer International Publishing.

Print ISBN Electronic ISBN Editor: Prof. Filippo Bracci. Lemma 5. Let us denote it by r.

### Illinois Journal of Mathematics

Remark 5. Theorem 5. Please note that, as said before, typical implementations of the Ishikawa algorithm are convergent at a faster pace than the corresponding Mann schema. In this section we provide an example how the results of the preceding sections can be utilized for constructing a stationary point of a process defined by the Urysohn operator. For the kernel k , we assume that. As proved by Khamsi in [ 5 ], the formula.

In Modular Function Spaces.

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Dekker, New York; Kozlowski WM: Advancements in fixed point theory in modular function. Nonlinear Anal. Khamsi MA: Nonlinear semigroups in modular function spaces. Khamsi MA: Fixed point theory in modular function spaces. MR 97m September Sevilla. Kozlowski WM: On the existence of common fixed points for semigroups of nonlinear mappings in modular function spaces. Bin Dehaish BA, Kozlowski WM: Fixed point iterations processes for asymptotic pointwise nonexpansive mappings in modular function spaces. Fixed Point Theory Appl. Mann WR: Mean value methods in iteration.

Nauk , — Ishikawa S: Fixed points by a new iteration method. Reich S: Fixed point iterations of nonexpansive mappings. Reich S: Weak convergence theorems for nonexpansive mappings in Banach spaces. Bose SC: Weak convergence to the fixed point of an asymptotically nonexpansive map. Passty GB: Construction of fixed points for asymptotically nonexpansive mappings.

Gornicki J: Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces. Schu J: Iterative construction of fixed points of asymptotically nonexpansive mappings. Schu J: Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Xu H-K: Existence and convergence for fixed points of asymptotically nonexpansive type. Rhoades BE: Fixed point iterations for certain nonlinear mappings.

## Geometric Function Theory in Higher Dimension

Kaczor W, Kuczumow T, Reich S: A mean ergodic theorem for nonlinear semigroups which are asymptotically nonexpansive in the intermediate sense. Kaczor W, Kuczumow T, Reich S: A mean ergodic theorem for mappings which are asymptotically nonexpansive in the intermediate sense.

Khamsi MA: On asymptotically nonexpansive mappings in hyperconvex metric spaces.

Nonlinear Convex Anal. Suzuki T: Common fixed points of one-parameter nonexpansive semigroup.

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Kozlowski WM: Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces. Kozlowski WM: Common fixed points for semigroups of pointwise Lipschitzian mappings in Banach spaces. Kozlowski WM: On the construction of common fixed points for semigroups of nonlinear mappings in uniformly convex and uniformly smooth Banach spaces.

Kozlowski WM: Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces. Kozlowski WM, Sims B: On the convergence of iteration processes for semigroups of nonlinear mappings in Banach spaces. Springer Proceedings in Mathematics and Statistics In Computational and Analytical Mathematics. Springer, New York; Kozlowski, WM: On common fixed points of semigroups of mappings nonexpansive with respect to convex function modulars.

Kozlowski WM: Notes on modular function spaces I.

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## Semigroups in Algebra, Geometry and Analysis

Chistyakov VV: Modular metric spaces, I: basic concepts. Bruck RE: A common fixed point theorem for a commuting family of nonexpansive mappings. Export citation. Export Cancel. References [1] M. Lecture Notes Math.

## Complex dynamics of Möbius semigroups

Complex Anal. Arosio and F. Bracci, Canonical models for holomorphic iteration , Trans. Zentralblatt MATH: