Iterations of Holomorphic Maps of Infinite Dimensional Homogeneous Domains.
Some Properties of Analytic Maps of Operators in J*-algebras.
Extension of Bernstein's Theorem for Polnomial Maps of Complex Banach Spaces.
Coefficient inequalities and maximalization of some functionals for pairs of vector functions
Area methods, extremal problems and extremal domains for pairs of conformal mappings
Estimates of derivatives and Schwarz derivatives for generalized Aharonov pairs and determination of the totality of extremal pairs
Admissible variations and the local maximum theorems for pairs of vector functions and for generalized Bieberbach-Eilenberg, bounded and Grunsky-Shah functions
Inequalities of Grunsky-Nehari type for pairs of vector functions
Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains
Results concerning the rigidity of holomorphic maps and the distortion of biholomorphic maps in infinite dimensional Siegel domains of -algebras are established. The homogeneity of the open unit balls in these algebras plays a key role in the arguments.
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of -algebras
The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in -algebras. Since -algebras are natural generalizations of -algebras, -algebras, -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.
Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains
An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.
The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces
A classical Julia-Carathéodory theorem concerning radial limits of holomorphic maps in one dimension is extended to hyperbolic contractions of bounded symmetric domains in J*-algebras.
Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces.
Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances.
Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems.
Fixed-point and coincidence theorems for set-valued maps with nonconvex or noncompact domains in topological vector spaces.
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