Description

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One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects includes: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory and others.

The book presents basic facts from this field.

About the Author

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Kazimierz Goebel, Professor (emeritus), Maria Curie-Sklodowska University, Lublin, Poland, Stanislaw Prus, Professor, Maria Curie-Sklodowska University, Lublin, Poland Professor emeritus Kazimierz Goebel obtained his PhD in mathematics in 1967 at Maria Curie-Sklodowska University in Poland. Since 1963, he has been employed by UMCS and has served two three-year terms (1993-1999) as Rector of the university. At the same time, he has served as the President of the Polish Mathematical Society. Professor Goebel is the author of five books and over 70 scientific papers. He is a specialist in nonlinear problems of functional analysis, in particular metric fixed point theory. He has supervised and promoted 15 PhD students and is the visiting professor at several universities in the USA, Italy, Japan, Spain, Australia, Thailand. Moreover, he is a frequent short-term visitor, invited speaker and member of committees to a number of conferences and seminars, workshops and schools all over the world. Professor Stanislaw Prus graduated from Maria Curie-Sklodowska University, Poland, in 1979. He then obtained a PhD in mathematics in 1984 from the Mathematical Institute of Polish Academy of Science, Warsaw. Since 1979, he has been employed at UMCS and is now the author of over 45 scientific papers. Professor Prus is a specialist in the geometry of Banach spaces and nonlinear problems of functional analysis, and in particular of metric fixed point theory. He is also a frequent invited speaker and a member of committees to a number of conferences and seminars world-wide.