We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
Mathematical texts are characterised by the occurrence of specificsymbols. They may be letters (as applied, for example, by Euclid), numbersymbols or graphic signs with context-independent meaning. Mathematicalsymbols store knowledge of previous generations that provides frameworkswith which to examine history of mathematical problems. In this paper, wedeal with symbols related to the concept of function and related concepts likelimit, and some other set theoretical or logical concepts. We focus...
The decree that officially brought Lodz University of Technology into being was signed on 24 May 1945. The university's first faculties were Mechanical Engineering, Electrical Engineering and Chemistry. Among researchers employed there were two mathematicians: Witold Pogorzelski and Edward Otto. Lectures of mathematics were provided by the Chairs of Mathematics and initially were shared by all faculties. In the paper we present the organization of classes, curricula in mathematics and direction...
Stefan Jan Kempisty was a Polish mathematician, working in the theory of real functions, set theory, integrals, interval functions and the thory of surface area. In 1919 he defended his Ph.D. thesis On semi{continuous functions at the Jagiellonian University in Krakow under supervision of Kazimierz Z_ orawski. In December 1924 he did habilitation at the Warsaw University and from 1920 to 1939 he worked at the Stefan Batory University in Vilnius. He published over forty scientic papers, three textbooks...
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