An Introduction to the Theory of Functional Equations and Inequalities: Cauchy's Equation and Jensen's InequalityMarek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszś, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)

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Contents
III  3 
IV  5 
V  6 
VI  8 
VII  10 
VIII  12 
IX  14 
X  15 
LXXIX  260 
LXXX  266 
LXXXI  267 
LXXXII  269 
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LXXXIV  276 
LXXXV  281 
LXXXVI  282 
XI  19 
XII  23 
XIII  25 
XIV  28 
XV  32 
XVI  35 
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XX  46 
XXI  54 
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XXVIII  75 
XXIX  78 
XXX  83 
XXXI  87 
XXXII  89 
XXXIII  95 
XXXIV  98 
XXXV  101 
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XXXVII  105 
XXXVIII  106 
XXXIX  108 
XL  115 
XLI  116 
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XLIII  130 
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XLVII  143 
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XLIX  150 
L  155 
LI  161 
LII  162 
LIII  164 
LIV  168 
LV  171 
LVI  174 
LVII  177 
LVIII  180 
LIX  188 
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LXX  227 
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LXXXVII  285 
LXXXIX  288 
XC  294 
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XCIX  330 
C  335 
CI  340 
CII  343 
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CIV  355 
CV  363 
CVI  367 
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CVIII  374 
CIX  376 
CX  380 
CXI  382 
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CXX  429 
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CXXIX  465 
CXXX  471 
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CXXXII  475 
CXXXIII  482 
CXXXIV  485 
CXXXV  486 
CXXXVI  490 
CXXXVII  498 
CXXXVIII  505 
CXXXIX  510 
CXL  515 
CXLI  524 
CXLII  534 
CXLIII  537 
CXLIV  540 
CXLV  546 
CXLVI  551 
CXLVII  556 
CXLVIII  560 
CXLIX  564 
CL  569 
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Other editions  View all
An Introduction to the Theory of Functional Equations and Inequalities ... Marek Kuczma Limited preview  2009 
An Introduction to the Theory of Functional Equations and Inequalities ... Marek Kuczma No preview available  2009 