Functional Equations and Ulam's Problem
暫譯: 函數方程與烏拉姆問題

Rassias, Themistocles M.

Functional Equations and Ulam's Problem
  • 出版商: Springer
  • 出版日期: 2026-03-03
  • 售價: $8,270
  • 貴賓價: 9.5 折 $7,856
  • 語言: 英文
  • 頁數: 497
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3032089484
  • ISBN-13: 9783032089489
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

The aim of this volume, Functional Equations and Ulam's Problem, is to publish a well-balanced collection of works devoted to the domain of functional equations with emphasis on stability results associated with Ulam's problem for approximate homomorphisms. This area has been a source of active and vibrant research for more than five decades. Efforts have been made for the book to constitute a valuable reference for graduate students and advanced research scientists who wish to be introduced to the state-of-the art knowledge on the problems treated, as well as to obtain an overview of important results on stability theory, from classical to the most recent.

The contributions in this collection investigate the following topics: functional equations on a semigroup, generalized Euler-Lagrange cubic functional equations, Ulam stability results for the Davison functional equation, Hyers-Ulam stability of a pexiderized functional equation, Ulam-Hyers stability in normed spaces, Hyers-Ulam stabilities for weighted operators, stability conditions for linear functional-differential equations, semilinear functional differential equations, general bi-Jensen functional equation, norm inequalities for the Chebyshev functional in Hilbert spaces, orthogonality and generalized additive mappings in Banach modules, permuting triderivations and permuting trihomomorphisms in complex Banach algebras, bi-quadratic derivations and bi-quadratic homomorphisms in Banach algebras, novel representations of mappings, linear and affine sets and relations, and solvability relations in groupoids.

商品描述(中文翻譯)

本卷的目標是出版一部平衡良好的作品集，專注於函數方程領域，特別是與 Ulam 問題相關的穩定性結果，針對近似同態的情況。這個領域已經成為活躍且充滿活力的研究來源，超過五十年。這本書的努力旨在成為研究生和希望了解所處理問題的最新知識的高級研究科學家的寶貴參考資料，同時提供有關穩定性理論的重要結果的概述，從經典到最新的研究成果。

本集中的貢獻探討以下主題：半群上的函數方程、廣義的歐拉-拉格朗日立方函數方程、針對 Davison 函數方程的 Ulam 穩定性結果、pexiderized 函數方程的 Hyers-Ulam 穩定性、在範數空間中的 Ulam-Hyers 穩定性、加權算子的 Hyers-Ulam 穩定性、線性函數-微分方程的穩定性條件、半線性函數微分方程、一般的 bi-Jensen 函數方程、希爾伯特空間中 Chebyshev 函數的範數不等式、巴拿赫模塊中的正交性和廣義加法映射、在複數巴拿赫代數中的置換三導數和置換三同態、巴拿赫代數中的二次導數和二次同態、映射的新表示法、線性和仿射集合及關係，以及群體中的可解性關係。

作者簡介

Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization.

作者簡介(中文翻譯)

德米斯托克利斯·M·拉西亞斯是雅典國立技術大學的數學教授。他的研究興趣包括非線性分析、全局分析、逼近理論、函數分析、函數方程、不等式及其應用。拉西亞斯教授於1976年在加州大學伯克利分校獲得數學博士學位；他的論文指導教授是斯蒂芬·斯梅爾，學術指導教授是陳省身。除了擁有廣泛的期刊發表列表外，拉西亞斯教授還作為作者或卷編輯出版了幾本與施普林格（Springer）合作的書籍。德米斯托克利斯·M·拉西亞斯獲得了多項獎項，並且是多本數學分析和優化期刊的活躍編輯委員會成員。

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