標(biāo)題: Titlebook: An Introduction to the Theory of Functional Equations and Inequalities; Cauchy‘s Equation an Marek Kuczma,Attila Gilányi Textbook 2009Lates [打印本頁] 作者: 誤解 時(shí)間: 2025-3-21 17:34
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書目名稱An Introduction to the Theory of Functional Equations and Inequalities讀者反饋學(xué)科排名
作者: 摸索 時(shí)間: 2025-3-21 20:44
Zusammenfassung und Schlu?folgerungeninearly independent over ?, and . = ?., there exists a Hamel basis . of ?. such that . ? . ? . In particular, every set belonging to any of the classes ., ?, .(.), ., . contains a Hamel basis (Theorems 9.3.6 and 10.7.3 and Exercise 10.7). On the other hand, we have the following . . .(.), ., ..作者: arboretum 時(shí)間: 2025-3-22 00:50
Properties of Hamel Basesinearly independent over ?, and . = ?., there exists a Hamel basis . of ?. such that . ? . ? . In particular, every set belonging to any of the classes ., ?, .(.), ., . contains a Hamel basis (Theorems 9.3.6 and 10.7.3 and Exercise 10.7). On the other hand, we have the following . . .(.), ., ..作者: 鐵塔等 時(shí)間: 2025-3-22 07:45
Textbook 2009Latest editionian 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...Be作者: 修正案 時(shí)間: 2025-3-22 12:01 作者: 劇毒 時(shí)間: 2025-3-22 14:40 作者: 草率男 時(shí)間: 2025-3-22 20:03
Die fahrleistungsabh?ngige LKW-Mautdamental role in the entire book. The mere existence of discontinuous additive functions and discontinuous convex functions depends on that axiom. Therefore the axiom of choice will equally be treated with the remaining axioms of the set theory and no special mention will be made whenever it is used.作者: 樹膠 時(shí)間: 2025-3-22 23:45
Zusammenfassung und Schlu?folgerungen? . is open and non-empty, and f is bounded above on T, then . is continuous in . Are there other sets . with this property? What are possibly weak conditions which assure the continuity of a convex function, or of an additive function? In this and in the next chapter we will deal with such questions.作者: 錯(cuò)事 時(shí)間: 2025-3-23 05:21 作者: fructose 時(shí)間: 2025-3-23 05:52 作者: 皮薩 時(shí)間: 2025-3-23 13:41 作者: 蔓藤圖飾 時(shí)間: 2025-3-23 13:54 作者: G-spot 時(shí)間: 2025-3-23 20:48 作者: 小卷發(fā) 時(shí)間: 2025-3-24 00:06
Set Theorydamental role in the entire book. The mere existence of discontinuous additive functions and discontinuous convex functions depends on that axiom. Therefore the axiom of choice will equally be treated with the remaining axioms of the set theory and no special mention will be made whenever it is used.作者: obsolete 時(shí)間: 2025-3-24 02:45
Boundedness and Continuity of Convex Functions and Additive Functions? . is open and non-empty, and f is bounded above on T, then . is continuous in . Are there other sets . with this property? What are possibly weak conditions which assure the continuity of a convex function, or of an additive function? In this and in the next chapter we will deal with such questions.作者: 較早 時(shí)間: 2025-3-24 08:18 作者: ENDOW 時(shí)間: 2025-3-24 14:10 作者: 老人病學(xué) 時(shí)間: 2025-3-24 14:54 作者: 愉快么 時(shí)間: 2025-3-24 20:12
Auswirkungen auf das Informationssystem,In 2.1–2.2 . is a topological space, so, e.g., . may be a metric space, or, in particular, ?.. A set . ? . is called . iff int cl . = ?. A set . ? . is said to be of the . iff . is a countable union of nowhere dense sets: 作者: 平庸的人或物 時(shí)間: 2025-3-25 00:02 作者: 按等級 時(shí)間: 2025-3-25 04:25 作者: 結(jié)構(gòu) 時(shí)間: 2025-3-25 09:27
https://doi.org/10.1007/978-3-8350-9566-3Let . ? ? be an arbitrary set. A non-empty set . ? ?. is called . iff ..作者: 危機(jī) 時(shí)間: 2025-3-25 15:29
Information - Organisation - ProduktionIn this chapter we discuss some properties of convex functions connected with their boundedness and continuity. We start with the following Lemma 6.1.1. . ? ?. .→ ? . . . ∈ . ∈ ?. . ∈ ? . 0 < . < . ± . ∈ ..作者: 低能兒 時(shí)間: 2025-3-25 16:33 作者: Hippocampus 時(shí)間: 2025-3-25 20:33
https://doi.org/10.1007/978-3-642-83229-1Since the convex functions are defined by a functional inequality, it is not surprising that this notion will lead to a number of interesting and important inequalities. Some inequalities connected with the notion of convexity will be presented in this chapter.作者: 我們的面粉 時(shí)間: 2025-3-26 03:28 作者: Mercantile 時(shí)間: 2025-3-26 07:47 作者: 停止償付 時(shí)間: 2025-3-26 09:19 作者: Adrenaline 時(shí)間: 2025-3-26 14:04
Die farbigen D?mmerungserscheinungenLet . ? ?. be a convex set, let f : . → ? be an arbitrary function, and let . ∈ ?. be arbitrary. The difference operator Δh with the span . is defined by the equality ..作者: 巨大沒有 時(shí)間: 2025-3-26 17:57
https://doi.org/10.1007/978-3-0348-5360-6The Jensen inequality (5.3.1) is not the natural counterpart of the Cauchy equation (5.2.1). The natural counterpart of the Cauchy equation would be the inequality ..作者: 貪婪的人 時(shí)間: 2025-3-26 23:48 作者: Radiation 時(shí)間: 2025-3-27 04:52 作者: Cabinet 時(shí)間: 2025-3-27 07:32
AlgebraLet . be a field (cf. 4.7), and let . be a set endowed with two operations: the addition of elements of ., and the multiplication of elements of . by elements of . such that ., +) is a commutative group (i.e., fulfils conditions (2.9.1)–(2.9.4); cf. 4.5), and moreover . for every .,. for every .,. for every ..作者: 國家明智 時(shí)間: 2025-3-27 09:31 作者: 袋鼠 時(shí)間: 2025-3-27 17:05
Elementary Properties of Convex FunctionsIn this chapter we discuss some properties of convex functions connected with their boundedness and continuity. We start with the following Lemma 6.1.1. . ? ?. .→ ? . . . ∈ . ∈ ?. . ∈ ? . 0 < . < . ± . ∈ ..作者: 傻瓜 時(shí)間: 2025-3-27 18:34
Continuous Convex FunctionsLet . ? ?. be a convex and open set. In 5.3 we saw that a convex function f : . → ? fulfills the inequality . for all . ∈ . and all λ ∈ ? ∩ [0, 1]. It was also pointed out that if, moreover, . is continuous, then inequality (7.1.1) holds actually for all real λ ∈ [0, 1].作者: FLUSH 時(shí)間: 2025-3-28 00:01
InequalitiesSince the convex functions are defined by a functional inequality, it is not surprising that this notion will lead to a number of interesting and important inequalities. Some inequalities connected with the notion of convexity will be presented in this chapter.作者: cringe 時(shí)間: 2025-3-28 02:11
Further Properties of Additive Functions and Convex FunctionsLet . ? ?. be a convex and open set, and let f : . → ? be a convex function. Let . be the lower hull of f (cf. 6.3). By Theorem 6.3.1 either . . = -∞ for all . ∈ ., or . : . → ∝ is a continuous and convex function.作者: 離開 時(shí)間: 2025-3-28 07:31 作者: fixed-joint 時(shí)間: 2025-3-28 12:53
Derivations and AutomorphismsIn this chapter we will deal with functions satisfying the Cauchy equation (5.2.1) and also, simultaneously, another equations of a similar type.作者: inculpate 時(shí)間: 2025-3-28 15:55 作者: Hot-Flash 時(shí)間: 2025-3-28 22:04
Subadditive FunctionsThe Jensen inequality (5.3.1) is not the natural counterpart of the Cauchy equation (5.2.1). The natural counterpart of the Cauchy equation would be the inequality ..作者: 慢跑 時(shí)間: 2025-3-29 01:06
Set Theorydamental role in the entire book. The mere existence of discontinuous additive functions and discontinuous convex functions depends on that axiom. Therefore the axiom of choice will equally be treated with the remaining axioms of the set theory and no special mention will be made whenever it is used作者: Lipoprotein(A) 時(shí)間: 2025-3-29 06:38
Boundedness and Continuity of Convex Functions and Additive Functions? . is open and non-empty, and f is bounded above on T, then . is continuous in . Are there other sets . with this property? What are possibly weak conditions which assure the continuity of a convex function, or of an additive function? In this and in the next chapter we will deal with such question作者: 虛弱 時(shí)間: 2025-3-29 09:03 作者: HALL 時(shí)間: 2025-3-29 14:14
Properties of Hamel Bases.2.1 (cf., in particular, Corollary 4.2.1) asserts that there exist Hamel bases. More exactly (Lemma 4.2.1), for every set . ? . ? ?. such that . is linearly independent over ?, and . = ?., there exists a Hamel basis . of ?. such that . ? . ? . In particular, every set belonging to any of the classe作者: Harass 時(shí)間: 2025-3-29 17:13
alities). 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 give978-3-7643-8748-8978-3-7643-8749-5作者: 詞匯記憶方法 時(shí)間: 2025-3-29 23:22
An Introduction to the Theory of Functional Equations and InequalitiesCauchy‘s Equation an作者: DUST 時(shí)間: 2025-3-30 03:44 作者: muscle-fibers 時(shí)間: 2025-3-30 06:02
Textbook 2009Latest editionut 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 give作者: TOM 時(shí)間: 2025-3-30 10:59
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