We describe the general continuous solution of sine and cosine addition formulas and a socalled sinecosine functional equation on a locally compact hypergroup in terms of exponential functions, sine functions, and secondorder generalized moment functions. Marek kuczma, introduction to the theory of functional equations and inequalities, second edition, birkhauser, 2009. Noncommutative variations on laplaces equation rosenberg, jonathan. The purpose is to study and solve these functional equations on metabelian groups, i. Functional equations on abelian groups with involution. The aim of this paper is to study the stability problem of the generalized dalembert, wilson, and jensen functional equations. We produce complete solution formulas of selected functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the heisenberg group and on the group sl2.
Dalemberts and wilsons equations on semigroups pdf. Disregarding the trivial solution f 0 and g any complex function, it is known that g satisfies a. Wilsons functional equation on metabelian groups ilie corovei abstract. A sine type functional equation on a topological group 223 where. I encompasses classical functional equations like d. Sabour, wilsons functional equation with an endomorphism, mathrecherche et application 15 2016, 3239. Functional equations on groups ebook by henrik stetk. Davison, dalemberts functional equation on topological groups. The solution of this problem for various classes of equations is an expanding area of research. The solution of a class functional equations on semigroups. Zeglami, functional equations on semigroups with an endomorphism, acta math. This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. Various authors studied the drygas equation, for example ebanks et al.
Moreover, the properties of the additive cauchy equation are. The wilson version of d alemberts functional equation on a class of 2divisible nilpotent groups ilie corovei and vasile pop abstract. Functional equations and inequalities with applications book. Lukasik, some generalization of cauchys and the quadratic functional equations, aequationes math. As such, it does a superb job in the presentation of the material.
Functional equations and inequalities themistocles m. A generalization of drygas functional equation scielo. Functional equations and inequalities with applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. We show thatg andh are associated to certainkspherical. Wilsons functional equation on c wilsons functional equation on c stetkaer, henrik 19970201 00.
This book on functional equations is written by one of the experts on the topic and it is intended for upper level undergraduate and graduate students. Characterization of groups, loops, and closure conditions. Iterative functional equations marek kuczma, bogdan. G, where the functions f, g 1, h 1 to be determined are complex valued functions on an abelian group g and where gg is an involution of g.
Stability of a jensen type functional equation chung, soonyeong and lee, youngsu, banach journal of mathematical analysis, 2007. The solutions of drygas equation in abelian group are obtained by stetk. Functional equation, semigroup, multiplicative function. Functional equations and how to solve them in searchworks. For instance, properties of functions can be determined by considering the types of functional equations they satisfy. If e has a neutral element 0, then we say that a function f. Rassias 2,3, 1 department of mathematics, faculty of sciences, ibn zohr university, agadir 80000, morocco. Functional equations on groups world scientific publishing co. A functional equation motivated by some trigonometric identities. On a quadratic type functional equation on locally compact abelian groups samir kabbaj and hajira dimou international conference on algebra and related topics icart2018 july 02 05, 2018, rabat, morocco. Wilsons functional equation on c stetkaer, henrik 19970201 00. Cauchys equation and jensens inequality birkhauser, basel, 2009. Functional equations on abelian groups with involution springerlink. Disregarding the trivial solution f 0 and g any complex function, it is known that g.
Solution of a functional equation on compact groups using. Functional equations in mathematical analysis roman. Its scope extends from the classical functional equations on the real line to those on groups, in particular, nonabelian groups. Generalized hyersulam stability of trigonometric functional. One of the most famous trigonometric functional equations is dalemberts functional equation. An integral functional equation on groups under two measures 567 an antihomomorphism such that.
Functional equation wikimili, the free encyclopedia. Wilsons functional equations on groups springerlink. An integral functional equation on groups under two measures. Aczels monograph 1 contains references to earlier works on 1. It covers almost all topics that you would like to know about although, since this. Orlicz it was shown that the ordinary polynomials on r or r n can be characterized by some conditions functional equations which allow one to define and study the analogues of polynomials on commutative groups, semigroups and linear spaces.
A cohesive and comprehensive account of the modern theory of iterative functional equations. Moreover, equation, and a fortiori equation, is a special case of levicivita functional equation. On a quadratic type functional equation on locally compact. Often, the equation relates the value of a function or functions at some point with its values at other points. We will need to use other words, such as relation, map or other, which are just synonyms of a. You cannot study functional equations without making some use of the properties of limits and continuous functions. We are committed to sharing findings related to covid19 as quickly and safely as possible. Institut for matematik aarhus universitet ny munkegade 118 8000 aarhus c. On the stability of generalized dalembert and jensen. Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences.
Solution of several functional equations on nonunital semigroups using wilsons functional equations with involution jaeyoung chung 1 and prasanna k. Kannappan, functional equations and inequalities with applications, springer, 2009. This is called also the sinecosine functional equation as g sinand f cosis a solution in the realtocomplex case. Research article solution of several functional equations. The fact is that many problems involving functional equations depend upon. Wilsons functional equation on c, aequationes mathematicae. Samir kabbaj and hajira dimou on a quadratic type functional equation on locally compact abelian groups.
Pdf wilsons functional equations on groups researchgate. This article deals with trigonometric functional equations on hypergroups. Sahoo 2 1 department of mathematics, kunsan national university, gunsan 573701, republic of korea. Szekelyhidi convolution type functional equations on topological abelian groups world scientific singapore 1991. With applications to mathematics, information theory and to the natural and social sciences. Iterative functional equations 7 proposition lety n bethesolutionof 3. In particular we give the description of the solutions of wilson s equations and onnonunital semigroups whereas in the description of the solutions of is given on commutative topological monoids i. On a quadratic type functional equation on locally compact abelian groups.
Encyclopedia of mathematics and its applications, vol. Solution of several functional equations on nonunital. Price new from used from hardcover, 1968 please retry. Pdf functional equations on abelian groups with involution. Functional equations in a single variable mathematics. We exploit results on the predalembert functional equation by davison publ math debrecen 7512. A functional equation motivated by some trigonometric.
In some cases, equations for functions between circles will also crop up. A functional equation on groups with involutions springerlink. Research article solution of several functional equations on. Solutions and stability of a variant of wilsons functional equation. Pdf on the quadratic functional equation on groups. In the last 20 years dalemberts and wilsons functional equations with an involution x x have been studied among others by bouikhalene and elqorachi 2, davison 4,5, ebanks and stetkaer. Through these examples, i will explain how the functional equations appear in the. For example, for the case of non abelian groups, as shown in works by y. We shall in this paper study extensions of equations 1. Moreover, we assume an addition formula of trigonometric type for our research is motivated by some earlier results related to a problem posed by s. We will be providing unlimited waivers of publication charges for accepted articles related to covid19. An integral functional equation on groups under two measures an integral functional equation. Theory and numerical analysis of volterra functional equations. Pdf dalemberts functional equations on metabelian groups.
Nowadays, the field of functional equations is an evergrowing branch of mathematics with farreaching applications. Functional equations and inequalities with applications. Stanford libraries official online search tool for books, media, journals, databases, government documents and more. So our point of departure was formulas of trigonometry. The aim of this paper is to investigate the stability problem for the pexiderized trigonometric functional equation f. Its scope extends from the classical functional equations on the real line to those on groups. Nonarchimedean meromorphic solutions of functional equations hu, peichu and luan, yongzhi, bulletin of the belgian mathematical society simon stevin, 2016. In particular, the pursuit of solutions to the hyersulam and hyersulamrassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. Lectures on functional equations and their applications. This is an updated and expanded version of the paper that originally appeared in acta numerica 2004, 55145. An integral functional equation on groups under two measures an integral functional equation on groups under two measures dalemberts and wilsons equations on semigroups aequationes mathematicae, mar 2020. A sine type functional equation on a topological group. An extension of van vlecks functional equation for the sine.
Equation 1, also called the cosine equation, as f cossatis. We solve these equations on more general domains than the domainsusedin. On polynomial functions on noncommutative groups sciencedirect. Functional equations in mathematical analysis roman badora. In mathematics, a functional equation is any equation in which the unknown represents a function. In this talk, i will present some applications of functional equations in physics. Solution of several functional equations on nonunital semigroups using wilsons functional equations with involution. System upgrade on tue, may 19th, 2020 at 2am et during this period, ecommerce and registration of new users may not be available for up to 12 hours.
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