On a quadratic type functional equation on locally compact. The solutions of drygas equation in abelian group are obtained by stetk. Research article solution of several functional equations. In this talk, i will present some applications of functional equations in physics. Nonarchimedean meromorphic solutions of functional equations hu, peichu and luan, yongzhi, bulletin of the belgian mathematical society simon stevin, 2016. Functional equations and inequalities with applications book. Solution of several functional equations on nonunital. Its scope extends from the classical functional equations on the real line to those on groups. Pdf on the quadratic functional equation on groups. An integral functional equation on groups under two measures an integral functional equation. Functional equation wikimili, the free encyclopedia.
Institut for matematik aarhus universitet ny munkegade 118 8000 aarhus c. Functional equations in mathematical analysis roman. Aczels monograph 1 contains references to earlier works on 1. Solution of several functional equations on nonunital semigroups using wilsons functional equations with involution. Functional equations in several variables with applications to mathematics, information theory and to the natural and social sciences. 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. On the stability of generalized dalembert and jensen.
An integral functional equation on groups under two measures. A generalization of drygas functional equation scielo. A sine type functional equation on a topological group 223 where. Equation 1, also called the cosine equation, as f cossatis. 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 metabelian groups ilie corovei abstract. A functional equation on groups with involutions springerlink. 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. With applications to mathematics, information theory and to the natural and social sciences. 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. Solution of a functional equation on compact groups using. Functional equations on groups ebook by henrik stetk. You cannot study functional equations without making some use of the properties of limits and continuous functions.
This is called also the sinecosine functional equation as g sinand f cosis a solution in the realtocomplex case. Wilsons functional equations on groups springerlink. Pdf functional equations on abelian groups with involution. This is an updated and expanded version of the paper that originally appeared in acta numerica 2004, 55145.
This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. The wilson version of d alemberts functional equation on a class of 2divisible nilpotent groups ilie corovei and vasile pop abstract. The purpose is to study and solve these functional equations on metabelian groups, i. 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. Nowadays, the field of functional equations is an evergrowing branch of mathematics with farreaching applications. Noncommutative variations on laplaces equation rosenberg, jonathan. Disregarding the trivial solution f 0 and g any complex function, it is known that g. We are committed to sharing findings related to covid19 as quickly and safely as possible. Various authors studied the drygas equation, for example ebanks et al. A sine type functional equation on a topological group.
Functional equations on groups world scientific publishing co. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the heisenberg group and on the group sl2. Lukasik, some generalization of cauchys and the quadratic functional equations, aequationes math. The solution of a class functional equations on semigroups. In some cases, equations for functions between circles will also crop up. Iterative functional equations marek kuczma, bogdan.
Cauchys equation and jensens inequality birkhauser, basel, 2009. Characterization of groups, loops, and closure conditions. Solutions and stability of a variant of wilsons functional equation. Through these examples, i will explain how the functional equations appear in the. We exploit results on the predalembert functional equation by davison publ math debrecen 7512. Functional equation, semigroup, multiplicative function. Functional equations and inequalities with applications. Rassias 2,3, 1 department of mathematics, faculty of sciences, ibn zohr university, agadir 80000, morocco. I encompasses classical functional equations like d. 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. Stability of a jensen type functional equation chung, soonyeong and lee, youngsu, banach journal of mathematical analysis, 2007. 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.
Sahoo 2 1 department of mathematics, kunsan national university, gunsan 573701, republic of korea. The solution of this problem for various classes of equations is an expanding area of research. We show thatg andh are associated to certainkspherical. In mathematics, a functional equation is any equation in which the unknown represents a function. 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. Davison, dalemberts functional equation on topological groups. We solve these equations on more general domains than the domainsusedin.
Price new from used from hardcover, 1968 please retry. Marek kuczma, introduction to the theory of functional equations and inequalities, second edition, birkhauser, 2009. 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. Encyclopedia of mathematics and its applications, vol.
Functional equations and inequalities with applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Moreover, equation, and a fortiori equation, is a special case of levicivita functional equation. Functional equations and how to solve them in searchworks. A functional equation motivated by some trigonometric. Pdf wilsons functional equations on groups researchgate. Functional equations in a single variable mathematics. We shall in this paper study extensions of equations 1. We produce complete solution formulas of selected functional equations.
Its scope extends from the classical functional equations on the real line to those on groups, in particular, nonabelian groups. Disregarding the trivial solution f 0 and g any complex function, it is known that g satisfies a. Generalized hyersulam stability of trigonometric functional. Iterative functional equations 7 proposition lety n bethesolutionof 3. Wilsons functional equation on c, aequationes mathematicae. Functional equations on abelian groups with involution springerlink. This article deals with trigonometric functional equations on hypergroups. 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. As such, it does a superb job in the presentation of the material. For example, for the case of non abelian groups, as shown in works by y. Functional equations and inequalities themistocles m.
On a quadratic type functional equation on locally compact abelian groups. Kannappan, functional equations and inequalities with applications, springer, 2009. Often, the equation relates the value of a function or functions at some point with its values at other points. The aim of this paper is to investigate the stability problem for the pexiderized trigonometric functional equation f. Solution of several functional equations on nonunital semigroups using wilsons functional equations with involution jaeyoung chung 1 and prasanna k. Theory and numerical analysis of volterra functional equations. Lectures on functional equations and their applications. The aim of this paper is to study the stability problem of the generalized dalembert, wilson, and jensen functional equations. Wilsons functional equation on c wilsons functional equation on c stetkaer, henrik 19970201 00. Functional equations in mathematical analysis roman badora. Moreover, the properties of the additive cauchy equation are. Sabour, wilsons functional equation with an endomorphism, mathrecherche et application 15 2016, 3239. An integral functional equation on groups under two measures 567 an antihomomorphism such that.
Research article solution of several functional equations on. We will be providing unlimited waivers of publication charges for accepted articles related to covid19. Wilsons functional equation on c stetkaer, henrik 19970201 00. One of the most famous trigonometric functional equations is dalemberts functional equation. We will need to use other words, such as relation, map or other, which are just synonyms of a. An extension of van vlecks functional equation for the sine. Pdf dalemberts functional equations on metabelian groups. Dalemberts and wilsons equations on semigroups pdf. Functional equations on abelian groups with involution. So our point of departure was formulas of trigonometry. If e has a neutral element 0, then we say that a function f. 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.
On polynomial functions on noncommutative groups sciencedirect. A functional equation motivated by some trigonometric identities. Zeglami, functional equations on semigroups with an endomorphism, acta math. It covers almost all topics that you would like to know about although, since this.
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