共查询到20条相似文献,搜索用时 0 毫秒
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Che Tat Ng 《Aequationes Mathematicae》2005,70(1-2):131-153
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Summary LetX be an abelian (topological) group andY a normed space. In this paper the following functional inequality is considered: {ie143-1} This inequality is a similar generalization of the Pexider equation as J. Tabor's generalization of the Cauchy equation (cf. [3], [4]). The solutions of our inequality have similar properties as the solutions of the Pexider equation. Continuity and related properties of the solutions are investigated as well.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
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Local Pexider and Cauchy equations 总被引:1,自引:0,他引:1
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Summary Letf be a map from a groupG into an abelian groupH satisfyingf(xy) + f(xy
–1) = 2f(x), f(e) = 0, wherex, y G ande is the identity inG. A set of necessary and sufficient conditions forS(G, H) = Hom(G, H) is given whenG is abelian, whereS(G, H) denotes all the solutions of the functional equation. The case whenG is non-abelian is also discussed. 相似文献
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Zhi-Hong Sun 《Journal of Number Theory》2003,102(1):41-89
Let p>3 be a prime, and denote the number of solutions of the congruence . In this paper, using the third-order recurring sequences we determine the values of Np(x3+a1x2+a2x+a3) and Np(x4+ax2+bx+c), and construct the solutions of the corresponding congruences, where a1,a2,a3,a,b,c are integers. 相似文献
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Zenon Moszner 《Aequationes Mathematicae》1995,50(1-2):17-37
Summary This paper gives a survey of the results of the general theory of translation equation which appeared after 1973. 相似文献
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C. T. Ng 《Aequationes Mathematicae》1990,39(1):85-99
Summary A natural extension of Jensen's functional equation on the real line is the equationf(xy) + f(xy
–1
) = 2f(x), wheref maps a groupG into an abelian groupH. We deduce some basic reduction formulas and relations, and use them to obtain the general solution on special groups. 相似文献
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Summary LetE be a real inner product space of dimension at least 2,F a topological Abelian group, andK a discrete subgroup ofF. Assume also thatF is continuously divisible by 2 (that is, the functionu 2u is a homeomorphism ofF ontoF). Iff: E F fulfils the conditionf(x + y) – f(x) – f(y) K for all orthogonalx, y E and is continuous at the origin then there exist continuous additive functionsa: R F andA: E F such thatf(x) – a(x
2)– A(x) K for everyx E.
Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
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