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2016 | 30 | 231--249
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The Sixteenth Debrecen-Katowice Winter Seminar Hernâdvécse (Hungary), January 27-30, 2016

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Let (S, +) be a commutative semigroup, c : S S be an endomorphism with c2 = id and let K be a field of characteristic different from 2. Inspired by the problem of strong alienation of the Jensen equation and the exponential Cauchy equation, we study the solutions f, g : S K of the functional equation f (x + y) + f (x + c(y)) + g(x + y) = 2f (x) + g(x)g(y) for x, y e S. We also consider an analogous problem for the Jensen and the d'Alembert equations as well as for the d'Alembert and the exponential Cauchy equations.(original abstract)
Opis fizyczny
  • Bessenyei M., Pales Zs., Characterization of higher-order monotonicity via integral inequalities, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), no. 4, 723-736.
  • Bernstein F., Doetsch G., Zur Theorie der konvexen Funktionen, Math. Ann. 76 (1915), 514-526.
  • Kominek Z., A continuity result on t-Wright convex functions, Publ. Mat. 63 (2003), 213-219.
  • Maksa Gy., Nikodem K., Pales Zs., Results on t-Wright convexity, C. R. Math. Rep. Acad. Sci. Canada 13 (1991), no. 6, 274-278.
  • Ng C.T., Functions generating Schur-convex sums, in: General inequalities, 5 (Ober- wolfach, 1986), Internat. Schriftenreihe Numer. Math. vol. 80, Birkhäuser, Basel, 1987, pp. 433-438.
  • Olbryś A., Some conditions implying the continuity of t-Wright convex functions, Publ. Math. Debrecen 68 (2006), no. 3-4, 401-418.
  • Olbryś A., Representation theorems for t-Wright convexity, J. Math. Anal. Appl. 384 (2011), no. 2, 273-283.
  • Olbryś A., On some inequalities equivalent to the Wright-convexity, J. Math. Inequal. 9 (2015), no. 2, 449-461.
  • Wright E.M., An inequality for convex functions, Amer. Math. Monthly 61 (1954), 620-622.
  • Draga S., Morawiec J., Reducing the polynomial-like iterative equations order and a generalized Zoltan Boros problem, Aequationes Math. (2016), DOI 10.1007/s00010-016- 0420-4.
  • Fine N.J., Cesàro summability of Walsh-Fourier series, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 558-591.
  • Gat G., Almost everywhere convergence ofFejér and logarithmic means ofsubsequences of partial sums of the Walsh-Fourier series of integrable functions, J. Approx. Theory 162 (2010), 687-708.
  • Gat G., Karagulyan G., On convergence properties of tensor products of some operator sequences, J. Geom. Anal. (2015), DOI 10.1007/s12220-015-9662-y.
  • Pales Zs., Characterization of quasideviation means, Acta. Math. Sci. Hungar. 40 (1982), 456-462.
  • Pales Zs., General inequalities for quasideviation means, Aequationes Math. 36 (1988), 32-56.
  • Bernau S.J., The square root of positive self-adjoint operator, J. Austral. Math. Soc. 8. (1968), 17-36.
  • Chmieliński J., Orthogonality equation with two unknown functions, Aequationes Math. 90 (2016), 11-23.
  • Łukasik R., Wójcik P., Decomposition of two functions in the orthogonality equation, Aequationes Math. 90 (2016), 495-499.
  • Riesz F., Nagy B.-Sz., Functional analysis, Dover Publications, Inc., New York, 1990.
  • Kuczma M., An introduction to the theory of functional equations and inequalities. Cauchy's equation and Jensen's inequality, Birkhäuser Verlag, Basel, 2009.
  • Pales Zs., Radacsi É.Sz., Characterizations of higher-order convexity properties with respect to Chebyshev systems, Aequationes Math. 90 (2016), 193-210.
  • Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1980), 64-66.
  • Gajda Z., On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), 431-434.
  • Hyers D.H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
  • Kalton N.J., The three space problem for locally bounded F-spaces, Compositio Math. 37 (1978), 243-276.
  • Kalton N.J., Convexity, type and the three space problem, Studia Math. 69 (1980/81), 247-287.
  • Kalton N.J., Peck N.T., Twisted sums ofsequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1-30.
  • Ribe M., Examples for the nonlocally convex three space problem, Proc. Amer. Math. Soc. 73 (1979), 351-355.
  • Roberts J.W., A nonlocally convex F-space with the Hahn-Banach approximation property, in: Banach spaces ofanalytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976), Lecture Notes in Math., Vol. 604, Springer, Berlin, 1977, pp. 76-81.
  • Fonseca I., Leoni G., Modern methods in the calculus of variations: Lp spaces. Springer Monographs in Mathematics, Springer Verlag, Berlin, 2007.
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