Abstract
In the present paper we prove a separation theorem for t-Wright convex and t-Wright concave functionals. We also consider the problem of supporting the t-Wright concave functions by t-Wright affine ones. As a consequence of these results we prove some decomposition theorems for t-Wright convex functions.
References
[1] Daróczy, Z.—Páles, Zs.: Convexity with given infinite weight sequences, Stochastica 11 (1987), 5–12.Suche in Google Scholar
[2] Kominek, Z.: A continuity result on t-Wright convex functions, Publ. Math. 63 (2003), 213–219.10.5486/PMD.2003.2782Suche in Google Scholar
[3] Kominek, Z.: Convex Functions in Linear Spaces, Prace Naukowe Uniwersytetu Śląskiego w Katowicach 1087, Katowice, 1989.Suche in Google Scholar
[4] König, H.: On the abstract Hahn-Banach theorem due to Rodé, Aequationes Math. 34 (1987), 89–95.10.1007/BF01840127Suche in Google Scholar
[5] Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Publishers and Silesian University Press, Warszawa-Kraków-Katowice, 1985.Suche in Google Scholar
[6] Kuhn, N.: A note on t-convex functions, General Inequalites 4 (1984), 269–276.10.1007/978-3-0348-6259-2_25Suche in Google Scholar
[7] Lajkó, K.: On a functional equation of Alsina and Garcia-Roig, Publ. Math. 52 (1998), 507–515.10.5486/PMD.1998.2023Suche in Google Scholar
[8] Maksa, Gy.—Nikodem, K.—Páles, Zs.: Result on t-Wright convexity, C. R. Math. Rep. Acad. Sci. Canada 13 (1991), 274–278.Suche in Google Scholar
[9] Matkowski, J.: On a-Wright convexity and the converse of Minkowki’s inequalty, Aequationes Math. 43 (1992), 106–112.10.1007/BF01840480Suche in Google Scholar
[10] Matkowski, J.—Wróbel, M.: A generalized α-Wright convexity and related functional equation, Ann. Math. Sil. 10 (1996), 7–12.Suche in Google Scholar
[11] Ng, C. T.: Functions generating Schur-convex sums. In: General Inequalities, S. Oberwolach, 1986, Internat Ser. Numer. Math. vol. 80, Birkhäuser, Boston, 1987, pp. 433–438.10.1007/978-3-0348-7192-1_35Suche in Google Scholar
[12] Ng, C. T.: On midconvex functions majorized by midpoint concave bounds, Proc. Amer. Math. Soc. 102 (1988), 538–540.10.1090/S0002-9939-1988-0928975-7Suche in Google Scholar
[13] Nikodem, K.: Midpoint convex functions majorized by midpoint concave functions, Aequationes Math. 32 (1987), 45–51.10.1007/BF02311298Suche in Google Scholar
[14] Nikodem, K.: On some class of midconvex functions, Ann. Polon. Math. 50 (1989), 145–151.10.4064/ap-50-2-145-151Suche in Google Scholar
[15] Olbryś, A.: A characterization of (t1,…,tn)-Wright affine functions, Commentationes Math. XLVII (2007), 47–56.Suche in Google Scholar
[16] Olbryś, A.: A support theorem for t-Wright convex functions, Math. Inequal. Appl. 14 (2011), 399–412.10.7153/mia-14-32Suche in Google Scholar
[17] Olbryś, A.: On the boundedness, Christensen measurability and continuity of t-Wright convex functions, Acta Math. Hungar. 141 (2013), 68–77.10.1007/s10474-013-0330-zSuche in Google Scholar
[18] Olbryś, A.: On the measurability and the Baire property of t-Wright convex functions, Aequationes Math. 68 (2004), 28–37.10.1007/s00010-003-2718-2Suche in Google Scholar
[19] Olbryś, A.: Representation theorems for t-Wright convexity, J. Math. Anal. Appl. 384 (2011), 273–283.10.1016/j.jmaa.2011.05.062Suche in Google Scholar
[20] Olbryś, A.: Some conditions implying the continuity of t-Wright convex functions, Publ. Math. Debrecen 68 (2006), 401–418.10.5486/PMD.2006.3243Suche in Google Scholar
[21] Roberts, A. W.—Varberg, D. E.: Convex Functions, Academic Press, New York and London, 1973.Suche in Google Scholar
[22] Rodé, G.: Eine abstrakte version des satzes von Hahn-Banach, Arch. Math. 31 (1978).10.1007/BF01226477Suche in Google Scholar
[23] Wright, E. M.: An inequality for convex functions, Amer. Math. Monthly 61 (1954), 620–622.10.2307/2307675Suche in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
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- A monotonicity property for generalized Fibonacci sequences
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Artikel in diesem Heft
- Some results in local Hilbert algebras
- A note on residuated po-groupoids and lattices with antitone involutions
- The first law of cubology for the Rubik’s Revenge
- Conditional associativity in orthomodular lattices
- A monotonicity property for generalized Fibonacci sequences
- Systems of conditionally independent sets
- On the k-th order lfsr sequence with public key cryptosystems
- On parametric spaces of bicentric quadrilaterals
- Character sums with an explicit evaluation
- Some remarks on formal power series and formal Laurent series
- The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
- On prime and semiprime generalized hyperaction of hypermonoid
- On O’Malley ϱ-upper continuous functions
- Uniqueness theorems for finitely additive probabilities on quantum structures
- Some results on differential-difference analogues of Brück conjecture
- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
- On support, separation and decomposition theorems for t-Wright-concave functions
- A characterization of holomorphic bivariate functions of bounded index
- Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
- A comparison of two tests in multivariate models
- Modelling prescription behaviour of general practitioners
- Characterization of congruence lattices of principal p-algebras