Report of Meeting. The Fourteenth Debrecen-Katowice Winter Seminar, Hajdúszoboszló (Hungary), January 29 - February 1, 2014
Abstract
Report of Meeting. The Fourteenth Debrecen-Katowice Winter Seminar, Hajdúszoboszló (Hungary), January 29 - February 1, 2014.
Keywords
functional equations and inequalities; convex functions; means
References
1. Aczél J., A mean value property of the derivative of quadratic polynomials – without mean values and derivatives, Math. Magazine 58 (1985), 42–45.
2. Aczél J., Chung J.K., Ng C.T., Symmetric second differences in product form on groups, in: Topics in mathematical analysis, Ser. Pure Math. 11, World Sci. Publ., Teaneck, NJ, 1989, pp. 1–22.
3. Albrecher H., Thonhauser S., Optimality results for dividend problems in Insurance, RACSAM Rev. R. Acad. Cien. Serie A. Mat. 103 (2009), 295–320.
4. Anschuetz R., Scherwood H., When is a function’s inverse equal to its reciprocal?, College Math. J. 27 (1997), 388–393.
5. Badora R., On a generalized Wilson functional equation, Georgian Math. J. 12 (2005), no. 4, 595–606.
6. Baják Sz., Páles Zs., Computer aided solution of the invariance equation for two-variable Gini means, Comput. Math. Appl. 58 (2009), 334–340.
7. Baják Sz., Páles Zs., Computer aided solution of the invariance equation for two-variable Stolarsky means, Appl. Math. Comput. 216 (2010), no. 11, 3219–3227.
8. Baják Sz., Páles Zs., Solving invariance equations involving homogeneous means with the help of computer, Appl. Math. Comput. 219 (2013), no. 11, 6297–6315.
9. Baranyi P., Csapo A., Cognitive infocommunications: Coginfocom, in: 11th International Symposium on Computational Intelligence and Informatics (CINTI), Budapest, Hungary, (2010), pp. 141–146.
10. Baranyi P., Csapo A., Definition and synergies of cognitive infocommunications, Acta Polytechnica Hungarica 9 (2012), 67–83.
11. Baranyi P., Gilányi A., Mathability: emulating and enhancing human mathematical capabilities, in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2-5 December 2013, Budapest, Hungary (2013), pp. 555–558.
12. Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187–189.
13. Baron K., Volkmann P., On orthogonally additive functions, Publ. Math. Debrecen 52 (1998), 291–297.
14. Bobecka K., Wesołowski J., Kshirsagar–Tan independence property of beta matrices and related characterizations, Bernoulli 14 (2008), 749–763.
15. Boros Z., Talk given during The Fifty International Symposium on Functional Equations, Aequationes Math. 86 (2013), 293.
16. Boros Z., Fechner W., An alternative equation for polynomial functions, Aequationes Math., DOI 10.1007/s00010-014-0258-6.
17. Borus G.Gy., Gilányi A., Solving systems of linear functional equations with computer, in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2–5 December 2013, Budapest, Hungary (2013), pp. 559–562.
18. Brillouët-Belluot N., Problem posed during The Forty-ninth International Symposium on Functional Equations, Aequationes Math. 84 (2012), 312.
19. Brodsky Y.S., Slipenko A.K., Functional equations, Vishcha Shkola, Kiev, 1983 (in Russian).
20. Chen L., Shi Y., The real solutions of functional equation $f^{[m]}= 1/f$, J. Math. Res. Exposition 28 (2008), 323–330.
21. Cheng R., Dasgupta A., Ebanks B.R., Kinch L.F., Larson L.M., McFadden R.B., When does $f^{− 1}= 1/f$ ?, Amer. Math. Monthly 105 (1998), 704–716.
22. Chudziak J., Approximate dynamical systems on interval, Appl. Math. Lett. 25 (2012), no. 3, 352–357.
23. Draga S., Ściśle wypukłe przenormowania przestrzeni Banacha [Strictly convexifiable Banach spaces], Master’s thesis, University of Silesia, 2013.
24. Euler R., Foran J., On functions whose inverse is their reciprocal, J. Math. Mag. 54 (1981), 185–189.
25. Förg-Rob W., Schwaiger J., A generalization of the cosine equation to n summands, Grazer Math. Ber. 316 (1992), 219–226.
26. Gajda Z., A remark on the talk of W. Förg-Rob, Grazer Math. Ber. 316 (1992), 234–237.
27. Gilányi A., On strongly Wright-convex functions of higher order, Talk, 13th Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities, Zakopane, Poland, January 30 – February 2, 2013.
28. Gilányi A., Solving linear functional equations with computer, Math. Pannon. 9 (1998), no. 1, 57–70.
29. Gilányi A., Páles Zs., A characterization of strongly Jensen-convex functions of higher order via the Dinghas derivative, Remark, Report of Metting. 13th Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities, Zakopane (Poland), January 30 – February 2, 2013, Annales Mathematicae Silesianae 27 (2013), 121–123.
30. Gilányi A., Merentes N., Nikodem K., Páles Zs., Characterizations and decomposition of strongly Wright-convex functions of higher order, Opuscula Math., to appear.
31. Házy A., Lineáris függvényegyenletek megoldási módszerei és t-konvex függvények stabilitása, doktori (PhD) értekezés , Debreceni Egyetem, 2004.
32. Házy A., Solving linear two variable functional equations with computer, Aequationes Math. 67 (2004), no. 1–2, 47–62.
33. Házy A., Solving functional equations with computer, in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2–5 December 2013, Budapest, Hungary (2013).
34. Járai A., Regularity Properties of Functional Equations in Several Variables, Springer, New York, 2005.
35. Járai A., Regularity properties of measurable functions satisfying a multiplicative type functional equation almost everywhere, to appear.
36. Járai A., Lajkó K., Mészáros F., On measurable functions satisfying multiplicative type functional equations almost everywhere, to appear.
37. Kominek Z., Reich L., Schwaiger J., On additive functions fulfilling some additional condition, Sitzungsber. Abt. II 207 (1998), 35–42.
38. Łukasik R., Some generalization of Cauchy’s and the quadratic functional equations, Aequationes Math. 83 (2012), 75–86.
39. Łukasik R., Some generalization of the quadratic and Wilson’s functional equation, Aequationes Math., DOI 10.1007/s00010-013-0185-y.
40. Łukasik R., Some generalization of Cauchy’s and Wilson’s functional equations on abelian groups, Aequationes Math., DOI 10.1007/s00010-013-0244-4.
41. Maksa Gy., 16. Remark (Solution of J. Matkowski’s problem 14), Report of Meeting: The Thirtieth International Symposium on Functional Equations, September 20–26, 1992, Oberwolfach, Germany, Aequationes Math. 46 (1993), p. 292.
42. Maksa Gy., Páles Zs., On Hosszú’s functional inequality, Publ. Math. Debrecen 36 (1989), no. 1–4, 187–189.
43. Matkowski J., 14. Problem Report of Meeting: The Thirtieth International Symposium on Functional Equations, September 20–26, 1992, Oberwolfach, Germany, Aequationes Math. 46 (1993), p. 291.
44. McLeod R., Mean value theorems for vector valued functions, Proc. Edin. Math. Soc. 14 (1965), 197–209.
45. Mészáros F., Lajkó K., Functional equations and characterization problems, WDM Verlag, 2011.
46. Massera J.L., Petracca A., Sobre la ecuación funcional $f(f(x)) = 1/x$, Rev. Un. Mat. Argentina 11 (1946), 206–211.
47. Moszner Z., Sur les définitions différentes de la stabilité des équations fonctionnelles. (On the different definitions of the stability of functional equations), Aequationes Math. 68 (2004), no. 3, 260–274.
48. Moszner Z., On the inverse stability of functional equations, Banach Center Publications 99 (2013), 111–121.
49. Moszner Z., Przebieracz B., Is the dynamical system stable?, Aequationes Math., to appear.
50. Nabeya S., On the functional equation $f(p+qx+rf(x)) =a+bx+cf(x)$, Aequationes Math. 11 (1974), 199–211.
51 Ng C.T., Functions generating Schur-convex sums, in: General Inequalities 5 (Oberwol-fach, 1986), Internat. Schriftenreihe Numer. Math. 80, Birkhäuser, Boston, 1987, pp. 433–438.
52. Ng C.T., Zhang W., When does an iterate equal a power?, Publ. Math. Debrecen 67 (2005), 79–91.
53. Ohlin J., On a class of measures of dispersion with application to optimal reinsurance, ASTIN Bulletin 5 (1969), 249–266.
54. Pečarić J.E., Two remarks on Hosszú’s functional inequality, Publ. Math. Debrecen 40 (1992), no. 3–4, 243–244.
55. Powązka Z., Über Hosszúfunktionalungleichung und die Jensenische Integralungleichung, Rocznik Nauk.-Dydakt. Prace Mat., 14 (1997), 121–128 (in German).
56. Przebieracz B., On the stability of the translation equation and dynamical systems, Nonlinear Anal. 75 (2012), no. 4, 1980–1988.
57. Rajba T., On The Ohlin lemma for Hermite–Hadamard–Fejér type inequalities, Math. Inequal. Appl., to appear.
58. Rätz J., On orthogonally additive mappings, Aequationes Math. 28 (1985), 35–49.
59. Rodé Gy., Eine abstrakte Version des Satzes von Hahn–Banach, Arch. Math. (Basel) 31 (1978), 474–481.
60. Sanderson J.D.E., A versatile vector mean value theorem, Amer. Math. Monthly 79 (1972), 381–383.
61. Schmidli H., Stochastic Control in Insurance, Springer-Verlag, London, 2008.
62. Stetkær H., On a signed cosine equation of N summands, Aequationes Math. 51 (1996), no. 3, 294–302.
63. Stetkær H., Wilson’s functional equation on C, Aequationes Math. 53 (1997), no. 1–2, 91–107.
64. Stetkær H., Functional equation on abelian groups with involution, Aequationes Math. 54 (1997), no. 1–2, 144–172.
65. Stetkær H., Functional equations involving means of functions on the complex plane, Aequationes Math. 56 (1998), 47–62.
66. Török M., Tóth M.J., Szöllősi A., Foundations and perspectives of mathability in relation to the CogInfoCom domain , in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2–5 December 2013, Budapest, Hungary (2013), pp. 869–872.
67. Veselý L., Zajiček L., Delta-convex mappings between Banach spaces and applications, Dissertationes Math. 289, Polish Scientific Publishers, Warszawa, 1989.
68. Yost D., M-ideals, the strong 2-ball property and some renorming theorems, Proc. Amer. Math. Soc. 81 (1981), 299–303.
2. Aczél J., Chung J.K., Ng C.T., Symmetric second differences in product form on groups, in: Topics in mathematical analysis, Ser. Pure Math. 11, World Sci. Publ., Teaneck, NJ, 1989, pp. 1–22.
3. Albrecher H., Thonhauser S., Optimality results for dividend problems in Insurance, RACSAM Rev. R. Acad. Cien. Serie A. Mat. 103 (2009), 295–320.
4. Anschuetz R., Scherwood H., When is a function’s inverse equal to its reciprocal?, College Math. J. 27 (1997), 388–393.
5. Badora R., On a generalized Wilson functional equation, Georgian Math. J. 12 (2005), no. 4, 595–606.
6. Baják Sz., Páles Zs., Computer aided solution of the invariance equation for two-variable Gini means, Comput. Math. Appl. 58 (2009), 334–340.
7. Baják Sz., Páles Zs., Computer aided solution of the invariance equation for two-variable Stolarsky means, Appl. Math. Comput. 216 (2010), no. 11, 3219–3227.
8. Baják Sz., Páles Zs., Solving invariance equations involving homogeneous means with the help of computer, Appl. Math. Comput. 219 (2013), no. 11, 6297–6315.
9. Baranyi P., Csapo A., Cognitive infocommunications: Coginfocom, in: 11th International Symposium on Computational Intelligence and Informatics (CINTI), Budapest, Hungary, (2010), pp. 141–146.
10. Baranyi P., Csapo A., Definition and synergies of cognitive infocommunications, Acta Polytechnica Hungarica 9 (2012), 67–83.
11. Baranyi P., Gilányi A., Mathability: emulating and enhancing human mathematical capabilities, in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2-5 December 2013, Budapest, Hungary (2013), pp. 555–558.
12. Baron K., Rätz J., On orthogonally additive mappings on inner product spaces, Bull. Polish Acad. Sci. Math. 43 (1995), 187–189.
13. Baron K., Volkmann P., On orthogonally additive functions, Publ. Math. Debrecen 52 (1998), 291–297.
14. Bobecka K., Wesołowski J., Kshirsagar–Tan independence property of beta matrices and related characterizations, Bernoulli 14 (2008), 749–763.
15. Boros Z., Talk given during The Fifty International Symposium on Functional Equations, Aequationes Math. 86 (2013), 293.
16. Boros Z., Fechner W., An alternative equation for polynomial functions, Aequationes Math., DOI 10.1007/s00010-014-0258-6.
17. Borus G.Gy., Gilányi A., Solving systems of linear functional equations with computer, in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2–5 December 2013, Budapest, Hungary (2013), pp. 559–562.
18. Brillouët-Belluot N., Problem posed during The Forty-ninth International Symposium on Functional Equations, Aequationes Math. 84 (2012), 312.
19. Brodsky Y.S., Slipenko A.K., Functional equations, Vishcha Shkola, Kiev, 1983 (in Russian).
20. Chen L., Shi Y., The real solutions of functional equation $f^{[m]}= 1/f$, J. Math. Res. Exposition 28 (2008), 323–330.
21. Cheng R., Dasgupta A., Ebanks B.R., Kinch L.F., Larson L.M., McFadden R.B., When does $f^{− 1}= 1/f$ ?, Amer. Math. Monthly 105 (1998), 704–716.
22. Chudziak J., Approximate dynamical systems on interval, Appl. Math. Lett. 25 (2012), no. 3, 352–357.
23. Draga S., Ściśle wypukłe przenormowania przestrzeni Banacha [Strictly convexifiable Banach spaces], Master’s thesis, University of Silesia, 2013.
24. Euler R., Foran J., On functions whose inverse is their reciprocal, J. Math. Mag. 54 (1981), 185–189.
25. Förg-Rob W., Schwaiger J., A generalization of the cosine equation to n summands, Grazer Math. Ber. 316 (1992), 219–226.
26. Gajda Z., A remark on the talk of W. Förg-Rob, Grazer Math. Ber. 316 (1992), 234–237.
27. Gilányi A., On strongly Wright-convex functions of higher order, Talk, 13th Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities, Zakopane, Poland, January 30 – February 2, 2013.
28. Gilányi A., Solving linear functional equations with computer, Math. Pannon. 9 (1998), no. 1, 57–70.
29. Gilányi A., Páles Zs., A characterization of strongly Jensen-convex functions of higher order via the Dinghas derivative, Remark, Report of Metting. 13th Katowice–Debrecen Winter Seminar on Functional Equations and Inequalities, Zakopane (Poland), January 30 – February 2, 2013, Annales Mathematicae Silesianae 27 (2013), 121–123.
30. Gilányi A., Merentes N., Nikodem K., Páles Zs., Characterizations and decomposition of strongly Wright-convex functions of higher order, Opuscula Math., to appear.
31. Házy A., Lineáris függvényegyenletek megoldási módszerei és t-konvex függvények stabilitása, doktori (PhD) értekezés , Debreceni Egyetem, 2004.
32. Házy A., Solving linear two variable functional equations with computer, Aequationes Math. 67 (2004), no. 1–2, 47–62.
33. Házy A., Solving functional equations with computer, in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2–5 December 2013, Budapest, Hungary (2013).
34. Járai A., Regularity Properties of Functional Equations in Several Variables, Springer, New York, 2005.
35. Járai A., Regularity properties of measurable functions satisfying a multiplicative type functional equation almost everywhere, to appear.
36. Járai A., Lajkó K., Mészáros F., On measurable functions satisfying multiplicative type functional equations almost everywhere, to appear.
37. Kominek Z., Reich L., Schwaiger J., On additive functions fulfilling some additional condition, Sitzungsber. Abt. II 207 (1998), 35–42.
38. Łukasik R., Some generalization of Cauchy’s and the quadratic functional equations, Aequationes Math. 83 (2012), 75–86.
39. Łukasik R., Some generalization of the quadratic and Wilson’s functional equation, Aequationes Math., DOI 10.1007/s00010-013-0185-y.
40. Łukasik R., Some generalization of Cauchy’s and Wilson’s functional equations on abelian groups, Aequationes Math., DOI 10.1007/s00010-013-0244-4.
41. Maksa Gy., 16. Remark (Solution of J. Matkowski’s problem 14), Report of Meeting: The Thirtieth International Symposium on Functional Equations, September 20–26, 1992, Oberwolfach, Germany, Aequationes Math. 46 (1993), p. 292.
42. Maksa Gy., Páles Zs., On Hosszú’s functional inequality, Publ. Math. Debrecen 36 (1989), no. 1–4, 187–189.
43. Matkowski J., 14. Problem Report of Meeting: The Thirtieth International Symposium on Functional Equations, September 20–26, 1992, Oberwolfach, Germany, Aequationes Math. 46 (1993), p. 291.
44. McLeod R., Mean value theorems for vector valued functions, Proc. Edin. Math. Soc. 14 (1965), 197–209.
45. Mészáros F., Lajkó K., Functional equations and characterization problems, WDM Verlag, 2011.
46. Massera J.L., Petracca A., Sobre la ecuación funcional $f(f(x)) = 1/x$, Rev. Un. Mat. Argentina 11 (1946), 206–211.
47. Moszner Z., Sur les définitions différentes de la stabilité des équations fonctionnelles. (On the different definitions of the stability of functional equations), Aequationes Math. 68 (2004), no. 3, 260–274.
48. Moszner Z., On the inverse stability of functional equations, Banach Center Publications 99 (2013), 111–121.
49. Moszner Z., Przebieracz B., Is the dynamical system stable?, Aequationes Math., to appear.
50. Nabeya S., On the functional equation $f(p+qx+rf(x)) =a+bx+cf(x)$, Aequationes Math. 11 (1974), 199–211.
51 Ng C.T., Functions generating Schur-convex sums, in: General Inequalities 5 (Oberwol-fach, 1986), Internat. Schriftenreihe Numer. Math. 80, Birkhäuser, Boston, 1987, pp. 433–438.
52. Ng C.T., Zhang W., When does an iterate equal a power?, Publ. Math. Debrecen 67 (2005), 79–91.
53. Ohlin J., On a class of measures of dispersion with application to optimal reinsurance, ASTIN Bulletin 5 (1969), 249–266.
54. Pečarić J.E., Two remarks on Hosszú’s functional inequality, Publ. Math. Debrecen 40 (1992), no. 3–4, 243–244.
55. Powązka Z., Über Hosszúfunktionalungleichung und die Jensenische Integralungleichung, Rocznik Nauk.-Dydakt. Prace Mat., 14 (1997), 121–128 (in German).
56. Przebieracz B., On the stability of the translation equation and dynamical systems, Nonlinear Anal. 75 (2012), no. 4, 1980–1988.
57. Rajba T., On The Ohlin lemma for Hermite–Hadamard–Fejér type inequalities, Math. Inequal. Appl., to appear.
58. Rätz J., On orthogonally additive mappings, Aequationes Math. 28 (1985), 35–49.
59. Rodé Gy., Eine abstrakte Version des Satzes von Hahn–Banach, Arch. Math. (Basel) 31 (1978), 474–481.
60. Sanderson J.D.E., A versatile vector mean value theorem, Amer. Math. Monthly 79 (1972), 381–383.
61. Schmidli H., Stochastic Control in Insurance, Springer-Verlag, London, 2008.
62. Stetkær H., On a signed cosine equation of N summands, Aequationes Math. 51 (1996), no. 3, 294–302.
63. Stetkær H., Wilson’s functional equation on C, Aequationes Math. 53 (1997), no. 1–2, 91–107.
64. Stetkær H., Functional equation on abelian groups with involution, Aequationes Math. 54 (1997), no. 1–2, 144–172.
65. Stetkær H., Functional equations involving means of functions on the complex plane, Aequationes Math. 56 (1998), 47–62.
66. Török M., Tóth M.J., Szöllősi A., Foundations and perspectives of mathability in relation to the CogInfoCom domain , in: 4th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), 2–5 December 2013, Budapest, Hungary (2013), pp. 869–872.
67. Veselý L., Zajiček L., Delta-convex mappings between Banach spaces and applications, Dissertationes Math. 289, Polish Scientific Publishers, Warszawa, 1989.
68. Yost D., M-ideals, the strong 2-ball property and some renorming theorems, Proc. Amer. Math. Soc. 81 (1981), 299–303.
AMSilR. (2014). Report of Meeting. The Fourteenth Debrecen-Katowice Winter Seminar, Hajdúszoboszló (Hungary), January 29 - February 1, 2014. Annales Mathematicae Silesianae, 28, 97-118. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13995
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annales.math@us.edu.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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