On the stability of a Cauchy type functional equation

• Autorzy: Najati A. , Lee J. R. , Park C. , Rassias T. M.

Identyfikatory

DOI

10.1515/dema-2018-0026

• Języki publikacji: EN

Abstrakty

EN

In this work, the Hyers-Ulam type stability and the hyperstability of the functional equation [wzór] are proved.

Słowa kluczowe

EN

Hyers-Ulam stability; additive mappings; hyperstability; topological vector space

PL

stabilność Hyersa-Ulama; odwzorowania addytywne; hiperstabilność; przestrzeń liniowo-topologiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 323--331
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Najati A.

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

autor

Lee J. R.

• Department of Mathematics, Daejin University, Kyunggi 11159, Republic of Korea

autor

Park C.

• Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea

autor

Rassias T. M.

• Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece

Bibliografia

• [1] Ulam S. M., Problems in Modern Mathematics, Chapter VI, Science ed., Wiley, New York, 1940
• [2] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27(4), 222–224
• [3] Aoki T., On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 1950, 2(1-2), 64–66
• [4] Rassias Th. M., On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 1978, 72, 297–300
• [5] Brzdek J., Fechner W., Moslehian M. S., Sikorska J., Recent developments of the conditional stability of the homomorphismequation, Banach J. Math. Anal., 2015, 9(3), 278–326
• [6] Brzdek J., Popa D., Rasa I., Xu B., Ulam Stability of Operators, Mathematical Analysis and its Applications, v. 1, Academic Press, Elsevier, Oxford, 2018
• [7] Czerwik S., Functional Equations and Inequalities in Several Variables, World Scientific, River Edge, NJ, 2002
• [8] Gordji M. E., Najati A., Approximately J*-homomorphisms: a fixed point approach, J. Geom. Phys., 2010, 60, 809–814
• [9] Forti G. L., Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 1995, 50(1-2), 143–190
• [10] Hyers D. H., Isac G., Rassias Th. M., Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998
• [11] Jung S., Hyers-Ulam-Rassias stability of functional equations in non linear analysis, Springer Optimization and its Applications, 48, Springer, New York, 2011
• [12] Najati A., Homomorphisms in quasi-Banach algebras associated with a pexiderized Cauchy-Jensen functional equation, Acta Math. Sin. (Engl. Ser.), 2009, 25(9), 1529–1542
• [13] Najati A., Park C., On the stability of an n-dimensional functional equation originating from quadratic forms, Taiwanese J. Math., 2008, 12(7), 1609–1624
• [14] Najati A., Rassias Th. M., Stability of a mixed functional equation in several variables on Banach modules, Nonlinear Anal.–TMA, 2010, 72(3-4), 1755–1767
• [15] Rassias Th. M., On the stability of functional equations and a problem of Ulam, Acta Appl. Math., 2000, 62(1), 23–130
• [16] Kannappan Pl., Sahoo P. K., Cauchy difference – a generalization of Hosszú functional equation, Proc. Nat. Acad. Sci. India,1993, 63(3), 541–550
• [17] Gajda Z., On stability of additive mappings, Int. J. Math. Sci., 1991, 14(3), 431-434

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).