Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (6): 1727-1739.doi: 10.1016/S0252-9602(17)30103-0
• Articles • Previous Articles Next Articles
Iz-iddine EL-FASSI1, Janusz BRZD?K2, Abdellatif CHAHBI3, Samir KABBAJ3
Received:2016-07-20
Revised:2016-12-07
Online:2017-12-25
Published:2017-12-25
Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J].Acta mathematica scientia,Series B, 2017, 37(6): 1727-1739.
| [1] Aczél J, Dhombres J. Functional Equations in Several Variables. Vol 31 of Encyclopedia of Mathematics and its Applications. Cambridge, UK:Cambridge University Press, 1989 [2] Agarwal R P, Xu B, Zhang W. Stability of functional equations in single variable. J Math Anal Appl, 2003, 288:852-869 [3] Aoki T. On the stability of the linear transformation in Banach spaces. J Math Soc Japan, 1950, 2:64-66 [4] Bahyrycz A, Piszczek M. Hyperstability of the Jensen functional equation. Acta Math Hungar, 2014, 142(2014):353-365 [5] Bahyrycz A, Olko J. Hyperstability of general linear functional equation. Aequationes Math, 2015, 89:1461-1476 [6] Bourgin D G. Classes of transformations and bordering transformations. Bull Amer Math Soc, 1951, 57:223-237 [7] Brzdȩk J. Remarks on hyperstability of the the Cauchy equation. Aequations Math, 2013, 86:255-267 [8] Brzdȩk J. Hyperstability of the Cauchy equation on restricted domains. Acta Math Hungar, 2013, 141:58-67 [9] Brzdȩk J. A hyperstability result for the Cauchy equation. Bull Austral Math Soc, 2014, 89:33-40 [10] Brzdȩk J, Chudziak J, Páles Z. A fixed point approach to stability of functional equations. Nonlinear Anal, 2011, 74:6728-6732 [11] Brzdȩk J, Ciepliński K. Hyperstability and superstability. Abstr Appl Anal, 2003, 2013:Article ID 401756, 13 pp [12] Brzdȩk J, Fechner W, Moslehian M S, Sikorska J. Recent developments of the conditional stability of the homomorphism equation. Banach J Math Anal, 2015, 9:278-327 [13] EL-Fassi I, Kabbaj S, Charifi A. Hyperstability of Cauchy-Jensen functional equations. Indagationes Math, 2016, 27:855-867 [14] EL-Fassi Iz, Kabbaj S. On the hyperstability of a Cauchy-Jensen type functional equation in Banach spaces. Proyecciones J Math, 2015, 34:359-375 [15] Forti G L. Hyers-Ulam stability of functional equations in several variables. Aequationes Math, 1995, 50:143-190 [16] Gajda Z. On stability of additive mappings. Int J Math Math Sci, 1991, 14:431-434 [17] Gselmann E. Hyperstability of a functional equation. Acta Math Hung, 2009, 124:179-188 [18] Hyers D H. On the stability of the linear functional equation. Proc Nat Acad Sci USA, 1941, 27:222-224 [19] Lee Y H. On the stability of the monomial functional equation. Bull Korean Math Soc, 2008, 45:397-403 [20] Moszner Z. Stability has many names, Aequationes Math, 2016, 90:983-999 [21] Lee Y H, Jung S M, Rassias M Th. On an n-dimensional mixed type additive and quadratic functional equation. Appl Math Comp, 2014, 228:13-16 [22] Jung S M, Rassias M Th, Mortici C. On a functional equation of trigonometric type. Appl Math Comp, 2015, 252:294-303 [23] Park W G, Bae J H. Stability of a bi-additive functional equation in Banach modules over a C*-Algebra. Discrete Dyn Nat Soc, 2012, 2012:Article ID 835893, 12 pages [24] Piszczek M. Remark on hyperstability of the general linear equation. Aequationes Math, 2014, 88:163-168 [25] Rassias Th M. On the stability of the linear mapping in Banach spaces. Proc Amer Math Soc, 1978, 72:297-300 [26] Rassias Th M. On a modified Hyers-Ulam sequence. J Math Anal Appl, 1991, 158:106-113 [27] Rassias Th M, Šemrl P. On the behavior of mappings which do not satisfy Hyer s-Ulam stability. Proc Amer Math Soc, 1992, 114:989-993 [28] Ulam S M. Problems in Modern Mathematics, Chapter IV. Science ed. New York:Wiley, 1960 [29] Zhang D. On hyperstability of generalised linear functional equations in several variables. Bull Austral Math Soc, 2015, 92:259-267 [30] Zhang D. On Hyers-Ulam stability of generalized linear functional equation and its induced Hyers-Ulam programming problem. Aequationes Math, 2016, 90:559-568 |
| [1] | Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS [J]. Acta mathematica scientia,Series B, 2018, 38(2): 377-390. |
| [2] | Wei SONG, Lin LI. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION [J]. Acta mathematica scientia,Series B, 2018, 38(1): 177-186. |
| [3] | Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON. A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1631-1640. |
| [4] | Yuji LIU. PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1492-1508. |
| [5] | Bouikhalene BELAID, Elqorachi ELHOUCIEN. SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON'S EQUATION [J]. Acta mathematica scientia,Series B, 2016, 36(3): 791-801. |
| [6] | Adnène ARBI, Farouk CHÉRIF, Chaouki AOUITI, Abderrahmen TOUATI. DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS [J]. Acta mathematica scientia,Series B, 2016, 36(3): 891-912. |
| [7] | A. Vinodkumar, K. Malar, M. Gowrisankar, P. Mohankumar. EXISTENCE, UNIQUENESS AND STABILITY OF RANDOM IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2016, 36(2): 428-442. |
| [8] | Anna BAHYRYCZ, Magdalena PISZCZEK. ON APPROXIMATELY (p, q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES [J]. Acta mathematica scientia,Series B, 2016, 36(2): 593-601. |
| [9] | M. MURSALEEN, Khursheed J. ANSARI, Asif KHAN. STABILITY OF SOME POSITIVE LINEAR OPERATORS ON COMPACT DISK [J]. Acta mathematica scientia,Series B, 2015, 35(6): 1492-1500. |
| [10] | Anna BAHYRYCZ, Krzysztof CIEPLINSKI, Jolanta OLKO. ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY [J]. Acta mathematica scientia,Series B, 2015, 35(6): 1349-1358. |
| [11] | Choonkil PARK. QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES [J]. Acta mathematica scientia,Series B, 2015, 35(6): 1501-1510. |
| [12] | A. AGHAJANI, M. MURSALEEN, A. SHOLE HAGHIGHI. FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS [J]. Acta mathematica scientia,Series B, 2015, 35(3): 552-566. |
| [13] | Krzysztof CIEPLINSKI, Angelika SUROWCZYK. ON THE HYERS-ULAM STABILITY OF AN EQUATION CHARACTERIZING MULTI-QUADRATIC MAPPINGS [J]. Acta mathematica scientia,Series B, 2015, 35(3): 690-702. |
| [14] | Xieping DING. EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES [J]. Acta mathematica scientia,Series B, 2015, 35(2): 339-347. |
| [15] | Zagharide Zine EL ABIDINE. COMBINED EFFECTS IN A SEMILINEAR POLYHARMONIC PROBLEM IN THE UNIT BALL [J]. Acta mathematica scientia,Series B, 2014, 34(5): 1404-1416. |
| Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
|
Full text 13
|
|
|||||||||||||||||||||||||||||||||||||||||||||
|
Abstract 105
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||
| Shared | ||||||||||||||||||||||||||||||||||||||||||||||
| Discussed | ||||||||||||||||||||||||||||||||||||||||||||||
|