Ulam stability for a delay differential equation

 Access to full text

 Full (PDF)

1. [1] Bota-Boriceanu M.F., Petruşel A., Ulam-Hyers stability for operatorial equations, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 2011, 57(suppl. 1), 65–74 Zbl1265.54158
2. [2] Castro L.P., Ramos A., Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations, Banach J. Math. Anal., 2009, 3(1), 36–43 Zbl1177.45010
3. [3] Guo D., Lakshmikantham V., Liu X., Nonlinear Integral Equations in Abstract Spaces, Math. Appl., 373, Kuwer, Dordrecht, 1996 Zbl0866.45004
4. [4] Hyers D.H., Isac G., Rassias Th.M., Stability of Functional Equations in Several Variables, Progr. Nonlinear Differential Equations Appl., 34, Birkhäuser, Boston, 1998 http://dx.doi.org/10.1007/978-1-4612-1790-9[Crossref] Zbl0907.39025
5. [5] Jung S.-M., A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl., 2007, #57064 
6. [6] Kolmanovskiĭ V., Myshkis A., Applied Theory of Functional-Differential Equations, Math. Appl. (Soviet Ser.), 85, Kluwer, Dordrecht, 1992 http://dx.doi.org/10.1007/978-94-015-8084-7[Crossref] Zbl0917.34001
7. [7] Otrocol D., Ulam stabilities of differential equation with abstract Volterra operator in a Banach space, Nonlinear Funct. Anal. Appl., 2010, 15(4), 613–619 Zbl1242.45011
8. [8] Petru T.P., Petruşel A., Yao J.-C., Ulam-Hyers stability for operatorial equations and inclusions via nonself operators, Taiwanese J. Math., 2011, 15(5), 2195–2212 Zbl1246.54049
9. [9] Radu V., The fixed point alternative and the stability of functional equations, Fixed Point Theory, 2003, 4(1), 91–96 Zbl1051.39031
10. [10] Rassias Th.M., On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 1978, 72(2), 297–300 http://dx.doi.org/10.1090/S0002-9939-1978-0507327-1[Crossref] 
11. [11] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001 
12. [12] Rus I.A., Gronwall lemmas: ten open problems, Sci. Math. Jpn., 2009, 70(2), 221–228 Zbl1223.47064
13. [13] Rus I.A., Ulam stability of ordinary differential equations, Stud. Univ. Babeş-Bolyai Math., 2009, 54(4), 125–133 Zbl1224.34165
14. [14] Rus I.A., Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 2009, 10(2), 305–320 Zbl1204.47071
15. [15] Ulam S.M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, 8, Interscience, New York-London, 1960 Zbl0086.24101

1. Mohammed A. Almalahi, Satish K. Panchal, Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space