Stability of \(\Psi\)-additive mappings: Applications to nonlinear analysis. (English) Zbl 0843.47036

Isac, George; Rassias, Themistocles M.

Int. J. Math. Math. Sci. 19, No. 2, 219-228 (1996).

Summary: The Hyers-Ulam stability of mappings is in development and several authors have remarked interesting applications of this theory to various mathematical problems. In this paper, some applications in nonlinear analysis are presented, especially in fixed point theory. These kinds of applications seem not to have ever been remarked before by other authors.

MSC:

47J05

Equations involving nonlinear operators (general)

Keywords:

cone; homomorphism; eigenvalue; bifurcation; Hammerstein equation; completely continuous operator; Hyers-Ulam stability; nonlinear analysis; fixed point theory