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Discontinuity, Nonlinearity, and Complexity 3(4) (2014) 379--388 | DOI:10.5890/DNC.2014.12.002

Jinrong Wang$^{1}$,$^{2}$; Michal Fečkan$^{3}$,$^{4}$

$^{1}$ Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China

$^{2}$ School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, China

$^{3}$ Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia

$^{4}$ Mathematical Institute, Slovak Academy of Sciences, ˇ Stef´anikova 49, 814 73 Bratislava, Slovakia

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Abstract

We study the Ulam-Hyers-Rassias stability for linear and semilinear equations on Banach spaces from a functional analysis point of view with several illustrative examples. More precisely, surjective linear equations on Banach spaces, linear equations on Banach spaces with closed ranges and surjective semilinear equations between Banach spaces are investigated one by one.

Acknowledgments

The first author acknowledges the support by National Natural Science Foundation of China (11201091), Key Project on the Reforms of Teaching Contents, Course System of Guizhou Normal College and Doctor Project of Guizhou Normal College (13BS010) and Guizhou Province Education Planning Project (2013A062). The second author acknowledges the support by Grants VEGA-MS 1/0071/14 and VEGA-SAV 2/0029/13.

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