A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

 Access to full text

 Full (PDF)

1. [1] Agarwal R.P., O’Regan D., Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: the projective limit approach, J. Appl. Math. Stoch. Anal., 2006, #92375 
2. [2] Banas J., Goebel K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Appl. Math., 60, Marcel Dekker, New York, 1980 Zbl0441.47056
3. [3] Burton T.A., Integral equations, implicit functions and fixed points, Proc. Amer. Math. Soc., 1996, 124(8), 2383–2390 http://dx.doi.org/10.1090/S0002-9939-96-03533-2[Crossref] Zbl0873.45003
4. [4] Burton T.A., A fixed-point theorem of Krasnoselskii, Appl. Math. Lett., 1998, 11(1), 85–88 http://dx.doi.org/10.1016/S0893-9659(97)00138-9[Crossref] Zbl1127.47318
5. [5] Garcia-Falset J., Latrach K., Moreno-Gálvez E., Taoudi M.-A., Schaefer-Krasnoselskii fixed point theorems using a usual measure of weak noncompactness, J. Differential Equations, 2012, 252(5), 3436–3452 http://dx.doi.org/10.1016/j.jde.2011.11.012[WoS][Crossref] Zbl1252.47047
6. [6] Granas A., Dugundji J., Fixed Point Theory, Springer Monogr. Math., Springer, New York, 2003 Zbl1025.47002
7. [7] Jachymski J.R., Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., 1997, 125(8), 2327–2335 http://dx.doi.org/10.1090/S0002-9939-97-03853-7[Crossref] Zbl0887.47039
8. [8] Krasnosel’skiĭ M.A., Some problems of nonlinear analysis, In: Amer. Math. Soc. Transl. Ser. 2, 10, American Mathematical Society, Providence, 1958, 345–409 
9. [9] Krasnosel’skiĭ M.A., Vaĭnikko G.M., Zabreĭko P.P., Rutitskii Ya.B., Stetsenko V.Ya., Approximate Solution of Operator Equations, Wolters-Noordhoff, Groningen, 1972 http://dx.doi.org/10.1007/978-94-010-2715-1[Crossref] 
10. [10] Kryszewski W., Mederski J., Fixed point index for Krasnosel’skii-type set-valued maps on complete ANRs, Topol. Methods Nonlinear Anal., 2008, 28(2), 335–384 Zbl1136.47039
11. [11] Liu Y., Li Z., Krasnoselskii type fixed point theorem and applications, Proc. Amer. Math. Soc., 2008, 136(4), 1213–1220 http://dx.doi.org/10.1090/S0002-9939-07-09190-3[Crossref] Zbl1134.47040
12. [12] Ngoc L.T.P., Long N.T., Applying a fixed point theorem of Krasnosel’skii type to the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation, Nonlinear Anal., 2011, 74(11), 3769–3774 http://dx.doi.org/10.1016/j.na.2011.03.021[Crossref][WoS] Zbl1214.47049
13. [13] O’Regan D., Fixed-point theory for the sum of two operators, Appl. Math. Lett., 1996, 9(1), 1–8 http://dx.doi.org/10.1016/0893-9659(95)00093-3[Crossref] 
14. [14] Sadovskiĭ B.N., Limit-compact and condensing operators, Uspehi Mat. Nauk, 1972, 27(1), 81–146 (in Russian) Zbl0232.47067
15. [15] Xiang T., Krasnosel’skii fixed point theorem for dissipative operators, Electron. J. Differential Equations, 2011, #147 

1. Artur Babiarz, Jerzy Klamka, Michał Niezabitowski, Schauder's fixed-point theorem in approximate controllability problems