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A novel approach regarding the fixed points of repelling nature. (English) Zbl 1498.37043


MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
47H10 Fixed-point theorems
Full Text: DOI

References:

[1] Adomian, G.; Rach, R., On the solution of algebraic equations by the decomposition method, J Math Anal Appl, 105, 141-166 (1985) · Zbl 0552.60060
[2] Alturk, A.; Cosgun, T., The use of lavrentiev regularization method in Fredholm integral equations of the first kind, Int J Adv Appl Math Mech, 7, 2, 70-72 (2019) · Zbl 1469.45001
[3] Banach, S., Sur les operations dans les ensembles abstrits et leur applications aux equations integrals, Fund Math, 3, 1, 133-181 (1922) · JFM 48.0201.01
[4] Bing, R. H., The elusive fixed point property, Am Math Mon, 76, 2, 119-132 (1969) · Zbl 0174.25902
[5] Boyce, W. E.; DiPrima, R. C., Elementary differential equations and boundary value problems (2004), John Wiley & Sons Inc.: John Wiley & Sons Inc. USA · Zbl 0128.30601
[6] Brouwer, L., Uber abbildungen von mannigfaltigkeiten, Math Ann, 71, 97-115 (1912) · JFM 42.0417.01
[7] Browder, F. E., Non-expansive nonlinear operators in a Banach space, Proc Natl Acad Sci USA, 54, 4, 1041-1044 (1965) · Zbl 0128.35801
[8] Browder, F. E.; Petryshyn, W. V., The solution by iteration of nonlinear functional equations in Banach spaces, Bull Am Math Soc, 72, 3, 571-575 (1966) · Zbl 0138.08202
[9] Cheney, W.; Kincaid, D., Numerical mathematics and computing (2008), Cengage Learning: Cengage Learning Florence
[10] Devaney, R. L., An introduction to chaotic dynamical systems (1989), Addison-Wesley: Addison-Wesley USA · Zbl 0695.58002
[11] Fan, K., A generalization of Tychonoff’s fixed point theorem, Math Ann, 142, 305-310 (1961) · Zbl 0093.36701
[12] Kakutani, S., A generalization of Brouwer’s fixed point theorem, Duke Math J, 8, 3, 457-459 (1941) · JFM 67.0742.03
[13] Kirk, W. A., A fixed point theorem for mappings which do not increase distances, Am Math Mon, 72, 9, 1004-1006 (1965) · Zbl 0141.32402
[14] Krasnosel’skii, M. A.; Vainikko, G. M.; Zabreyko, R. P.; Ruticki, Y. B.; Stet’senko, V. V., Approximate solution of operator equations (1972), Wolters-Noordhoff Publishing: Wolters-Noordhoff Publishing Groningen · Zbl 0231.41024
[15] 1
[16] Layek, G. C., An introduction to dynamical systems and chaos (2015), Springer: Springer India · Zbl 1354.34001
[17] MATHEMATICA 12. 2019. UK: Wolfram Research
[18] Mathews, J. H.; Fink, K. D., Numerical methods: using MATLAB (1999), Prentice-Hall, Inc.: Prentice-Hall, Inc. Upper Saddle River NJ
[19] Ostrowski, A., Solution of equations in euclidean and banach spaces (1973), Academic Press: Academic Press New York · Zbl 0304.65002
[20] Schauder, J., Der fixpunktsatz in funktionalraumen, Stud Math, 2, 1, 171-180 (1930) · JFM 56.0355.01
[21] Stepleman, R. S., A characterization of local convergence for fixed point iterations in \(\mathbb{R}^1\), SIAM J Numer Anal, 12, 6, 887-894 (1975) · Zbl 0319.65037
[22] A member of the Perseus Books Group · Zbl 1343.37001
[23] 27(41): 249-258 · Zbl 0466.54036
[24] Tigan, G., Controlling chaos of a dynamical system with feedback control, Carpathian J Math, 22, 1-2, 153-161 (2006) · Zbl 1150.93398
[25] Tychonoff, A., Ein fixpunktsatz, Math Ann, 111, 767-776 (1935) · Zbl 0012.30803
[26] Wazwaz, A. M., Linear and nonlinear integral equations: methods and applications (2011), Springer-Verlag: Springer-Verlag Germany · Zbl 1227.45002
[27] Zemyan, S. M., The classical theory of integral equations: a concise treatment (2012), Birkhäuser: Birkhäuser Basel · Zbl 1270.45001
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