Geodesic
Mixed nonlinear functional equations and approximation of their solutions. The theory of J. Descloux and J. Rappaz. I. Regular and critical points. Bifurcation
Mathematica Applicanda, Tome 12 (1985) no. 24, pp. 123-139.

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The contents of part I lie in the compilation of papers by Descloux and Rappaz ["On numerical approximation of solution branches of nonlinear equations'', École Polytech. Lausanne, Lausanne, 1981; per bibl.; RAIRO Anal. Numér. 16 (1982), no. 4, 319–349; MR0684829]. In Banach spaces the author investigates the implicit nonlinear operator equation F(x)=0 with a sufficiently smooth operator F. He formulates the notions of regular and critical points of an operator and studies the behaviour of the solutions of the equation in the neighbourhood of such points. The theoretical considerations are based on a version of the implicit function theorem.
DOI : 10.14708/ma.v12i24.1626
Classification : 47H15 (58E07 65J15)
Mots-clés : Methods for solving equations involving nonlinear operator, Abstract bifurcation theory, Equations with nonlinear operators 
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Krzysztof Moszyński. Mixed nonlinear functional equations and approximation of their solutions. The theory of J. Descloux and J. Rappaz. I. Regular and critical points. Bifurcation. Mathematica Applicanda, Tome 12 (1985) no. 24, pp.  123-139. doi : 10.14708/ma.v12i24.1626. http://geodesic.mathdoc.fr/articles/10.14708/ma.v12i24.1626/

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