Trenogin, V. A. Functional analysis. Textbook. (Funktsional’nyj analiz. Uchebnoe posobie). (Russian) Zbl 0517.46001 Moskva: “Nauka”. 495 p. R. 1.30 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 121 Documents MSC: 46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 46B10 Duality and reflexivity in normed linear and Banach spaces 47-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory 46G05 Derivatives of functions in infinite-dimensional spaces 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 58-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis 65J05 General theory of numerical analysis in abstract spaces 47H10 Fixed-point theorems 58C15 Implicit function theorems; global Newton methods on manifolds Keywords:Banach spaces; Lebesgue and Sobolev spaces; method of the small parameter; method of parametric extension; conjugate spaces; Hahn-Banach theorem; compact sets; completely continuous operators; normally solvable operators; Fredholm theory; spectral theory of linear operators; selfadjoint operators; approximate solution; abstract approximation schemes; fixed points of nonlinear operators; Frechet and Gateaux differentials; abstract implicit function theorem; monotone coercive and demicontinuous operators; Fatou theorem; adjoint operator PDF BibTeX XML OpenURL