Fixed point theorems without convexity
Analyse non convexe (Pau, 1977), Mémoires de la Société Mathématique de France, no. 60 (1979), pp. 129-152.
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     author = {Penot, Jean-Paul},
     title = {Fixed point theorems without convexity},
     booktitle = {Analyse non convexe (Pau, 1977)},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     pages = {129--152},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {60},
     year = {1979},
     doi = {10.24033/msmf.266},
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     zbl = {0454.47044},
     url = {http://www.numdam.org/articles/10.24033/msmf.266/}
}
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Penot, Jean-Paul. Fixed point theorems without convexity, in Analyse non convexe (Pau, 1977), Mémoires de la Société Mathématique de France, no. 60 (1979), pp. 129-152. doi : 10.24033/msmf.266. http://www.numdam.org/articles/10.24033/msmf.266/

Amann H. (1975) : Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundary value problems in Nonlinear operators and the calculus of variations. Bruxelles 1975, Lecture notes in math n° 543, Springer Verlag. New-York, 1-55. | MR | Zbl

Assad N.A. - Kirk W.A. (1972) : Fixed point theorems for set-valued mappings of contractive type. Pacific J. Math. 43 (3), 553-561. | MR | Zbl

Aubin J-P. (1977) : Microcours : gradients généralisés. Univ. de Montréal. Cahiers de l'IRMADE.

Aubin J-P. : Mathematical methods of game and economic theory (to be published) by North Holland. | Zbl

Belluce L.P. - Kirk W.A. (1969) : Some fixed point theorems in metric and Banach spaces. Canadian Bull. Math. 12, 481-492. | MR | Zbl

Birkhoff G. (1948) : Lattice theory. Amer. Math. Soc. Colloq. Publ. XXV, New-York. | MR | Zbl

Bony J.M. (1969) : Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés. Ann. Inst. Fourier. Grenoble 19, 277-304. | Numdam | MR | Zbl

Borwein J. - O'Brien R. (1976) : Tangent cones and convexity. Canad. Math. Bull. 19 (3) 257-261. | MR | Zbl

Bourgin D.G. (1973) : Fixed points and minimax theorems. Pacific. J. Math 45, 403-412. | MR | Zbl

Brezis H. (1965) : Points fixes. Séminaire Choquet 4è année, 11-01, 11-23. | Numdam | Zbl

Brezis H. (1967) : Sur certains problèmes non linéaires. Séminaire Choquet, Paris. 6e année, 18-01, 18-18. | Numdam | MR | Zbl

Brezis H. - Browder F.E. (1976) : A general ordering principle in nonlinear functional analysis. Advances in Math 21, 355-168. | MR | Zbl

Brodskǐi M.S. - Milman D.P. (1948) : On the center of a convex set (russian). Dokl. Akad. Nauk SSSR, 59, 837-840. | Zbl

Brønsted A. (1976) : Fixed points and partial orders. Proc. Amer. Math. Soc. 60 365-366. | MR | Zbl

Browder F.E. (1965) : Nonexpansive nonlinear operators in a Banach space. Proc. Nat. Acad. Sci. 54, 1041-1044. | MR | Zbl

Browder F.E. (1965) : Fixed points theorems on infinite dimensional manifolds. Trans. Amer. Math. Soc. 119, 179-194. | MR | Zbl

Browder F.E. (1967) : Nonlinear mappings of nonexpansive and accretive type in Banach spaces. Bull. Amer. Math. Soc. 73, 875-882. | MR | Zbl

Browder F.E. (1968) : The fixed-point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177, 283-301. | MR | Zbl

Browder F.E. (1975) : The Lefschetz fixed point theorem and asymptotic fixed point theorems in Partial Differential Equations and related topics. Lecture Notes in Math. n° 446, Springer-Verlag, New-York, 96-122. | MR | Zbl

Brown R.F. (1965) : On the Lefschetz fixed point theorem. Amer. J. Math. 87, 1-10. | MR | Zbl

Brown R.F. (1971) : The Lefschetz fixed point theorem, Scott, Foresman., Glenview, Illinois. | MR | Zbl

Caristi J. (1975) : Fixed point theorem for mappings satisfying inwardness conditions. Trans. Amer. Math. Soc. 215, 241-251. | MR | Zbl

Caristi J. - Kirk W.A. (1975) : Geometric fixed point theory and inwardness conditions in the Geometry of metric and linear spaces, Michigan 1974, L.M. Kelly editor, Lecture Notes in Math. N° 490, Springer Verlag New-York, 74-83. | MR | Zbl

Conti G. - Nistri P. (1975) : A fixed point theorem for non compact acyclic-valued maps. Rend. Accad. Sc. Fis. Mat. Napoli 42 (4), 510-517. | MR | Zbl

Cornet B. (1975) : Fixed point and surjectivity theorems for correspondances ; applications. Cahiers Math. de la décision, Univ. Paris-Dauphine n° 7521.

Deimling K. (1974) : Zeros of accretive operators. Manuscripta Math 13, 365-374. | MR | Zbl

Dotson W.G. (1972) : Fixed point theorems for non expansive mappings on star-shaped subsets of Banach spaces. J. London Math Soc. 4 (2), 408-410. | MR | Zbl

Edelstein M. (1961) : An extension of Banach's contraction principle. Proc. Amer. Math. Soc. 12, 7-10. | MR | Zbl

Edelstein M. (1962) : On fixed and periodic points under contractive mappings. J. London Math. Soc. 37, 74-79. | MR | Zbl

Edelstein M. (1964) : On non expansive mappings. Proc. Amer. Math. Soc. 15, 689-695. | MR | Zbl

Edelstein M. (1968) : On nearest points of sets in uniformly convex Banach spaces. J. London Math. Soc. 43, 375-377. | MR | Zbl

Edelstein M. (1975) : On some aspects of fixed point theory in Banach spaces in the Geometry of metric and linear spaces, Michigan 1974, L.M. Kelly editor. Lecture notes in Math. n° 490, Springer-Verlag New-York, 84-90. | MR | Zbl

Eilenberg S. - Montgomery D. (1946) : Fixed point theorems for multi-valued transformations. Amer. J. Math. 58, 214-222. | MR | Zbl

Eisenfeld J. - Lakshmikantham V. (1976) : Fixed point theorems on closed sets through abstract cones. Univ. of Texas at Arlington, tech. report n° 89.

Ekeland I. (1974) : On the variational principle. J. Math. Anal. and Appl. 47, 324-353. | MR | Zbl

Fakhoury H. (1972) : Sélections linéaires associées au théorème de Hahn-Banach. J. Funct. Anal. 11, 436-452. | MR | Zbl

Fan K. (1961) : A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 305-310. | MR | Zbl

Fan K. (1969) : Extension of two fixed points of F.E. Browder. Math. 2 112, 234-240. | MR | Zbl

Fort Jr. M.K. (1950) : Essential and non essential fixed points. Amer. J. Math. 72, 315-322. | MR | Zbl

Fournier G. (1975) : Généralisation du théorème de Lefschetz pour des espaces non compacts I, II, III, Bull. Acad. Pol. Sci. 23 (6), 693-699 ; 701-706 ; 707-711. | MR | Zbl

Gatica J.A. (1974) : Fixed point theorems for k-set contractions and pseudo-contractive mappings. J. Math. Anal. Appl. 46 (3), 555-564. | MR | Zbl

Glicksberg I.L. (1952) : A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Amer. Math. Soc. 3, 170-174. | MR | Zbl

Goebel K. (1969) : An elementary proof of the fixed point theorem of Browder and Kirk. Michigan Math. J. 16, 381-384. | MR | Zbl

Gohde D. (1965) : Zum prinzip der kontraktiven abbildung. Math. Nach. 30, 251-258. | MR | Zbl

Gorniewicz L. (1973) : Some consequences of the Lefschetz fixed point theorem. Bull. Acad. Pol. Sc. 21 (2) 165-170. | MR | Zbl

Gossez J-P. - Lami-Dozo E. (1969) : Structure normale et base de Schauder. Bull. CI. Sc. Ac. R. Belgique 55, 673-681. | MR | Zbl

Gossez J.P. - Lami-Dozo E. (1972) : Some geometric properties related to the fixed point theory for nonexpansive mappings. Pacific J. Math 40 (3), 565-573. | MR | Zbl

Granas A. (1972) : Generalizing the Hopf-Lefschetz fixed point theorem for non-compact A.N.R.S. Symp. Infinite dimensional topology, Baton Rouge, R.D. Anderson ed. Annals of Math. Study n°69, Princeton Univ. Press, Princeton New-Jersey, 119-130. | MR | Zbl

Granas A. (1976) : Sur la méthode de continuité de Poincaré, C.R. Acad. Sci. Paris 282, 983-985. | MR | Zbl

Halpern B.R. (1965) : Fixed point theorems for outward maps. Ph. D. Thesis, Univ. Calif. Los Angeles.

Halpern B.R. (1970) : Fixed point theorems for set-valued maps in infinite dimensional spaces, Math. Ann. 189, 87-98. | MR | Zbl

Halpern B.R. - Bergman G. (1968) : A fixed point theorem for inward and outward maps. Trans. Amer. Math. Soc. 130, 353-358. | MR | Zbl

Himmelberg C.J., Porter J.R., Van Vleck F.S. (1969) : Fixed point theorems for condensing multifunctions. Proc. Amer. Math. Soc. 23, 635-641, MR 39 # 7480. | MR | Zbl

Holmes R.D. (1976) : Fixed points for local radial contractions, in Swaninathan S. (1976). pp. 79-89. | Zbl

Jaworowski J.W. (1970) : Set-valued fixed points theorems for approximative retracts in Set-valued mappings, selections, and topological properties of 2X Lecture notes in Math. n° 171, Springer Verlag, New-York, 34-390. | MR | Zbl

Kakutani S. (1938) : Two fixed point theorems concerning bicompact convex sets. Proc. Imp. Acad. Tokyo 14, 242-245. | JFM | Zbl

Kirk W.A. (1965) : A fixed point theorem for mappings which do not increase distance. Amer. Math. Monthly 72, 1004-1006. | MR | Zbl

Kirk W.A. (1970) : Fixed points theorems for non expansive mappings. in Nonlinear functional analysis, F.E. Browder editor. Proc. Symp. Pure Math n° 18, vol. 1, Amer. Math. Soc. Providence R.I., 162-134. | MR | Zbl

Kirk W.A. (1976) : Caristi's fixed point theorem and the theory of normal solvability. in Fixed point theory and its applications, S. Swaminanthan ed. Academic Press, New-York, 109-120. | MR | Zbl

Knaster B. (1928) : Un théorème sur les fonctions d'ensembles. Ann. Soc. Pol. Math. 6, 133-134. | JFM

Kuhfittig P. : Fixed point theorems for mappings with non convex domain and range. Rocky Mountain J. Math. 7 (I) (1977) 141-145. | MR | Zbl

Lasry J.M. - Robert R. (1976) : Analyse non lineaire multivoque. Cahiers Math. de la Décision, Univ. Paris-Dauphine n° 7611.

Leader S. (1977) : Fixed points for operators on metric spaces with conditional uniform equivalence of orbits. J. Math. Anal. Appl. 61 (2), 466-474. | MR | Zbl

Leray J. (1972) : Fixed point index and Lefschetz number. Symp. infinite dimensional topology. Baton-Rouge, R.D. Anderson ed. Annals of Math. Studies n°69, Princeton Univ. Press, Princeton New-Jersey, 219-234. | MR | Zbl

Lim T.C. (1976) : Remarks on some fixed point theorems. Proc. Amer. Math. Soc. 60 (1) 179-182. | MR | Zbl

Lim T.C. (1977) : Fixed point theorems for mappings of non expansive type. Proc. Amer. Math. Soc. 66 (1) 69-74. | MR | Zbl

Martelli M. - Vignoli A. (1974) : A generalization of Leray-Schauder condition. Atti. Accad. Naz. Lincei (8) 57 (5), 374-379. | MR | Zbl

Markin J.T. (1969) : A fixed point theorem for set valued mappings. Bull. Amer. Math. Soc. 74 (4), 639-640. | MR | Zbl

Martin R.M. Jr (1973) : Differential equations on closed subsets of a Banach space Trans. Amer. Math. Soc. 179, 399-414. | MR | Zbl

Mayer C. (1965) : Points invariants dans les espaces localement convexes. Séminaire Choquet 4e année, 10-01, 10-11. | Numdam | Zbl

Meir A. - Keeler E. (1969) : A theorem on contraction mappings. J. Math. Anal. Appl. 28, 326-329, MR 40#3530. | MR | Zbl

Meyer P.A. (1966) : Probabilités et potentiel. Act. Sci. et Ind. N° 1318, Hermann Paris. | MR | Zbl

Nadler S.B. (1969) : Multivalued contraction mappings. Pacific J. Math. 30, 475-488. | MR | Zbl

Opial Z. (1967) : Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73, 591-597. | MR | Zbl

Opial Z. (1967) : Nonexpansive and monotone mappings in Banach spaces. Lecture Notes 67-1, Division of Applied Math. Brown Univ.

Penot J.P. (1976) : A short constructive proof of Caristi's fixed point theorem. Publications Math. de Pau, X-1 - X-3.

Petryshyn V.W. (1973) : Fixed point theorems for various classes of 1-set contractive and 1-ball contractive mappings in Banach spaces. Trans. Amer. Math. Soc. 182, 323-352. | MR | Zbl

Petryshyn V.W. - Fitzpatrick P.M. (1974) : Fixed-point theorems for multivalued non-compact inward maps. J. Math. Anal. and Appl. 46 (3), 756-767. | Zbl

Powers M.J. (1970) : Multivalued mappings and Lefschetz fixed point theorems. Proc. Cambridge Phil. Soc. 68, 619-630. | MR | Zbl

Powers M.J. (1972) : Lefschetz fixed point theorems for a new class of multivalued maps. Pacific J. Math 42, 211-220. | MR | Zbl

Reich S. (1972) : Fixed points in locally convex spaces, Math. Z 125, 17-31. | MR | Zbl

Reich S. (1976) : On fixed point theorems obtained from existence theorems for differential equations. J. Math. Anal. Appl. 54, 26-36. | MR | Zbl

Reich S. : Approximate selections, best approximations, fixed points, and invariant sets (to appear). | Zbl

Reinermann J. (1972) : Fixed point theorems for generalized contractions. Comment. Math. Univ. Carol 13 (4) 617-627. | MR | Zbl

Reinermann J. - Schőneberg R. (1976) : Some results and problems in the fixed point theory for nonexpansive and pseudocontractive mappings in Hilbert space. in Swaminathan (1976) 187-196. | Zbl

Rogalski M. (1972) : Surjectivité d'applications multivoques dans les convexes compacts. Bull. Soc. Math. de France, 96, 83-87. | MR | Zbl

Sehgal V.M. (1969) : A fixed point theorem for mappings with a contractive iterate. Proc. Amer. Math. Soc. 23, 631-634. | MR | Zbl

Sehgal V.M. (1977) : A simple proof of a theorem of Ky Fan. Proc. Amer. Math. Soc. 63 (2) ; 368-369. | MR | Zbl

Siegel J. (1977) : A new proof of Caristi's fixed point theorem. Proc. Amer. Math. Soc. 66 (1) 54-56. | MR | Zbl

Smart D.R. (1974) : Fixed point theorems, Cambridge Univ. Press. | MR | Zbl

Swaminathan S. (1976) : Fixed point theory and its applications. Academic Press, New-York. | MR | Zbl

Talman L.A. (1977) : Fixed points of differentiable maps in ordered locally convex spaces. Ph. D. thesis Univ. of Kansas.

Tartar L. (1974) : Inequations variationnelles abstraites. C.R. Acad. Sc. Paris, 278, 1193-1196. | MR | Zbl

Terkelsen F. (1974) : A short proof of Fan's fixed point theorem. Proc. Amer. Math. Soc. 42 (1974) 643-644. | Zbl

Van Der Walt T. (1967) : Fixed and almost fixed points. Math. Center Tracts, Amsterdam.

Vidossich G. : How to get zeros of nonlinear operators using the theory of ordinary differential equations. Actas Sem. Anal. Func. Sao Paulo (to appear).

Weinstein A. (1968) : A fixed point theorem for positively curved manifolds. J. Math. Mech. 18 (2), 149-153. | MR | Zbl

Weinstein A. (1977) : Lectures an symplectic manifolds. CBMS Regional Conference Univ. North Carolina (lecture n°7). Amer. Math. Soc. Providence, R.I. | MR | Zbl

Wong C.S. (1976) : On a fixed point theorem of contractive type. Proc. Amer. Math. Soc. 57 (2), 283-284. | MR | Zbl

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