Drop theorems and lipschitzianness tests via maximality procedures

M. Altman, Contractor directions, directional contractors and directional contractions for solving equations,Pacific J. Math.,62 (1976), 1–48. J. P. Aubin andJ. Siegel, Fixed points and stationary points of dissipative multivalued maps,Proc. Amer. Math. Soc.,78 (1980), 391–398. E. Bishop andR. R. Phelps, The support functional of a convex set,Proc. Symp. Pure Math.,VII (Convexity), pp. 27–36, Amer. Math. Soc., 1963. N. Bourbaki, Sur le théorème de Zorn,Archiv der Math.,2 (1949/1950), 434–437. H. Brezis andF. E. Browder, A general principle on ordered sets in nonlinear functional analysis,Advances in Math.,21 (1976), 355–364. A. Brøndsted, On a lemma of Bishop and Phelps,Pacific J. Math. 55 (1974), 335–341. A. Brøndsted, Common fixed points and partial orders,Proc. Amer. Math. Soc.,77 (1979), 365–368. F. E. Browder, Normal solvability for nonlinear mappings in Banach spaces,Bull. Amer. Math. Soc.,77 (1971), 73–77. F. E. Browder, Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds,J. Functional Anal.,8 (1971), 250–274. F. E. Browder, On a theorem of Caristi and Kirk,Fixed Point Theory and its Applications, pp. 23–27, Academic Press, 1976. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions,Trans. Amer. Math. Soc.,215 (1976), 241–251. J. Daneš, A geometric theorem useful in nonlinear functional analysis,Boll. Un. Mat. Ital.,6 (1972), 369–375. D. Downing andW. A. Kirk, A generalization of Caristi's theorem with applications to nonlinear mapping theory,Pacific J. Math.,69 (1977), 339–346. I. Ekeland, On the variational principle,J. Math. Anal. Appl.,47 (1974), 324–353. I. Ekeland, Nonconvex minimalization problems,Bull. Amer. Math. Soc., (N. S.),1 (1979), 443–474. S. A. Husain andV. M. Sehgal, A remark on a fixed point theorem of Caristi,Math. Japonica,25 (1980), 27–30. S. Kasahara, On fixed points in partially ordered sets and Kirk-Caristi theorem,Math. Sem. Notes Kobe Univ.,3 (1975), 229–232. L. Kelley,General topology, Springer Verlag, 1975. W. A. Kirk, Caristi's fixed point theorem and metric convexity,Colloq. Math.,36 (1976), 81–86. W. A. Kirk andW. O. Ray, A remark on directional contractions,Proc. Amer. Math. Soc.,66 (1977), 279–283. C. Kuratowski,Topologie, vol. I (Warszawa, 1958). J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point,Proc. Amer. Math. Soc.,62 (1977), 344–348. L. Nachbin,Topology and order, Van Nostrand, 1965. J. Siegel, A new proof of Caristi's fixed point theorem,Proc. Amer. Math. Soc.,66 (1977), 54–56. M. Turinici, Nonlinear contractions and applications to Volterra functional equations,An. St. Univ. “Al. I. Cuza” Iaşi,23 (1977), 43–50. M. Turinici, Maximal elements in partially ordered topological spaces and applications,An. St. Univ. “Al. I. Cuza” Iaşi,24 (1978), 259–264. M. Turinici, Maximal elements in a class of order complete metric spaces,Math. Japonica,25 (1980), 511–517. M. Turinici, Local and global lipschitzian mappings on ordered metric spaces,Math. Nachrichten (to appear). C. Ursescu, Sur le contingent dans les espaces de Banach,Proc. Inst. Math. Laşi, pp. 183–184 (Bucureşti, 1976). J. D. Weston, A characterization of metric completeness,Proc. Amer. Math. Soc.,64 (1977), 186–188. C. S. Wong, On a fixed point theorem of contractive type,Proc. Amer. Math. Soc.,57 (1976), 283–284. P. P. Zabreiko andM. A. Krasnoselskii, Solvability of nonlinear opeartor equations (in Russian),Funct. Analiz i Prilož.,5 (1971), 42–44.