Posts by Costica Mustata

[1] D. Andrica, C. Mustata, An abstract Korovkin type theorem and applications, Studia Univ. Babes-Bolyai, Ser. Math. 34 (1989), 41-44.
[2] R. F. Arens, J. Eells Jr., On embedding uniform and topological spaces, Pacific J. Math. 6 (1956), 397-405.
[3] Zvi Artstein, Extensions of Lipschitz selections and an application to differential inclusions, Nonlinear Anal. 16(1991), 701-704.
[4] G. Aronsson, Extension of Lipschitz functions satisfying a Lipschitz condition, Arkiv Math. 6 (1976), 551-561.
[5] N. Aronszajn, P. Panichpakdi, Extension of uniformly continuous and hyperconvex metric spaces, Pacific J. Math 6 (1956), 405-439.
[6] S. Banach, Wstep do teorii funcji rzeczwistych(Polish),[Introduction to the theory of real functions], Warszawa/Wroclaw 1951.
[7] I. Beg, M. Iqbal, Extension of linear 2-operators, Math. Montesnigri 2 (1993), 1-10.
[8] C. Bessaga, A. Pelczynski, Selected Topics in Infinite Dimensional Topology, PWN Warszawa, 1975.
[9] J. M. Borwein, M. Fabian, Characterizations of Banach spaces via convex and other locally Lipschitz functions, Acta Math. Vietnam. 22 (1997), 53-69.
[10] W. W. Breckner, Holder continuity of certain generalized convex functions, Optimization 28 (1994), 201-209.
[11] A. Bressan, A. Cortesi, Lipschitz extensions of convex-valued maps, Atti. Acad. Naz. Lincei, Rendinconti Classe Sci. Fis. Mat. Natur. (8) 80 (1986), 530-532.
[12] H. Brezis, Prolongement d’applications lipschitziennes et des semi-groupes de contractions, Seminaire Choquet: Initiation a l’analyse, 9 e anne, no. 19 (1969/70).
[13] B. M. Brown, D. Elliot, D. F. Paget, Lipschitz constant for the Bernstein polynomials of Lipschitz continuous functions, J. Approx. Theory 49 (1982), 196-199.
[14] T. Caputti, A note on the extension of Lipschitz functions, Rev. Un. Mat. Argentina 31 (1984), 122-129.
[15] E. W. Cheney, D. E. Wulbert, The existence and unicity of best approximation, Math. Scand. 24 (1969), 113-140, Corrigendum: Math. Scand. 27 (1970), 245.
[16] S. Cobzas, On the Lipschitz properties of continuous convex functions, Mathematica 21 (1979), 123-125.
[17] S. Cobzas, Lipschitz properties of convex functions, Seminar on Mathematical Analysis, Babes-Bolyai University, Faculty of Mathematics, Research Seminaries, Preprint No. 7, Cluj-Npoca 1985, 77-84.
[18] S. Cobzas, Extreme points in Banach spaces of Lipschitz functions, Mathematica 31 (1989), 25-33.
[19] S. Cobzas, I. Muntean, Continuous and locally Lipschitz convex functions, Mathematica 18 (1976), 41-51.
[20] S. Cobzas, C. Mustata, Norm preserving extension of convex Lipschitz functions, J. Approx. Theory 24 (1978), 555-564.
[21] S. Cobzas, C. Mustata, Selections associated to the metric projection, Rev. Anal. Numer. Theor. Approx. 24 (1995), 45-52.
[22] S. Cobzas, C. Mustata, Extension of bilinear operators and best approximation in 2-normed spaces, Rev. Anal. Numer. Theor. Approx. 25 (1996), 63-75
[23] S. Cobzas, C. Mustata, Extension of bilinear operators and best approximation in 2-normed spaces, Proc. 6th Workshop of the DGOR-Working Group-Multicriteria and Decision Theory, Halle 1996, A. Gopfert, J. Seelander, Chr. Tammer, Eds. Deutsche Hochschulschriften vol. 2398, Hansel-Hohenhausen Frankfurt 1997, pp. 19-29.
[24] S. Cobzas, C. Mustata, Extension of bilinear functionals and best approximation in 2-normed spaces, Studia Univ. Babes-Bolyai, Ser. Math. (in print).
[25] J. Czipser, L. Geher, Extension of functions satisfying a Lipschitz condition, Acta Math. Sci. Acad. Sci. Hungar.6 (1955), 213-220.
[26] L. Danzer, B. Grunbaum, V. Klee, Helly’s theorem and its relatives, in Convexity, Proc. Symp. Pure Appl. Math. vol. 7, Amer. Math. Soc, Providence RI 1963, pp. 101-180.
[27] V. F. Demyanov, Point derivations for Lipschitz functions and Clarke’s generalized derivative, Appl. Math. (Warsaw),24 (1997), 465-474.
[28] F. Deutsch, Linear selections for the metric projection, J. Func. Anal. 49 (1982), 269-292.
[29] F. Deutsch, A survey of the metric selections, Contemporary Mathematics vol. 18, Amer. Math. Soc., ProvidenceRI 1983, pp. 49-71.
[30] F. Deutsch, Wu Li, Sung-Ho Park, Tietze extensions and continuous selections for the metric projection, J. Approx.Theory 64 (1991), 56-68.
[31] F. Deutsch, Wu Li, Sizwe Mabizela, Helly extensions and best approximation, in Parametric Optimization and Related Topics, Approx. Optim., 3, Lang, Frankfurt am Main, 1993, pp. 107-120.
[32] M. Dorfner, The extension of Lipschitz continuous operators, Istit. Lombardo Accad. Sci. Lett. Rend. A 129 (1995),47-59.
[33] J. Dugundji, An extension of Tietze’s theorem, Pacific J. Math. 1 (1951), 353-367.
[34] R. Engelking, General Topology, PWN Warszawa 1977.
[35] H. Fakhouri, Selections lineaires associees au theoreme de Hahn-Banach, J. Func. Anal. 11 (1972), 436-452.
[36] J. D. Farmer, Extreme points of the unit ball of the space of Lipschitz functions, Proc. Amer. Math. Soc. 121 (1994), 807-813.
[37] D. de Figueiredo, L. Karlovitz, On the projection into convex sets and the extension of contractions, in Proc.Conf. on Projections and Related Topics, Clemson Unic. 1967.
[38] D. de Figueiredo, L. Karlovitz, On the extension of contractions on normed spaces, in Proc. Symp. Pure Math. vol.18, part.1, Amer.Math.Soc., RI 1970.
[39] T.M. Flett, Extension of Lipschitz functions, J. London Math. Soc. 7 (1974), 604-608.
[40] C. Franchetti, Lipschitz maps on the unit ball of normed spaces, Confer. Sem. Mat. Univ. Bari vol. 202 (1985).
[41] C. Franchetti, Lipschitz maps and the geometry of the unit ball in normed spaces, Arch. Math. 46 (1986), 76-84.
[42] N. Furukama, Convexity and local Lipschitz continuity of fuzzy-valued mappings, Fuzzy Sets and Systems, 93 (1998), 113-119.
[43] S. Gahler, Linear 2-normierte Raume, Math. Nachr. 28 (1965), 1-45.
[44] B. Grunbaum, A generalization of theorems of Kirszbraun and Minty, Proc. Amer. Math. Soc. 13 (1962), 812-814.
[45] B. Grunbaum, On a theorem of Kirszbraun, Bull. Res. Council Israel 7F (1958), 129-132.
[46] B. Grunbaum, E. Zarantonello, On the extension of unniformly continuous mappings, Michigan Math. J. 15 (1968), 65-78.
[47] P. Harmand, D. Werner, W. Werner, M-ideals in Banach Spaces and Banach Algebras, Lect. Notes Math. vol. 1547 Springer-Verlag, Berlin 1993.
[48] M. Hasumi, The extension property of complex Banach spaces, Tohoku Math. J. 10 (1958), 135-142.
[49] T. Hayden, J. Wells, On the extension of Lipschitz-Holder maps of order β, J. Math. Anal. Appl. 33 (1971), 627-640.
[50] J.-B. Hiriart-Urruty, Extension of Lipschitz functions, J. Math. Anal. Appl. 77 (1980), 539-554.
[51] J.-B. Hiriart-Urruty, Extension of Lipschitz integrands and minimization of nonconvex integral functionals . Applications to the optimal resource problem in discrete time, Prob. Math. Stat. 3 (1982), 19-36.
[52] J.-B. Hiriart-Urruty, Enveloppe k-lipschitzienne d’une fonction, Rev. Math. Speciales 106 (1995-1996), 785-793.
[53] R. B. Holmes, A Course on Optimization and Best Approximation, Lect. Notes Math. vol. 257, Springer-Verlag, Berlin 1972.
[54] R. B. Holmes, Geometric Functional Analysis and its Applications, Springer-Verlag, Berlin 1975.
[55] R. B. Holmes, B. Scranton, J.D. Ward, Approximation from the space of compact operators and other M-ideals, Duke Math. J. 42 (1975(, 259-269.
[56] R. Jensen, Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient, Arch. Rat. Mech. Anal. 123 (1993), 51-74.
[57] J. A. Johnson, Banach spaces of Lipschitz functions and vector-valued Lipschitz functions, Trans. Amer. Math. Soc. 148 (1970), 147-171.
[58] J. A. Johnson, Lipschitz spaces, Pacific J. Math. 51 (1974), 177-186.
[59] J. A. Johnson, A note on Banach spaces of Lipschitz functions, Pacific J. Math. 58 (1975), 475-482.
[60] W. B. Johnson, J. Lindenstrauss and G. Schechtman, Extensions of Lipschitz maps into Banach spaces, Israel J. Math. 54 (1986), 129-138.
[61] V. M. Kadets, Lipschitz mappings on metric spaces, Matematika, Izvestija VUZOV (1985) no.1, 30-34, (in Russian).
[62] H. Kamowitz, S. Scheinberg, Some properties of endomorphisms of Lipschitz algebras, Studia Math. 96 (1990), 61-67.
[63] J. L. Kelley, Banach spaces with the extension property, Trans. Amer. Math. Soc. 72 (1952), 323-326.
[64] M. Kirszbraun,  Uber die zusammenziehenden und Lipschitzschen Transformationen, Fund. Math. 22 (1934), 77-108.
[65] S.V. Konyagin, On the level sets of Lipschitz functions, Tatra Mount. Math. Publ. 2 (1993), 51-59.
[66] A. Langenbach, Uber lokale eigenschaften von Lipschitz-Abbildungen, Math. Nachr. 194 (1998), 127-137.
[67] K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math. 21 (1961), 55-66.
[68] R. Levi, M. D. Rice, The approximation of uniformly continuous mappings by Lipschitz and Holder mappings, in General Topology and its Relations to Modern Analysis and Algebra V, Prague 1981, 455-461.
[69] J. Lindensstrauss, Non-linear projections in Banach spaces, Michigan Math. J. 11 (1964), 263-287.
[70] J. Lindenstrauss, Extension of compact operators, Memoirs Amer. Math. Soc. vol. 48 (1964).
[71] S. Mabizela, On bounded 2-linear functionals, Math. Japonica 35 (1990), 51-55.
[72] S. Mabizela, The relationship between Lipschitz extensions, best approximations, and continuous selections, Quaestiones Math. 14 (1991), 261-268.
[73] L. Marco, J. A. Murillo, Locally Lipschitz and convex functions, Mathematica 38 (1996), 121-131.
[74] J. Matousek, Extension of Lipschitz mappings on metric trees, Comment. Math. Univ. Carol. 31 (1990), 99-101.
[75] J. Matousek, Note on bi-Lipschitz embeddings into normed spaces, Comment. Math. Univ. Carol. 33 (1992), 51-55.
[76] J. Matousek, On Lipschitz mappings onto square, in: The Mathematics of P. Erdos, vol. II, Springer-Verlag, Berlin 1997
[77] W. E. Mayer-Wolf, Isometries between Banach spaces of Lipschitz functions, Israel J. Math. 38 (1981), 58-74.
[78] J. A. McShane, Extension of range of functions, Bull. Amer. Math. Soc. 40 (1934), 837-842.
[79] E. Mickle, On the extension of a transformation, Bull. Amer. Math. Soc. 55 (1949), 160-164.
[80] V. A. Milman, Extension of functions preserving the modulus of continuity, Mat. Zametki 61 (1997), 236-245 (in Russian).
[81] V. A. Milman, Lipschitz extensions of linearly bounded functions, Mat. Sbornik 189 (1998), 67-92 (in Russian).
[82] G. J. Minty, On the extension of Lipschitz-Holder continuous, and monotone functions, Bull. Amer. Math. Soc. 76 (1970), 334-339.
[83] C. Mustata, On some Chebyshevian subspaces of the normed space of Lipschitz functions, Rev. Anal. Numer. Teor. Aprox. 2 (1973), 81-87 (in Romanian).
[84] C. Mustata, On the unicity of the extension of continuous p-seminorms, Rev. Anal. Numer. Teor. Aprox. Vol.2 Fasc.2 (1973), 173-177 (Romanian).
[85] C. Mustata, M-ideals in metric spaces, Babes-Bolyai University Reserch Seminaries, Preprint No. 7 (1988), 65-74.
[86] C. Mustata, On the best approximation in metric spaces, Rev. Anal. Numer. Theor. Approx. 4 (1975), 45-50.
[87] C. Mustata, Norm preserving extension of starshaped Lipschitz functions, Rev. Anal. Numer. Theor. Approx. 19 (1977), 183-187.
[88] C. Mustata, Best approximation and unique extension of Lipschitz functions, J. Approx. Theory 19 (1977), 222-230.
[89] C. Mustata, A characterization of Chebyshevian subspaces of Y ?-type, Rev. Anal. Numer. Theor. Approx. 6 (1977), 51-56.
[90] C. Mustata, The extension of starshaped Lipschitz functions, Rev. Anal. Numer. Theor. Approx. 9 (1980), 93-99.
[91] C.Mustata, On the extension of Holder functions, Babes-Bolyai University Reserch Seminaries, Seminar on Functional Analysis and Numerical Methods, Preprint No. 7 (1985), 71-86.
[92] C. Mustata, On the unicity of the extension of odd Lipschitz functions, Babes-Bolyai University, Seminar on Optimization Theory, Report No. 8 (1987), 75-80.
[93] C. Mustata, Extension of Holder functions and some related problems of best approximation, Babes-Bolyai University, Faculty of Mathematics Research Seminaries, Preprint no. 7 (1991), 71-86.
[94] C. Mustata, Selections associated to McShane’s extension theorem for Lipschitz functions, Rev. Anal. Numer. Theor. Approx. 21 (1992, 135-145.
[95] C. Mustata, On the metric projection and quotient mapping, Rev. Anal. Numer. Theor. Approx. 24 (1995, 191-199.
[96] L. Nachbin, On the Hahn-Banach theorem, Anais Acad. Brasil. Ci. 21 (1949), 151-154.
[97] L. Nachbin, A theorem of Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28-46.
[98] L. Nachbin, Some problems in extending and lifting continuous linear transformations, in Proc. International Symp. Linear Spaces, Jerusalem 1960, Jerusalem Acad. Press and Pergamon Press, Jerusalem and London 1961, pp. 340- 350.
[99] Nguyen Van Khue, Nguyen To Xhu, Extending locally Lipschitz maps with values in an infinite dimensional nuclear Frechet space, Bull. Acad. Polon. Sci. Ser. Math. 29 (1981), 609-616.
[100] Nguyen Van Khue, Nguyen To Xhu, Lipschitz extensions and Lipschitz retractions in metric spaces, Colloq. Math. 45 (1981), 245-250.
[101] E. Oja, On the uniqueness of the norm preserving extension of the linear functional in the Hahn-Banach theorem, Proc. Acad. Sci. Estonian SSR 33 (1984), 424-433.
[102] D. O’Keee, The tangent stars of a set, and extensions of functions in Lipschitz classes, Proc. Roy. Irish Acad. Sect. A, 97 (1997), 5-13.
[103] G. Pantelidis, Approximationstheorie fur metrische lineare Raume, Math. Ann. 184 (1969), 30-48.
[104] Sung-Ho Park, Quotient mapping, Helly-extensions, Hahn-Banach extension, Tietze extension, Lipschitz extension and best approximation, J. Korean Math. Soc. 29 (1992), 239-250.
[105] J. Partanen, J. Vaisala, Extension of bi-Lipschitz maps on compact polyhedra, Math. Scand. 72 (1993), 235-264.
[106] R. R. Phelps, Uniqueness of Hahn-Banach extension and unique best approximation, Trans. Amer. Math. Soc. 95 (1960), 238-255.
[107] B. H. Pourciau, Analysis and optimization of Lipschitz continuous mappings, J. Optim. Theory Appl. 22 (1977), 311-351.
[108] B. H. Pourciau, Hadamard’s theorem for locally Lipschitzian mappings, J. Math. Anal. Appl. 85 (1982), 279-285.
[109] B. H. Pourciau, Univalence and degree for Lipschitz continuous maps, Arch. Rat. Mech. Anal. 81 (1983), 289-299.
[110] B. H. Pourciau, Global properties of proper Lipschitzian maps, SIAM J. Math. Anal. 14 (1983), 796-799.
[111] K. Przeslawski, Lipschitz retracts, selections, and extensions, Michigan Math. J. 42 (1995), 555-571.
[112] K. Przeslawski, Lipschitz continuous selections. I. Linear selections, J. Convex Anal. 5 (1998), 249-267.
[113] S. Rolewicz, Metric Linear Spaces, PWN Warszawa 1972.
[114] S. Rolewicz, On Lipschitz projection{a geometrical approach, Ann. Univ. Maria Sklodowska-Curie 38 (1984), 135-138.
[115] S. Rolewicz, On extremal points of the unit ball in Banach spaces of Lipschitz continuous functions, J. Austral. Math. Soc. Ser. A 41 (1986), 95-98.
[116] S. Rolewicz, Generalized Asplund inequalities on Lipschitz functions, Arch. Math. 61 (1993), 484-488.
[117] S. Rolewicz, On optimal observability of Lipschitz systems, in Selected Topics in Oper. Res. and Math. Economics, Lect. Notes in Economics and Math. Systems vol 226, pp. 151-158, Springer-Verlag, Berlin 1993.
[118] S. Rolewicz, On an extension of Mazur’s theorem on Lipschitz functions, Arch. Math. 63 (1994), 535-540.
[119] S. Rolewicz, Duality and convex analysis in the absence of linear structure, Math. Japon. 44 (1996), 165-182.
[120] A. K. Roy, Extreme points and linear isometries of the Banach spaces of Lipschitz functions, Canad. J. Math. 20 (1968), 1150-1164.
[121] W. Ruess, Ein Dualkegel fur p-konvexe topologische lineare Raume, Geselschaft fur Mathematik und Datenverarbeitung Nr. 60 (1973).
[122] W. Rzymowski, Convex extension preserving Lipschitz constants, J. Math. Anal. Appl. 212 (1997), 30-37.
[123] I. Sawashima, Methods of duals in nonlinear analysis-Lipschitz duals of Banach spaces and some applications, Lect. Notes Econ. Math. Syst. vol. 419, Springer-Verlag 1975, pp.247-249.
[124] K. Schnatz, Approximationstheorie in metrischen Vektorraumen, Dissertation. Frankfurt am Main, 1985.
[125] K. Schnatz, Nonlinear duality and best approximation in metric linear spaces, J. Approx.Theory 49 (1987), 201-218.
[126] I. Schoenberg, On a theorem of Kirszbraun and Valentine, Amer. Math. Monthly 44 (1953), 620-622.
[127] S. O. Schonbeck, Extension of nonlinear contractions, Bull. Amer. Math. Soc. 72 (1966), 99-101.
[128] S. O. Schonbeck, On the extension of Lipschitz maps, Ark Math. 7 (1967-1969), 201-209.
[129] D. R. Sherbert, Banach algebras of Lipschitz functions, Pacific J. Math. 13 (1963), 1387-1399.
[130] D. R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc., 111 (1964), 240-272.
[131] D. R. Shubert, A sequential method seeking the global maximum of function, SIAM J. Numer. Anal., 9 (1972), 379-388.
[132] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Ed. Academiei and Springer Verlag, Bucharest-Berlin 1970.
[133] I. Singer, Extension with larger norm and separation with double support in normed linear spaces, Bull. Austral. Math. Soc. 21 (1980), 93-106.
[134] R. Smarzewski, Extreme points of unit balls in Lipschitz functions spaces, Proc. Amer. Math. Soc. 125 (1997), 1391-1397.
[135] Ch. Stegall, Spaces of Lipschitz functions on Banach spaces, In Funct. Anal. (Essen 1991), 265-278. M. Dekker, New York 1994.
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[137] S. Ustunel, Extension of Lipschitz functions on Wiener space, in Stochastic Anal. and Appl. (Powys 1995), 465-470, World Sci. 1996
[138] J. Vaisala, Bi-Lipschitz and quasi-symmetric extension properties, Ann. Acad. Sci. Fenn. Ser. I Math. 11 (1986), 239-274.
[139] J. Vaisala, Banach spaces and bi-Lipschitz maps, Studia Math. 103 (1992), 291-294.
[140] F. Valentine, A Lipschitz condition preserving extension of a vector function, Amer. J. Math. 67 (1945), 83-93.
[141] F. Valentine, On the extension of a vector function so as to preserve a Lipschitz condition, Bull. Amer. Math. Soc. 49 (1943), 100-108.
[142] F. Valentine, Contractions in non-euclidean spaces, Bull. Amer. Math. Soc. 50 (1944), 710-713.
[143] L. Waelbroeck, Closed ideals of Lipschitz functions, in Function Algebras (F. T. Birtel ed.), pp. 322-325, Scott Foresman 1966,
[144] N. Weaver, Lattices of Lipschitz functions, Pacific J. Math. 164 (1994), 179-193.
[145] N. Weaver, Isometries of noncompact Lipschitz spaces, Canad. Math. Bull. 38 (1995), 242-249.
[146] N. Weaver, Subalgebras of little Lipschitz algebras, Pacific J. Math. 173 (1996), 283-293.
[147] N. Weaver, Lipschitz algebras and derivations of von Neumann algebras, J. Func. Anal. 139 (1996), 261-300.
[148] J. H. Wells, L. R. Williams, Embeddings and Extensions in Analysis, Springer-Verlag, Berlin 1975.
[149] L. Williams, J. Wells, T. Hayden, On the extension of Lipschitz-Holder maps on Lp spaces, Studia Math. 39 (1971), 29-38.