Some of My Research Papers and Books

(These are listed in reverse chronological order.)

[2]  Deutsch, Frank.
The role of the strong conical hull intersection property in convex optimization and approximation.
Approximation theory IX, Vol. I. (Nashville, TN, 1998), 105--112, Innov. Appl. Math.,
Vanderbilt Univ. Press, Nashville, TN, 1998.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[3]  Deutsch, Frank; Li, Wu; Ward, Joseph D.
Best approximation from the intersection of a closed convex set and a polyhedron in Hilbert space,
weak Slater conditions, and the strong conical hull intersection property.
SIAM J. Optim. 10 (1999), no. 1, 252--268 (electronic).
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[4]  Deutsch, Frank; Li, W.; Swetits, J.
Fenchel duality and the strong conical hull intersection property.
J. Optim. Theory Appl. 102 (1999), no. 3, 681--695.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[5]  Deutsch, Frank; Yamada, Isao.
Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings.
Numer. Funct. Anal. Optim. 19 (1998), no. 1-2, 33--56.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[6] Deutsch, Frank; Li, Wu; Ward, Joseph D.
A dual approach to constrained interpolation from a convex subset of Hilbert space.
J. Approx. Theory 90 (1997), no. 3, 385--414.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[7] Hundal, Hein; Deutsch, Frank.
Two generalizations of Dykstra's cyclic projections algorithm.
Math.  Programming 77 (1997), no. 3, Ser. A, 335--355.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[8] Deutsch, Frank; Hundal, Hein.
The rate of convergence for the method of alternating projections. II.
J. Math. Anal. Appl. 205 (1997), no. 2, 381--405.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[9] Brosowski, Bruno; Deutsch, Frank.
Rivlin's problem. The heritage of P. L. Chebyshev: a Festschrift in honor of the 70th birthday of T. J. Rivlin.
Ann. Numer. Math. 4 (1997), no. 1-4, 95--109.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[10] Deutsch, Frank; Ubhaya, V. A.; Ward, J. D.; Xu, Yuesheng.
Constrained best approximation in Hilbert space. III. Applications to $n$-convex functions.
Constr. Approx. 12 (1996), no. 3, 361--384.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[11]  Deutsch, Frank; Mabizela, Sizwe.
Best interpolatory approximation in normed linear spaces.
J. Approx. Theory 85 (1996), no. 3, 250--268.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[12]  Deutsch, Frank.
The angle between subspaces of a Hilbert space.
Approximation theory, wavelets and applications (Maratea, 1994), 107--130,
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[13]  Deutsch, Frank.
Interpolation from a convex subset of Hilbert space: a survey of some recent results.
Approximation theory, wavelets and applications (Maratea, 1994), 95--105,
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[14]  Deutsch, Frank; Ubhaya, Vasant A.; Xu, Yuesheng.
Dual cones, constrained $n$-convex $L\sb p$-approximation, and perfect splines.
J. Approx. Theory 80 (1995), no. 2, 180--203.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[15]  Deutsch, Frank; Hundal, Hein.
The rate of convergence of Dykstra's cyclic projections algorithm: the polyhedral case.
Numer. Funct. Anal. Optim. 15 (1994), no. 5-6, 537--565.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[16]  Deutsch, Frank.
The convexity of Chebyshev sets in Hilbert space.
Topics in polynomials of one and several variables and their applications, 143--150,
World Sci. Publishing, River Edge, NJ, 1993.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[17]  Deutsch, Frank; Li, Wu; Mabizela, Sizwe.
Helly extensions and best approximation.
Parametric optimization and related topics, III (Güstrow, 1991), 107--120,
Approx. Optim., 3, Lang, Frankfurt am Main, 1993.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[18]  Deutsch, Frank.
Dykstra's cyclic projections algorithm: the rate of convergence.
Approximation theory, wavelets and applications (Maratea, 1994), 87--94,
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[19]  Deutsch, Frank; Zhong, Jun.
Best comonotone approximation.
Trans. Amer. Math. Soc. 344 (1994), no. 2, 617--627.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[20]  Deutsch, Frank; Singer, Ivan.
On single-valuedness of convex set-valued maps.
Set-Valued Anal. 1 (1993), no. 1, 97--103.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[21]  Deutsch, Frank.
Constrained $N$-convex approximation.
Approximation theory (Memphis, TN, 1991), 275--284,
Lecture Notes in Pure and Appl. Math., 138, Dekker, New York, 1992.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[22]  Chui, Charles K.; Deutsch, Frank; Ward, Joseph D.
Constrained best approximation in Hilbert space. II.
J. Approx. Theory 71 (1992), no. 2, 213--238.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[23]  Deutsch, Frank.
Selections for metric projections.
Approximation theory, spline functions and applications (Maratea, 1991), 123--137,
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 356, Kluwer Acad. Publ., Dordrecht, 1992.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[24]  Deutsch, Frank.
The method of alternating orthogonal projections.
Approximation theory, spline functions and applications (Maratea, 1991), 105--121,
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 356, Kluwer Acad. Publ., Dordrecht, 1992.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[25]  Deutsch, Frank; Li, Wu.
Strong uniqueness, Lipschitz continuity, and continuous selections for metric projections in $L\sb 1$.
J. Approx. Theory 66 (1991), no. 2, 198--224.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[26]  Deutsch, Frank; Li, Wu; Park, Sung Ho.
Tietze extensions and continuous selections for metric projections.
J. Approx. Theory 64 (1991), no. 1, 55--68.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[27]  Deutsch, Frank.
Constrained best approximation.
Approximation theory VI, Vol. I (College Station, TX, 1989), 165--173,
Academic Press, Boston, MA, 1989.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[28]  Chui, Charles K.; Deutsch, Frank; Ward, Joseph D.
Constrained best approximation in Hilbert space.
Constr. Approx. 6 (1990), no. 1, 35--64.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[29]  Deutsch, Frank.
An exposition of recent results on continuous metric selections.
Numerical methods of approximation theory, Vol. 8 (Oberwolfach, 1986), 67--79, Internat.
Schriftenreihe Numer. Math., 81, Birkhäuser, Basel-Boston, MA, 1987.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[30]  Deutsch, Frank; Li, Wu; Park, Sung Ho.
Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces.
J. Approx. Theory 58 (1989), no. 3, 297--314.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[31]  Deutsch, Frank; Indumathi, V.; Schnatz, Klaus.
Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings.
J. Approx. Theory 53 (1988), no. 3, 266--294.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[32]  Deutsch, Frank.
Best approximation in the space of continuous vector-valued functions.
J. Approx. Theory 53 (1988), no. 1, 112--116.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[33]  Deutsch, Frank.
Simultaneous interpolation and norm-preservation.
Delay equations, approximation and application (Mannheim, 1984), 122--132, Internat.
Schriftenreihe Numer. Math., 74, Birkhäuser, Basel-Boston, Mass., 1985.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[34]  Deutsch, Frank.
Rate of convergence of the method of alternating projections.
Parametric optimization and approximation (Oberwolfach, 1983), 96--107, Internat.
Schriftenreihe Numer. Math., 72, Birkhäuser, Basel-Boston, Mass., 1985.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[35]  Deutsch, Frank.
Some open problems concerning metric selections.
Approximation theory and applications (St. John's, Nfld., 1984), 30--34,
Res. Notes in Math., 133, Pitman, Boston, Mass.-London, 1985.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[36] Edited by B. Brosowski and Frank Deutsch.
Parametric optimization and approximation.   Proceedings of the international symposium
held at the Mathematical Research Institute Oberwolfach, Oberwolfach, October 16--22, 1983.
Internationale Schriftenreihe zur Numerischen Mathematik [International Series of Numerical Mathematics],
72. Birkhäuser Verlag, Basel-Boston, Mass., 1985. 263 pp. ISBN: 3-7643-1671-3 41-06
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[37]  Deutsch, Frank.
Applications of von Neumann's alternating projections algorithm.
Mathematical methods in operations research (Sofia, 1983), 44--51, Bulgar. Acad. Sci., Sofia, 1983.
Abstract:    *.dvi file;        *.ps file;     *.pdf file.

[38]  Deutsch, Frank.
von Neumann's alternating method: the rate of convergence.
Approximation theory, IV (College Station, Tex., 1983), 427--434, Academic Press, New York-London, 1983.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[39]  Deutsch, Frank.
When does the metric projection admit a linear selection?
Second Edmonton conference on approximation theory (Edmonton, Alta., 1982),
135--141, CMS Conf. Proc., 3, Amer. Math. Soc., Providence, R.I., 1983.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[40]  Deutsch, Frank.
A survey of metric selections.
Fixed points and nonexpansive mappings (Cincinnati, Ohio, 1982), 49--71,
Contemp. Math., 18, Amer. Math. Soc., Providence, R.I., 1983.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[41]  Deutsch, Frank; Mach, Jaroslav; Saatkamp, Klaus.
Approximation by finite rank operators.
J. Approx. Theory 33 (1981), no. 3, 199--213.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[42]  Deutsch, Frank.
Which closed convex subsets of an inner product space are Chebyshev?
Multivariate approximation theory, II (Oberwolfach, 1982), 125--129, Internat.
Ser. Numer. Math., 61, Birkhäuser, Basel-Boston, Mass., 1982.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[43]  Deutsch, Frank; Nürnberger, Günther.
Weakly interpolating subspaces.
Numer. Funct. Anal. Optim. 5 (1982/83), no. 3, 267--288.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[44]  Deutsch, Frank; Kenderov, Petar.
Continuous selections and approximate selection for set-valued mappings and applications to metric projections.
SIAM J. Math. Anal. 14 (1983), no. 1, 185--194.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[45]  Deutsch, Frank.
Representers of linear functionals, norm-attaining functionals, and best approximation
by cones and linear varieties in inner product spaces.
J. Approx. Theory 36 (1982), no. 3, 226--236.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[46]  Deutsch, Frank.
Linear selections for the metric projection.
J. Funct. Anal. 49 (1982), no. 3, 269--292.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[47]  Deutsch, Frank; Lambert, Joseph M.
On continuity of metric projections.
J. Approx. Theory 29 (1980), no. 2, 116--131.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[48]  Deutsch, Frank; Lapidot, Eitan.
Convergence from approximating subspaces.
J. Approx. Theory 32 (1981), no. 4, 281--291.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[49]  Deutsch, Frank; Kenderov, Petar.
When does the metric projection admit a continuous selection?
Approximation theory, III (Proc. Conf., Univ. Texas, Austin, Tex., 1980), pp. 327--333,
Academic Press, New York-London, 1980.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[50]  Brosowski, Bruno; Deutsch, Frank; Nürnberger, Günther.
Parametric approximation.
J. Approx. Theory 29 (1980), no. 4, 261--277.
Abstract:    *.dvi file;        *.ps file;     *.pdf file.

[51]  Deutsch, Frank; Nürnberger, Günther; Singer, Ivan.
Weak Chebyshev subspaces and alternation.
Pacific J. Math. 89 (1980), no. 1, 9--31.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[52]  Deutsch, Frank.
Existence of best approximations.
J. Approx. Theory 28 (1980), no. 2, 132--154.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[53]  Brosowski, Bruno; Deutsch, Frank.
An elementary proof of the Stone-Weierstrass theorem.
Proc. Amer. Math. Soc. 81 (1981), no. 1, 89--92.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[54]  Amir, Dan; Deutsch, Frank.
Approximation by certain subspaces in the Banach space of continuous vector-valued functions.
J. Approx. Theory 27 (1979), no. 3, 254--270.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[55]  Deutsch, Frank.
A general existence theorem for best approximations.
Approximation in Theorie und Praxis (Proc. Sympos., Siegen, 1979), pp. 71--83,
Bibliographisches Inst., Mannheim, 1979.
Abstract:    *.dvi file;        *.ps file;     *.pdf file.

[56]  Deutsch, Frank.
The alternating method of von Neumann.
Multivariate approximation theory (Proc. Conf., Math. Res. Inst., Oberwolfach, 1979),
pp. 83--96, Internat. Ser. Numer. Math., 51, Birkhäuser, Basel-Boston, Mass., 1979.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[57]  Amir, Dan; Deutsch, Frank.
Another approximation theoretic characterization of inner product spaces.
Proc. Amer. Math. Soc. 71 (1978), no. 1, 99--102.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[58]  Brosowski, B.; Deutsch, Frank; Lambert, J.; Morris, P. D.
Some suns in $L\sb{1}$.
J. Approximation Theory 16 (1976), no. 4, 310--314.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[59]  Deutsch, Frank.
On some geometric properties of the unit sphere.
Linear operators and approximation (Proc. Conf., Math. Res. Inst., Oberwolfach, 1971),
pp. 186--195. Internat. Ser. Numer. Math., Vol. 20, Birkhäuser, Basel, 1972.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[60]  Deutsch, Frank; McCabe, John H.; Phillips, George M.
Some algorithms for computing best approximations from convex cones.
SIAM J. Numer. Anal. 12 (1975), 390--403.
Abstract:     *.dvi file;        *.ps file;     *.pdf file.

[61]  Brosowski, B.; Deutsch, Frank; Lambert, J.; Morris, P. D.
Chebychev sets which are not suns.
Math. Ann. 212 (1974/75), 89--101.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[62]  Deutsch, Frank.
New and unsolved problems.
Linear operators and approximation (Proc. Conf., Math. Res. Inst., Oberwolfach, 1971),
pp. 493--503. Internat. Ser. Numer. Math., Vol. 20, Birkhäuser, Basel, 1972.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[63]  Amir, Dan; Deutsch, Frank.
Suns, moons, and quasi-polyhedra.  Collection of articles dedicated to J. L. Walsh
on his 75th birthday, VI (Proc. Internat. Conf. Approximation Theory,
Related Topics and their Appl.,  Univ. Maryland, College Park, Md., 1970).
J. Approximation Theory 6 (1972), 176--201.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[64]  Brosowski, Bruno; Deutsch, Frank.
On some geometric properties of suns.
J. Approximation Theory 10 (1974), 245--267.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[65]  Brosowski, Bruno; Deutsch, Frank.
Radial continuity of set-valued metric projections.
J. Approximation Theory 11 (1974), 236--253.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[66]  Deutsch, Frank.
Cardinality of extreme points of the unit sphere with applications to
nonexistence theorems in approximation theory.
Approximation theory (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1973),
pp. 319--323. Academic Press, New York, 1973.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[67]  Biggs, J. H.; Deutsch, Frank; Huff, R. E.; Morris, P. D.; Olson, J. E.
Interpolating subspaces in $l\sb{1}$-spaces.
J. Approximation Theory 7 (1973), 293--301.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[68]  Deutsch, Frank; Lindahl, Robert J.
Minimal extremal subsets of the unit sphere.
Math. Ann. 197 (1972), 251--278.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[69]  Deutsch, Frank; Pollul, Walter; Singer, Ivan.
On set-valued metric projections, Hahn-Banach extension maps, and spherical image maps.
Duke Math. J. 40 (1973), 355--370.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[70]  Brosowski, Bruno; Deutsch, Frank.
Some new continuity concepts for metric projections.
Bull. Amer. Math. Soc. 78 (1972), 974--978.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[71]  Ault, D. A.; Deutsch, Frank; Morris, P. D.; Olson, J. E.
Interpolating subspaces in approximation theory.
J. Approximation Theory 3 (1970), 164--182.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[72]  Deutsch, Frank; Morris, P. D.
Simultaneous approximation and interpolation with preservation of norm.
1970.  Approximation Theory
(Proc. Sympos., Lancaster, 1969) pp. 309--313, Academic Press, London.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[73]  Ault, D. A.; Deutsch, Frank; Morris, P. D.; Olson, J. E.
Interpolating subspaces in approximation theory.
1970.Approximation Theory (Proc. Sympos., Lancaster, 1969) pp. 291--307,
Academic Press, London.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[74]  Deutsch, Frank; Morris, Peter D.; Singer, Ivan.
On a problem of T. J. Rivlin in approximation theory.
J. Approximation Theory 2  (1969), 342--354.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[75]  Deutsch, Frank; Morris, Peter D.
On simultaneous approximation and interpolation which preserves the norm.
J. Approximation Theory 2  (1969), 355--373.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[76]  Deutsch, Frank; Morris, Peter D.
On simultaneous approximation and interpolation which preserves the norm.
Bull. Amer. Math. Soc. 75 (1969), 812--814.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[77]  Deutsch, Frank.
On uniform approximation with interpolatory constraints.
J. Math. Anal. Appl. 24(1968), 62--79.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.

[78]  Deutsch, Frank; Maserick, P. H.
Applications of the Hahn-Banach theorem in approximation theory.
SIAM Rev. 9  (1967), 516--530.
Abstract:    *.dvi file;        *.ps file;      *.pdf file.

[79]  Deutsch, Frank.
Simultaneous interpolation and approximation in topological linear spaces.
SIAM J. Appl. Math. 14 (1966), 1180--1190.
Abstract:     *.dvi file;        *.ps file;      *.pdf file.