Publications

(A)

Books

(1)

Fundamentals of Approximation Theory (with H.N. Mhaskar), Narosa
Publishing House, New Delhi, August, 2000.

(2)

Methods of Functional Analysis in Approximation Theory (coedited
with C.A. Micchelli and B.V. Limaye), ISNM
76, Birkhauser Verlag,
Basel, 1986.

(B)

Articles

(I)

Items reviewed in Mathematical Reviews (MR)

1.

Laurent, PierreJean and Pai, Devidas, On simultaneous approximation, Numer.
Funct. Anal. Optim. 19 (1998), no.910. 10451064. MR 99h:41027.

2.

Pai, D.V. and Deshpande, B.M., On continuity of the prox map and the restricted
center map, Approximation theory VIII, Vol. I (College Station, TXD,
1995), 451458, Ser. Approx. Decompos., 6, World Sci. Publishing,
River Edge, NJ, 1995. MR 98h:49028.

3.

Sengadir, T., Pai, D.V. and Pani, A.K., A LeraySchauder type theorem and
applications to boundary value problems for neutral equations, Nonlinear
Anal. 28 (1997), no.4, 701719. MR 98b:47072.

4.

Pai, D.V. and Deshpande, B.M., Topologies related to the prox map and the
restricted center map, Numer. funct. Anal. Optim. 16 (1995),
no.910, 12111231. MR 96k:41048.

5.

Pai, D.V. and Nowroji, P.T., Restricted pcenters and weighted restricted
centers, Advances in computational mathematics (New Delhi, 1993),
279302, Ser. Approx. Decompos., 4, World Sci. Publishing, River Edge,
NJ 1 1994. MR 96g:41020.

6.

Shunmugaraj, P. and Pai, D.V., On stability of approximate solutions of
minimization problems, Numer. Funct. Anal. Optim. 12 (1991),
no.56, 593610 (1992). MR 93e:49042.

7.

Pai, D.V. and Nowroji, P.T., On restricted centers of sets,
J. Approx.
Theory 66 (1991), no.2, 170189. MR 92i:46035.

8.

Beer, Gerald and Pai, Devidas, The Prox map, J. Math. Anal. Appl. 156
(1991), no.2, 428443, MR 92d:46035.

9.

Shunmugaraj, P. and Pai, D.V., On approximate minima of a convex functional
and lower semicontinuity of metric projections, J. Approx. Theory64
(1991), no.1, 2537. MR 91m:49011.

10.

Beer, Gerald and Pai, Devidas, On convergence of convex sets and relative
Chebyshev centers, J. Approx. Theory62 (1990), no.2, 147169.
MR 91j:41044.

11.

Beer, Gerald and Pai, Devidas, Proximal maps, prox maps and coincidence
points, Numer. Funct. Anal. Optim. 11 (1990), no.56, 429448.
MR 91i:41027.

12.

Pai, D.V., Optimal recovery: a selective survey, Optimization, design
of experiments and graph theory (Bombay, 1986), 406416, Indian
Inst. Tech., Bombay, 1988. MR 90i:90122.

13.

Pai, D.V., Abstract minimization problems, restricted centers and fixed
points, Methods of functional analysis in approximation theory (Bombay,
1985), 231244, Internat. Schriftenreihe Numer. Math., 76, Birkhauser,
BaselBoston, MA, 1986. MR 89b:90228.

14.

Pai, D.V. and Naimpally, S.A., Fixed points of multimappings related to
minimization problems, Nonlinear analysis and applications (Arlington,
Tex., 1986), 399403, Lecture Notes in Pure and Appl. Math., bf 109,
Dekker,
New York, 1987. MR 89b:47081.

15.

Methods of functional analysis in approximation theory, Proceedings of
the international conference held in Bombay, December 1620, 1985, edited
by C.A. Micchelli, D.V. Pai and B.V. Limaye, Internationale Schriftenreihe
zur Numerischen Mathematik [International Series of Numerical Mathematics],
76.
Birkhauser Verlag, BaselBoston,Mass., 1986, 410 pp., ISBN:376431761,
4106. MR 88f:41002.

16.

Naimpally, S.A. and Pai, D.V., Best weighted approximation of vectorvalued
functions, Approximation theory and applications (St. John's, Nfld.,
1984), 140158, Res. Notes in Math., 133, Pitman, Boston,
Mass.London, 1985. MR 88e:41057

17.

Govindarajulu, P. and Pai, D.V., On solar properties of sets and radial
continuity of setvalued fprojections, Indian J. Pure Appl. Math.17
(1986), no.3, 360366. MR 87f:41059.

18.

Pai, D.V. and Veeramani, P., Some fixed point theorems for multimappings,
Indian
J. Pure Appl. Math. 14 (1983), no.9, 11571165. MR 85m:54051.

19.

Pai, D.V. and Govindarajulu, P., On setvalued fprojections and ffarthest
point mappings, J. Approx. Theory 42 (1984), no.1, 413 MR.85h:54031.

20

Govindarajulu, P. and Pai, D.V., On ffarthest points of sets, Indian
J. Pure Appl. Math. 14 (1983), no.7, 873882. MR 85h:41081.

21.

Pai, D.V., On nonlinear minimization problems and Lfsplines, I, J.
Approx. Theory 39 (1983), no.3, 228235. MR 85a:49012.

22.

Pai, D.V. and Veeramani, P., Applications of fixed point theorems to problems
in optimization and best approximation, Nonlinear analysis and applications
(St.
Johns, Nfld., 1981), pp.393400, Lecture Notes in Pure and Appl. Math.,
80, Dekker, New York, 1982. MR84b:47074.

23.

Veeramani, P. and Pai, D.V., On a fixed point theorem on uniformly convex
Banach spaces, Indian J. Pure Appl. Math.13 (1982), no.6,
647650. MR 83k:47045.

24.

Pai, D.V. and Veeramani, P., On some fixed point theorems in Banach spaces,
Internat.
J. Math. Math. Sci. 5 (1982), no.1, 113122. MR 83k:47042.

25.

Pai, D.V. and Naoum, R.S., On some fixed point theorems in uniform spaces,
Indian
J. Pure Appl. Math. 13 (1982), no.6, 676681. MR 83i:54042.

26.

Pai, D.V. and Veeramani, P., Fixedpoint theorems for multimappings, Indian
J. Pure Appl. Math. 11 (1980), no.7, 891896. MR 82k:54076.

27.

Pai, D.V. and Veeramani, P. Fixed point theorems for multimapings, Yokohama
Math., J. 28 (1980), no.12, 714. MR82i:54079.

28.

Govindarajulu, P. and Pai, D.V., On properties of sets related to fprojections,
J.
Math. Anal. Appl. 73 (1980), no.2, 457465. MR 81d:41039.

29.

Pai, D.V. and Govindarajulu, P., On fproximal points of pairs of sets,Optimizing
methods in statistics (Proc. Internat. Conf., Indian Inst. Tech., Bombay,
1977), pp. 367384, Academic Press, New YorkLondon, 1979. MR 81a:41060.

30.

Pai, D.V., Multioptimum of a convex functional, J. Approximation Theory19
(1977), no.1, 8399. MR 58#30251.

31.

Pai, D.V., A characterization of smooth normed linear spaces, J. Approximation
Theory 17 (1976), no. 4, 315320. MR 54#3366.

32.

Kaulgud, N.N. and Pai, D.V., Fixed point theorems for setvalued mappings,
Nieuw
Arch. Wisk (3) 23 (1975), no.1, 4966. MR 52#15422.

33.

Pai, Devidas, Multioptimum d'une fonctionnelle convexe sur des ensembles
reguliers, (French) C.R. Acad. Sci. Paris Ser. AB 280 (1975),
no.24, Aii, A1673A1676. MR 52#8938.

34.

Pai, D.V., Uniform weightfunction approximation of functions with values
in Hilbert space, Publ. Inst. Math. (Beograd) (N.S.) 14(28)
(1972), 115122. MR 52#8746.

35.

Pai, Devidas, Multioptimum d'une fonctionnelle convexe sur des ensembles
reguliers, (French) C.R. Acad. Sci. Paris Ser. AB 280 (1975),
Ai, A1185A1188. MR 51#13828.

36.

Pai, D.V., Proximal points of convex sets in normed linear spaces, Yokohama
Math. J 22 1974), 5378. MR #14024.

37.

Pai, D.V. and Jain P.C., Approximation theorems of the Korovkintype for
complexvalued functions, Indian J. Math.13 (1971), 123129.
MR 49#966.

38.

Pai, D.V., Uniform approximation of vectorvalued functions using a weight
function, Yokohama Math. J. 20 (1972), 3544. MR 46 #7778.

(II)

Papers accepted for publication

(1)

On hypertopologies and the YoungFenchel transform (with B.M. Deshpande),
to appear in Numer. Funct. Anal. Optim.

(2)

Continuity results for value function, level sets and approximate minima
(with P. Shunmugaraj), to appear in
Nonlinear Analysis and Its Applications
edited by S.P. Singh and Bruce Watson, Marcel Dekker, Inc.

(3)

Strong uniqueness of simultaneous approximants, to appear in J. Indian
Math. Soc.

(III)

Papers in Conference Proceedings, Seminars, Symposia
etc.

(1)

On wellposed, wellset, and conditioned problems in approximation (with
K. Indira), in : Mathematical modelling of nonlinear systems
(J.C. Misra and S.B. Sinha Eds.), Proceedings of the International Conference
on Mathematical Modelling of Nonlinear Systems, I.I.T. Kharagpur, Dec.
1999, pp. 175190.

(2)

On wellposedness of some problems in approximation, to appear in the proceedings
of the conference KHAJURAHO ATA 99 being edited by A.L. Brown.

(3)

Strong unicity in simultanoeus approximation (with K. Indira), to appear
in the Proceedings of the Conference on Analysis, Wavelets and Applications,
Feb. 1214, 2000, being edited by H.P. Dikshit.

(4)

Characterization of strong uniqueness of best simultaneous approximation,
Proceedings of the Fifth Annual Conference of Indian Society of Industrial
and Applied Mathematics (ISIAM), Bhopal, 1998.

(5)

LeraySchauder type theorem for multivalued maps in topological vectorspaces
(with T.Sengadir), in : Approximations Theory and Its Applications
ed. by Geetha S. Rao, New Age International Limited, Publishers, New Delhi,
1996, pp.116129.

(6)

On pcenters and fixed points (with S.P. Singh), in : Approximation
Theory and Its Applications ed. by Geetha S. Rao, New Age International
Limited, Publishers, New Delhi, 1996, pp. 8788.

(7)

An algorithm for parameter optimization problems of continuous systems
(with Le Van Bang and S.D. Agashe), Proc. National Systems Conf., NSC84
(1984), 396400.

(8)

Parameter optimization problems with tolerances for nonlinear discrete
and onlinear continuous systems (with Le Van Bang and S.D. Agashe), Proc.
National Systems Conf., NSC85 (1985) CS 8.1  CS 8.7.

(9)

A computational method to test for satisfaction of stability criteria in
frequency domain (with Le Van Bang and S.D. Agashe), in : Recent
Advances in Systems Theory and Applications, NSC86, ed. by P.S. Satsangi
and A.L. Agarwal.

(10)

Secondorder optimality conditions for a class of semiinfinite programming
problems in control systems design (with Le Van Bang and S.D. Agashe),
in : Recent Advances in Systems Theory and Applications, NSC86,
ed. by P.S. Satsangi and A.L. Agarwal.

(11)

On proximal points of pairs of sets (with H.G. ter Morsche), T.H. Report
75  Wsk  01 (1985), Department of Mathematics, Technological University,
Eindhoven

(12)

Characterizations of multioptimum of a convex functional, Expose No.193,
Seminaire
d'Analyse Numerique, (1974), Grenoble, France.

(IV)

Book Review

1.

On anniversary volume on approximation theory and functional analysis,
ISNM
65, ed. by P.L. Butzer, R.L. Stens and B.Sz.Nagy, Birkhauser Verlag,
Basel, 1984 in : J. Indian Inst. Sci., 66 (1986), 300301.