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 (co-edited 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, Pierre-Jean and Pai, Devidas, On simultaneous approximation, Numer. Funct. Anal. Optim. 19 (1998), no.9-10. 1045-1064. 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), 451-458, 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 Leray-Schauder type theorem and applications to boundary value problems for neutral equations, Nonlinear Anal. 28 (1997), no.4, 701-719. 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.9-10, 1211-1231. MR 96k:41048.
5.
Pai, D.V. and Nowroji, P.T., Restricted p-centers and weighted restricted centers, Advances in computational mathematics (New Delhi, 1993), 279-302, 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.5-6, 593-610 (1992). MR 93e:49042.
7.
Pai, D.V. and Nowroji, P.T., On restricted centers of sets, J. Approx. Theory 66 (1991), no.2, 170-189. MR 92i:46035.
8.
Beer, Gerald and Pai, Devidas, The Prox map, J. Math. Anal. Appl. 156 (1991), no.2, 428-443, 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, 25-37. MR 91m:49011.
10.
Beer, Gerald and Pai, Devidas, On convergence of convex sets and relative Chebyshev centers, J. Approx. Theory62 (1990), no.2, 147-169. MR 91j:41044.
11.
Beer, Gerald and Pai, Devidas, Proximal maps, prox maps and coincidence points, Numer. Funct. Anal. Optim. 11 (1990), no.5-6, 429-448. MR 91i:41027.
12.
Pai, D.V., Optimal recovery: a selective survey, Optimization, design of experiments and graph theory (Bombay, 1986), 406-416, 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), 231-244, Internat. Schriftenreihe Numer. Math., 76, Birkhauser, Basel-Boston, 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), 399-403, 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 16-20, 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, Basel-Boston,Mass., 1986, 410 pp., ISBN:3-7643-1761, 41-06. MR 88f:41002.
16.
Naimpally, S.A. and Pai, D.V., Best weighted approximation of vector-valued functions, Approximation theory and applications (St. John's, Nfld., 1984), 140-158, 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 set-valued f-projections, Indian J. Pure Appl. Math.17 (1986), no.3, 360-366. 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, 1157-1165. MR 85m:54051.
19.
Pai, D.V. and Govindarajulu, P., On set-valued f-projections and f-farthest point mappings, J. Approx. Theory 42 (1984), no.1, 4-13 MR.85h:54031.
20
Govindarajulu, P. and Pai, D.V., On f-farthest points of sets, Indian J. Pure Appl. Math. 14 (1983), no.7, 873-882. MR 85h:41081.
21.
Pai, D.V., On nonlinear minimization problems and Lf-splines, I, J. Approx. Theory 39 (1983), no.3, 228-235. 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.393-400, 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, 647-650. 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, 113-122. 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, 676-681. MR 83i:54042.
26.
Pai, D.V. and Veeramani, P., Fixed-point theorems for multimappings, Indian J. Pure Appl. Math. 11 (1980), no.7, 891-896. MR 82k:54076.
27.
Pai, D.V. and Veeramani, P. Fixed point theorems for multimapings, Yokohama Math., J. 28 (1980), no.1-2, 7-14. MR82i:54079.
28.
Govindarajulu, P. and Pai, D.V., On properties of sets related to f-projections, J. Math. Anal. Appl. 73 (1980), no.2, 457-465. MR 81d:41039.
29.
Pai, D.V. and Govindarajulu, P., On f-proximal points of pairs of sets,Optimizing methods in statistics (Proc. Internat. Conf., Indian Inst. Tech., Bombay, 1977), pp. 367-384, Academic Press, New York-London, 1979. MR 81a:41060.
30.
Pai, D.V., Multioptimum of a convex functional, J. Approximation Theory19 (1977), no.1, 83-99. MR 58#30251.
31.
Pai, D.V., A characterization of smooth normed linear spaces, J. Approximation Theory 17 (1976), no. 4, 315-320. MR 54#3366.
32.
Kaulgud, N.N. and Pai, D.V., Fixed point theorems for set-valued mappings, Nieuw Arch. Wisk (3) 23 (1975), no.1, 49-66. MR 52#15422.
33.
Pai, Devidas, Multioptimum d'une fonctionnelle convexe sur des ensembles reguliers, (French) C.R. Acad. Sci. Paris Ser. A-B 280 (1975), no.24, Aii, A1673-A1676. MR 52#8938.
34.
Pai, D.V., Uniform weight-function approximation of functions with values in Hilbert space, Publ. Inst. Math. (Beograd) (N.S.) 14(28) (1972), 115-122. MR 52#8746.
35.
Pai, Devidas, Multi-optimum d'une fonctionnelle convexe sur des ensembles reguliers, (French) C.R. Acad. Sci. Paris Ser. A-B 280 (1975), Ai, A1185-A1188. MR 51#13828.
36.
Pai, D.V., Proximal points of convex sets in normed linear spaces, Yokohama Math. J 22 1974), 53-78. MR #14024.
37.
Pai, D.V. and Jain P.C., Approximation theorems of the Korovkin-type for complex-valued functions, Indian J. Math.13 (1971), 123-129. MR 49#966.
38.
Pai, D.V., Uniform approximation of vector-valued functions using a weight function, Yokohama Math. J. 20 (1972), 35-44. MR 46 #7778.
(II)
Papers accepted for publication
(1)
On hypertopologies and the Young-Fenchel 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 well-posed, well-set, 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 Non-linear Systems, I.I.T. Kharagpur, Dec. 1999, pp. 175-190.
(2)
On well-posedness 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. 12-14, 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)
Leray-Schauder type theorem for multi-valued maps in topological vector-spaces (with T.Sengadir), in :  Approximations Theory and Its Applications ed. by Geetha S. Rao, New Age International Limited, Publishers, New Delhi, 1996, pp.116-129.
(6)
On p-centers 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. 87-88.
(7)
An algorithm for parameter optimization problems of continuous systems (with Le Van Bang and S.D. Agashe), Proc. National Systems Conf., NSC-84 (1984), 396-400.
(8)
Parameter optimization problems with tolerances for non-linear discrete and on-linear continuous systems (with Le Van Bang and S.D. Agashe), Proc. National Systems Conf., NSC-85 (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, NSC-86, ed. by P.S. Satsangi and A.L. Agarwal.
(10)
Second-order optimality conditions for a class of semi-infinite programming problems in control systems design (with Le Van Bang and S.D. Agashe), in : Recent Advances in Systems Theory and Applications, NSC-86, 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 multi-optimum 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), 300-301.