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Applied Math Research

Tanmoy Som

Designation: Professor

Phone: +919236916279

E-mail: tsom.apm@itbhu.ac.in, som_tanmoy@yahoo.co.in

Research Areas: Functional Analysis, Optimization theory, Mathematical Modeling, Fuzzy Set Theory, Soft Set Theory, Pattern Recognition

 

 

Biography:

Dr. T.Som did his M.Sc. and Ph.D. from Banaras Hindu University.

Courses offered:
Functional Analysis, Numerical Analysis, Operations Research, Switching Theory, Number Theory and Discrete Mathematics.

     M.Phil. dissertation guided : 6 (Awarded)
A.  Ph.D.s guided : 6 (awarded), 5 (working)

Projects:

YEAR

PROJECT

SPONSORING AGENCY

Aug 83 - Sept 85

Fixed Point Theory in Metric, Banach and Hilbert Spaces and their Applications

Council of Scientific and Industrial Research, NewDelhi

1995

Optimization of Agricultural products of Cachar

Assam University, Silchar

Awards

i.

MERIT SCHOLARSHIP in I.Sc. and B.Sc. (1974-78)

ii.

 Ist in Aptitude test held by Gorakhpur University in 1974-75

iii.

SENIOR RESEARCH FELLOWSHIP (CSIR, NEW DELHI)

Publications:

Number of papers: Published- (International Journal 16+1(accepted) + National Journal 35) , Conference Proceedings- 3

List Of Publications:

B.   International Journal (published: 27+3 accepted)

  1. (with R.N.Mukherjee) Some generalizations of a fixed-point theorem of Khan, Bull. Tech. Univ. Istanbul, 36(1983), no.2, 201-211.
  2. (with R.N.Mukherjee) Generalization of Leader’s fixed point principle, Bull. Austral. Math. Soc. 29(1984), 349-356.
  3. (with R.N.Mukherjee) An application of Meyer’s theorem on converse of Banach’s contraction principle, Bull. Inst. Math. Acad. Sinica, 12(1984) (3), 253-255.
  4. (with R.N.Mukherjee) A note on fixed point theorems for some non-linear mappings, Math. Chronicle. 13(1984), 59-62.
  5. (with R.N.Mukherjee) On fixed point theorems for mappings on a metric space involving several points of the space, Bull. Tech. Univ. Istanbul. 37(3)(1984) 313-322.
  6. (with R.N.Mukherjee) Some results on unique fixed points for mappings on Hausdorff space, Communications. 33 (1984), 215-223.
  7. (with R.N.Mukherjee) On mappings whose powers are contractions on a metric space, Communications, 34(1985), 17-23.
  8. (with S. Sessa & R.N. Mukherjee) A common fixed point theorem for weakly commuting mappings, Math, Japonica, 31(2) (1986), 235-245.
  9. Nonlinear mappings in metric and Hausdorff spaces and their common fixed point,Kyungpook Math J. 28(1) (1988), 97-106.
  10. (with R.N. Mukherjee) Some fixed point theorems for fuzzy mappings, Fuzzy Setsand Systems, 33(1989) 213-219.
  11. (with R.N. Mukherjee & V. Verma) On weak convergence to fixed point of a generalized asymptotically nonexpansive map, Publ. Del. Inst. Math. 45(59) (1989),179-183.
  12. Some fixed point results in 2-Banach space, Internat. Jour. Math. Scs. 4(2) (2005),  323-328.
  13. Some results on common fixed point in fuzzy metric spaces, Soochow Journal of Mathematics 33(4)(2007), 553-561.
  14. On soft relation and fuzzy soft relation, Jour. Fuzzy Mathematics (16(3)(2008)).
  15. (S.Begum, B.S.Purkayastha and A. Chakrabarty) "An efficient psFCM Clustering Algorithm", 2009 IEEE International Advance Computing Conference (IACC 2009) Patiala, India, March 6-7, 2009, 383-389.
  16. (with S.Begum and B.S.Purkyastha) A New Cluster Validity Index for Fuzzy Clustering, Int. J. Computational Intelligence Research 5(4) (2009), 403-428.
  17. (with N.Sen and B.Sinha) A study of Transportation Problem for an Essential Iteam of Southerrn Part of North Eastern Region of India as an OR Model and use of Object Oriented Programming, Int. J. of Comp. Sci. and Network Security, 10(4) (2010), 76-86.
  18. (with A.Choudhury) Some common fixed point results for a pair of self maps under weak compatibility condition, Int. J. Math. Sci. & Engg. Appl. 4(5) (2010), 249-261.
  19. (with P. Borah) The Governing Equations for Electro-Rheological Fluid within the Context of the Full Electro-Dynamical Theory, Int. J. Appld. Math. 23(5) (2010), 809-824.
  20. (with S.Saha) Handwritten character recognition by using Neural-network and Euclidean distance metric, Int. J. Comp. Sci. & Intelligent Computing, 2(1) (2010), 1-5.
  21. (with N.Sen and B.Sinha) A Mathematical Approach to the Transportation Related Data of South Assam for the optimal age of Replacement of Vehicle and daily Expenditure Minimization, AJMCSR, 4(1) (2011), 6-17.
  22. (with R. Chakravarty) Gravitational Potential of an Ellipsoidal Mass of Oblate shape at any point outside the Oblate, Int. J. Math. Sci. & Engg. Appl. 5(3) (2011), 347-359.
  23. (with B.S.Choudhury and K.Das) Two common fixed point results in fuzzy metricspaces, Internat. Review of Fuzzy Math. 6(1) (2011), 21-32.
  24. (with A.Choudhury) Some study on the theory of fixed points in metric space, Jour. Internat. Acad. Phy. Sci. 15(2) (2011), 141-152.
  25. (with S. Saha) Handwritten character recognition by using Fuzzy membership function, Int. J. Emerg. Tech. Sci. & Engg. 5(2) (2011), 11-15.
  26. (with A. Choudhury) Compatible Mapping and some Common Fixed Point Results, Amer. J. Math. Stat. 1(1) (2012), 17-20.
  27. (with Lokesh Kumar) Generalized Consitional Convergence and Common Fixed Point Principle for Operators on Metric Spaces, Int. Math. Forum 7(2) (2012), 57-64.
  28. (with A. Choudhury) Common Fixed Points for two self maps under strongly partially commuting condition, J. Adv.Res.Pure Math. (USA) (to appear in 2012).
  29. (with Lokesh Kumar)Extension of Caristi's theorem to Banach space and it's application in Cone Metric Space, Int. J. Math. Sci. & Appl. (to appear).
  30. (with R. Chakravarty) Gravitational Potential of an Ellipsoidal Mass of Prolate shape at any point outside the prolate, Amer. J. Math. and Stat. (2012) (to appear).

C.  National Journal: (published: 38 + 1 accepted)

  1. (with R.N. Mukherjee) A generalization of a fixed-point theorem of Jaggi, Indian J. Pure Appl. Math. 14(15) (1983), 572-74.
  2. (with R.N. Mukherjee)  Fixed point theorems in L-space, Indian J. Pure Appl. Math. 14(5) (1983), 635-640.
  3. (with R.N. Mukherjee) A fixed-point theorem in generalized Hillbert space, Indian J. Pure Appl. Math. 14(7) (1983), 930-933.
  4. (with R.N. Mukherjee) On some fixed-point theorems for generalized multivalued mappings, Indian J. Pure Appl. Math. 14(12) (1983) , 1506-1509.
  5. (with R.N. Mukherjee) Solution of simultaneous equations in Hausdorff space and a common fixed point theorem, Bull. Cal. Math. Soc. 76(1984), 231-235.
  6. (with R.N. Mukherjee) Construction of fixed points of strictly-pseudocontractive mappings in a generalized Hilbert space and related applications, Indian J. Pure Appl. Math. 15(11)(1984), 1183-1189.
  7. (with R.N. Mukherjee) A note on an application of a fixed point theorem in approximation theory, Indian J. Pure Appl. Math. 16(1984) , 243-244.
  8. (with R.N. Mukherjee) Some fixed point theorems for nonexpansive multivalued mappings, Jour. Pure Appl. Math. Sci. 23(1986), 1-5.
  9. Some fixed point theorems on metric and Banach spaces, Indian J. Pure Appl. Math. 16(6) (1985), 575-585.
  10. (with R.N. Mukherjee) A common fixed point theorem for two nonself mappings, Proc. Nat. Acad. Sci. (India), (56)(A)(1986), 230-233.
  11. An abstract fixed point principle for K-operators on cone valued metric spaces. Pure Math. Manuscript, 5(1986), 51-58.
  12. A common fixed point result for asymptotically regular mappings, Jour. Math. Phy. Sci. 20(6)(1986), 517-523.
  13. Some fixed point results for single-valued mappings on a metric space, Ganita, 38(1987), 11-20.
  14. (with R.N. Mukherjee) On Phi-monotone operators and variational in equalities, Bull.Cal. Math. Soc. 80(1988), 401-405.
  15. (with R.N. Mukherjee) Some results on generalized contractive modulii of a pair of operators, Proc.Nat. Acad. Sci. (India) 58(1988), 393-398.
  16. Common fixed point theorems for asymptotically commuting mappings in uniformlyconvex Banach spaces, Indian Jour. Math. 31(2) (1989),193-200.
  17. Some results on generalised nonlinear contractions through abstract cones, Ganita,40(1989), 41-45.
  18. Fixed point principle for K-operators on cone valued metric spaces, Pure Math.Manuscript, 8(1989), 19-29.
  19. (with R.N. Mukherjee & V. Verma) On common fixed points of nonlinear mappingsin certain Banach Lattices, Bull. Cal. Math. Soc, 82(1990) (1), 1-3.
  20. Fixed point of condensing multivalued mappings, Pure Math. Manuscript,9(1990-91), 181-186.
  21. An extension of a fixed  point theorem of Achari, Ganita, 42(1991), 59-64.
  22. Some fixed point results for quasi and generalized nonexpansive mappings, J. AssamUniv. 2(1) (1997), 185-188.
  23. Some convergence principles and fixed point theorems, Ganita, 48(2) (1997), 121-124.
  24. A step towards optimization of agricultural products in the district of Cachar, J. Assam Univ. 3 (1998), 136-150.
  25. On the theory of fixed point in metric space, Math. Forum, 12 (1998), 11-18.
  26. Convergence of modified Mann type of iterates and fixed point, Proc. Nat. Acad.      Sci.(A) (India) 70(2000), 185-189.
  27. Some fixed point theorems on cone-valued L-spaces and spaces with cone-valued 2-metric,Ganita 51(2000), 127-134.
  28. Difference approximations in optimal control problems with multiple costfunctionals, J. Assam Univ. 5(1) (2000), 6-12.
  29. Some results on common fixed points, Bull. GUMA, 6(2000), 65-71 (published in Nov 2002).
  30. Few common fixed point results for compatible mappings. Bull. Cal. Math. Soc.95(4) (2003), 307-312.
  31. Generalized exponential and it’s applications to partial differential equations, Ganita 55(2)(2004), 161-167.
  32. (with Saha, S.) Noise erosion and segmentation of line from handwritten document, Assam Univ. Jour. Sc. & Tech. 3(1) (2008), 15-17.
  33. (with Sen, N.) Mathematical modeling of transportation related problem of South Assam and its optimal solution, Assam Univ. Jour. Sc. & Tech. 3(1) (2008), 22-27.
  34. (with N.Sen) Mathematical modeling of transportation related fare minimization problem of South Assam and an approach to its optimal solution, Indian Jour.Transport Management 32(3) (2008), 201-208.
  35. (with A.Choudhury) A common fixed point for three self maps using compatibility, Jour. Tripura Math.Soc.11(2009).
  36. (with N.Sen) an Optimal Model for the Daily Profit of the Transporting Agency in South Assam, Jour. Tripura Math.Soc.11(2009), 42-48.
  37. Some common fixed point results for compatible mapping, Proc. Math. Soc., BHU 25(2009), 17-21.
  38. 2-Banach space and some fixed point results, J. Ind. Acad. Math. 33(2) (2011), 411-418.

D.  Publication as a chapter in a book:

1.   Agricultural development of North-Eastern Region in the Post-Reform period-A case study of Cachar District of South Assam, Edited book : Economic Reforms and Agricultural Development in North-East India (Ed. K Sengupta & N. Roy), Mittal Publ., New Delhi, 2003, p115-140.

2. Mathematical Modeling of Rainwater Harvesting, Edited Book: Water Harvesting and Water Utilisation in North East India, Assam University Publ. 2007,144-150.

3. On the Theory of Vague Soft sets, Proceeding of the International Conference on Rough sets, Fuzzy sets and Soft computing, Dept. of Mathematics, Tripura University, Agartala, Serials Publications, 146-161, 2011.

E. List Of Conferences/Short Term Courses Participated/Organized:

a.  Organized :
                 i) National Conference on ‘Recent Developments in Mathematics and  Applications’ during March 14-16’ 2001 at Assam University, Silchar.
                     ii) ‘Winter School on Image Processing and Analysis’ during Jan 18-22, 2007 at Assam University, Silchar (in collaboration with ISI, Kolkata).                                           iii) National Conference on 'Recent Trends in Mathematical Modeling and Simulation' during March 18-20, 2010 at the Department of Applied                                             Mathematics, Institute of Technology, Banaras Hindu University, Varanasi.
                    iv) National Conference on 'Mathematical Modeling and Computer Simulation' during March 25-27, 2011 at the Department of Applied Mathematics,                                 Institute of Technology, Banaras Hindu University, Varanasi.
                     v) National Conference on 'Mathematical Modeling and Computer Simulation' during March 23-25, 2012 at the Department of Applied Mathematics,                                 Institute of Technology, Banaras Hindu University, Varanasi.    

b.  Participated and Presented :

  1.  "Generalization of Leader’s fixed point principle" at the 48th Annual Conference of I.M.S held at Bhagalpur University from Dec 26-28, 1982.
  2. "Some results on comparison principle and generalized nonlinear contractions in abstract spaces" at the ‘International Symposium on Modern  Analysis and its Applications’ held at I.I.T. Delhi between Dec. 21-24, 1983.
  3. "Nonlinear mappings in metric and Hausdorff spaces and their common fixed point" at the 71st session of  I.S.C.A. held at Ranchi University between Jan 3-6, 1984.
  4. "A note on a fixed point result of Ray" at the 72th session of  I.S.C.A. held at Lucknow University between Jan. 3-8, 1985.
  5. "Fixed point principle for a pair of operators and some related results at the 50th Annual Conference of  I.M.S. held at S.P. University, Ballabh Vidyanagar between Feb. 6-8, 1985.
  6. "A common fixed point result for two nonself mappings" at the 73rd session of I.S.C.A. held at Delhi University between Jan. 3-8, 1986.
  7. "Common fixed point results for asymptotically commuting mappings in uniformly convex Banach spaces" at the 53rd Annual Conference of  I.M.S. held at Gorakhpur University between Dec. 29. 29, 1987 and Jan 1, 1988.
  8.  Attended ‘National Seminar on Analysis and Its Applications’ held at Burdwan University between Dec. 27-29, 1994.
  9. "Convergence of modified Mann type of iterates and fixed point" at the 62th Annual Conference of I.M.S. held at I.I.T. Kanpur between Dec. 22-25, 1996.
  10. "A step towards optimization of agricultural products in the district of Cachar" at the North East Regional Conference on Mathematics held by Assam Academy of Mathematics at Gauhati University between Apl. 25-26, 1997.
  11. "Recent concepts on the theory of common fixed points and few results" at the ‘International Conf. on Geometry, Analysis and Applications’ organised by Dept. of Mathematics, B.H.U, Varanasi, Aug 21-24, 2000.
  12. Attended the ‘Conference on Functional Analysis and Its Applications’ organised by Theoretical Statistics and Mathematics  Division, I.S.I., Kolkata, June 13-15, 2001.
  13. "Some common fixed point results on fizzy metric spaces" at the conf. of  ISFUMIP on ‘Fuzzy set Theory and its Mathematical Aspects and Applications’ held at B.H.U., Varanasi , Dec 26-28’ 2002.
  14. Attended  the Ist ‘International Conference on Pattern Recognition and Machine Intelligence’ organized by Machine Intelligence Unit of ISI, Kolkata during Dec. 20-22, 2005.
  15. "Handwritten character recognition using fuzzy membership function" at the ‘National Conference &Workshop on High Performance Computing & Applications’ organized by Dept. of Computer Science, BHU, Varanasi, Feb 9-11’ 2009.

c.  INVITED TALKS  DELIVERED AT VARIOUS CONFERENCES/SEMINARS:

1.  "Fixed point theorems on fuzzy metric spaces" at the International Conf. on Recent  Developments in Mathematical Analysis with Applications to Industrial Problems       at  B.H.U., Varanasi, March 2-5, 1998
2.  "Fixed point results on 2 " Banach spaces" at National seminar on recent Developments in Mathematics at the University of Burdwan, Feb 1-3, 2000.

3. "Some results on approximating fixed points" at the National Seminar on Mathematics and its Applications at the University of Burdwan, Dec 26-28, 2001.
4.  "Agricultural development of  North Eastern Region (A case study of Cachar)" at the Regional Seminar on Agricultural Development and Economic Reforms in the     context of  North Eastern Region at the Dept. of Economics, Assam University, Silchar, Feb 5, 2002.
5.  "On soft relation and Fuzzy soft relation " at the National Seminar on Recent Advances in Mathematics and Applications at the University of Burdwan,
     Jan 18-20, 2006.
6.   "On fixed point theory via biased maps" at the International Conference on Frontiers of Mathematics & Applications at the University of Burdwan, Jan 16-18, 2008.
7.  "On the theory of Soft sets, soft relation and Fuzzy soft relational' at the National Seminar on Fuzzy Mathematics and Its Applications organized by Tripura                     Mathematical Society, School of IT and Comp. Sci. at Tripura University, Agartala, Nov 25-26, 2006.
8. "On fixed point theory via biased maps" at the International Conference on Frontiers of Mathematics and Applications at the University of Burdvan, Jan 16-18, 2009.
9. "On the theory of Soft sets and Soft relation" at the National Conference on Analysis and Its Application at the Dept. of Mathematics, BHU,Varanasi, Mar 19-21, 2009.
10. "On the theory of Vague Soft sets" at the International Conference on Rough Sets, Fuzzy Sets and Soft Computing at the Dept. of Mathematics, Tripura University,          Agartala, Nov 5-7, 2009.
11. "On the theory of fixed and common fixed points" at the National Conference on Recent Advances in Mathematical Sciences and their Applications at the Dept. of      Mathematics, Assam University, Silichar, Nov. 25-27, 2010.
12. "Vague Soft Sets and Related Algebraic Properties" at the National seminar on Mathematics and Applications at the Dept. of Mathematics, University of Burdwan,      Feb 24-25, 2011.
13. "Extention of Caristi's Theorem to Banach Space and its Application in cone Metric Space" at the National Seminar on Analysis and Applications organized by              Callutta Mathematical Society, Sept 6-7, 2011.
14. "Common fixed points for two self maps under strongly partially commuting condition" at the 14th International Conference of the International Academy of Physical       Sciences (CONIAPS XIV), NIT, Surat (India) during December 22-24, 2011.
15. "Concepts on soft sets, soft relation, fuzzy soft relation and vague soft sets" at the symposium on "Modeling and Uncertainty" in the 77th annual conference at the           SRTM University, Nanded, Maharastra during 27-30 Dec, 2011.

 

d.  INVITED  LECTURES  AS  RESOURCE  PERSON AT  REFRESHER COURSES: 

1. Three lectures on ‘Boolean Algebra and Applications’ at the 7th  refresher course in Mathematics at Gauhati University, Dec.15-17, 2001.
2. Six lectures on ‘Boolean Algebra and Applications and Fuzzy Sets’ at the 3rd  refresher course in Mathematics at  Manipur University,  Dec. 18-21, 2001.
3. Three lectures on ‘Analysis’ at the 7th refresher course in Mathematics at Manipur University, June 4-7, 2002.
4. Three lectures on ‘Boolean Algebra and Applications’ at the 1st refresher course in Mathematics at Assam University, Nov.14 -Dec 4, 2002.
5. Four lectures on ‘Fuzzy Set Theory and Soft Set Theory’ at the refresher course in Computer Science at Kalyani University, Jan.7 -Jan 27, 2008


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