D. Vamshee Krishna

Dr. D. Vamshee Krishna

9849146222

vamsheekrishna@nehu.ac.in
vamsheekrishna1972@gmail.com

Faculty members

Dr. D. Vamshee Krishna

Designation: Associate Professor

Department: Mathematics

Qualifications:

  1. B. Ed. (From Government College of Education, Nagarjuna Sagar, Affiliated to Osmania University, Hyderabad)
  2. M. Sc. (From Kakatiya University, Warangal)
  3. Ph. D. (From Kakatiya University, Warangal)

Title of Ph.D. Thesis: “An Application of Toeplitz Determinants for an Upper bound to the second Hankel Functional for certain subclasses of Univalent and Multivalent Analytic Functions,” under the supervision of Prof. T. RamReddy.

Area of Interest

Complex Analysis/ Hankel determinants

Teaching/Research Experience: 30 years/14years

Ph.D.’s Awarded/Submitted/Ongoing: 02/00/01

Number of Ph. D. Thesis Evaluated: 06

External Examiner for Conduction of Ph. D. Open Viva-Voce: 03

Web address:

  1. To see Google scholar citations >https://scholar.google.co.in/citations?user=qlYuV7MAAAAJ&hl=en
  2. ORCID Number https://orcid.org/0000-0002-3334-9079
  3. Research Gate: Active Member: https://www.researchgate.net/profile/Vamshee-Krishna-Deekonda
  4. MR Author ID: 987184
  5. Scopus ID: https://www.scopus.com/authid/detail.uri?authorId=55318038100
  6. Web of Science:https://publons.com/researcher/2127791/vamshee-krishna-deekonda/

Professional Affiliation:

  1. Member of INTERNATIONAL ASSOCIATION OF ENGINEERS (IAENG), with Membership No.187052.
  2. Life Member of THE INDIAN SCIENCE CONGRESS ASSOCIATION, with Membership No. L31203.
  3. Life      Member     of    ANDHRA     PRADESH      SOCIETY      FOR  MATHEMATICAL SCIENCES (APSMS), with Membership No. 434.
  4. Member of the National Centre for Mathematics (A Joint Center of IIT Bombay and TIFR, Mumbai).

Publications

  1. Vijaya Kumar. Ch, Biswajit Rath , Sanjay Kumar. K, & D. Vamshee Krishna. D, The sharp bound of certain second Hankel determinants for inverse functions of the class of convex functions with respect to symmetric points, Bol. Soc. Paran. Mat., v. 2025 (43) : pp. 1–9. (Scopus Indexed Journal) DOI: .https://doi.org10.5269/bspm.64878
  2. Winne Bareh , Vamshee Krishna, D & Rath, B. ,  Exact bounds to the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for the functions associated with the lemniscate of Bernoulli, Bulletin des Sciences Mathématiques, 199 (2025), 103585, pp. 1-17, DOI https://doi.org/10.1016/j.bulsci.2025.103585 (Science Cited & Scopus Indexed Journal).
  3. Vamshee Krishna, D.  Vani, N. Rath, B. Sanjay Kumar, Bound Associated with Certain Hankel Determinants and Zalcman Conjecture for Multivalent Functions of Bounded Turning, Sahand Communications in Mathematical Analysis (SCMA), 21(3) (2024), pp. 127-146 (Scopus Indexed Journal).        DOI: https://doi.org10.22130/scma.2023.1986093.1227
  4. Rath, B. Sanjay Kumar, K. Vamshee Krishna, D.  & Surya Viswanadh, G. K., The sharp bound of the third Hankel determinant of kth-root transformation for analytic functions, Afrika Matematika, 35(2) (2024), Article 34, pp. 1–14, DOI Afrika Matematika https://doi.org/10.1007/s13370-024-01174-9 (Scopus Indexed Journal).
  5. Srivastava, H. M. , Rath, B.  Sanjay Kumar, K. &  Vamshee Krishna, D.,  Some sharp bounds of the third-Hankel determinant for the inverses of the Ozaki type close-to-convex functions, Bulletin des Sciences Mathématiques, 191 (2024), 103381, pp.1909 -1915, DOI https://doi.org/10.1016/j.bulsci.2023.103381 (Science Cited & Scopus Indexed Journal).
  6. Rath, B. Sanjay Kumar, K. Vamshee Krishna, D.  & Surya Viswanadh, G. K., The sharp bounds of the Hankel determinants for the class of convex functions with respect to symmetric points, J. Indian Math. Soc. (N. S). , 91 (1–2) (2024), pp. 253 –264. https://doi.org/10.18311/jims/2024/31402 (Scopus Indexed Journal).
  7. Sanjay Kumar, K., Rath, B.  , Vani, N. &  D. Vamshee Krishna, The sharp bound of certain second Hankel determinants for the class of inverse of starlike functions with respect to symmetric points, Ukranian Mathematical Journal, 75(10)  (2023),  pp.1377 -1386, https://doi.org/10.1007/s11253-023-02177-8 (Science Cited & Scopus Indexed Journal).
  8. Srivastava, H. M.  Rath, B.  Sanjay Kumar, K. &  Vamshee Krishna, D.,  The sharp bound of the third Hankel determinant  of the k-th-root   transformation for  bounded turning functions, Acta et Commentationes Universitatis Tartuensis de Mathematica, 27(2) (2023), pp. 185–210 (Scopus Indexed Journal).
  9. Vani, N. Vamshee Krishna, D.   Vijaya Kumar, Ch. . Rath, B.  & Sanjay Kumar, K., Coefficient bound associated with certain Hankel determinants and Zalcman conjecture  for a subfamily of multivalent bounded turning functions, Funct. Approx. Comment. Math.  69 (2)(2023) pp. 177-192, (Scopus Indexed Journal).
    DOI: https://doi.org/10.7169/facm/2076
  10. Rath, B.  Sanjay Kumar, K. &  Vamshee Krishna, D.,  An exact estimate of the third Hankel determinants for functions inverse to convex functions, Mat. Stud. , 60 (2)(2023) pp. 34-39.,(Scopus Indexed Journal). https://doi.org/10.30970/ms.60.1., pp. 34-39
  11. Vani, N. Vamshee Krishna, D. & Shalini, D. Some Coefficient bounds associated with transforms of Bounded turning functions, Ukrainian Math. J., 74(12) (2023), pp.1909 -1915 (Science Cited & Scopus Indexed Journal).
  12. Vani, N.  Vamshee Krishna, D.  &     Rath, B. Sharp bounds associated with the Zalcman conjecture for the initial coefficients and second Hankel determinants for certain subclass of analytic functions, Mathematical Notes of NEFU, 30(2) (2023), pp. 92–100 (Scopus Indexed Journal).
  13. Vamshee Krishna, D. & Shalini, D. An upper bound of the Hankel determinant of third order for the inverse of reciprocal of bounded turning functions, Stud. Univ. Babes-Bolyai Math., 68(2)(2023), pp. 261-268 (Scopus Indexed Journal).
  14. Rath, B. Sanjay Kumar, K. Vamshee Krishna, D.  Vijaya Kumar, Ch. & Vani, N. Fifth Hankel determinant for multivalent bounded turning functions of order α, J. Indian Math. Soc. (N. S),90 (3-4)(2023), pp.289- 308. (Scopus Indexed Journal).
  15. Surya Viswanadh, G. K. Rath, B. Sanjay Kumar, K.& Vamshee Krishna,  D. The sharp bound for the third Hankel determinant of the inverse of functions associated with lemniscate of Bernoulli, Asian-Eur. J. Math., 16(7)(2023), Article Id: 2350126, pp.1-13 (Scopus Indexed Journal).
  16. Vamshee Krishna, D. Vijaya Kumar, Ch. and Rath, B. The sharp estimates for certain coefficient inequalities for transforms of a starlike function associated with Bernoulli’s lemniscate, Asian-Eur. J. 16(3)(2023), Article Id: 2350042, pp.1-9 (Scopus Indexed Journal).
  17. Sanjay Kumar,  K. Rath, B.  and Vamshee Krishna, D.  The Sharp Bound of the Third Hankel Determinant for the Inverse of Bounded Turning Functions, Contemporary Math. (Singapore), 4(1)(2023), pp. 30-41 (Scopus Indexed Journal).
  18. Rath, B. Sanjay Kumar, K. Vamshee Krishna, D.& Surya Viswanadh, G. K., The sharp bound of the third hankel Determinants for inverse of starlike functions with respect to symmetric points, Mat. Stud., 58(1)(2022), pp.45-50 (Scopus Indexed Journal).
  19. Vamshee Krishna, D.  and      Shalini, D. Hankel determinant of certain orders for some subclasses of holomorphic functions, Ural Math. J., 8(1) (2022), pp. 128-135 (Scopus Indexed Journal).
  20. Rath, B. Sanjay Kumar, K. Vamshee Krishna, D. & Lecko Adam, The Sharp Bound of the Third Hankel Determinant for Starlike Functions of Order ½, Complex Anal. & Operator Th. (CA0T), 16(5) (2022), pp. 1–8. (Science Cited & Scopus Indexed Journal).
  21. Rath, B.  Sanjay Kumar, K. Vamshee Krishna,  D.  Vijaya Kumar, Ch.  & Vani, N. Hankel Determinant of certain order for Bounded turning functions of order alpha, Indian J. Math., 64(3)(2022), pp. 401-416 (Scopus Indexed Journal).
  22. Vamshee Krishna, D. &         Shalini, D. Certain coefficient inequalities associated with Hankel determinant for a specific subfamily of holomorphic mappings, Publ. Inst. Math. (Beograd) (N.S.),111(125)(1)(2022), pp.127-132 (Scopus Indexed Journal).
  23. Vamshee Krishna, D. Third Hankel determinant for certain subclass of p- valent analytic functions, Miskolc Math. Notes, 22(1) (2021), pp.375–382. (Science Cited & Scopus Indexed Journal).
  24. Vamshee Krishna, D. & Shalini, D. Third kind Hankel determinant for Multivalent bounded turning functions of order alpha, TWMS J. of Appl. & Eng. Math., 11(3) (2021), pp. 789-794 (Scopus Indexed Journal).
  25. Vamshee Krishna, D. &     Shalini, D. On H3(1) Hankel determinant for certain subclass of analytic functions, Extracta Math., 35(1)(2020), pp.35-42 (Scopus Indexed Journal).
  26. Vamshee Krishna, D. & Shalini, D. Hankel determinant of Third kind for certain subclass of multivalent analytic functions, Vladikavkaz Math. J., 22(1)  (2020), pp. 43-48      (Scopus Indexed Journal).
  27. Vamshee Krishna, D. RamReddy, T. &     Shalini, D. Third order Hankel determinant for transforms of reciprocal of bounded turning functions, Math. Notes, 105(3-4) (2019), pp. 535-542 (Science Cited & Scopus Indexed Journal).
  28. Vamshee Krishna, D. & Shalini, D. , Best bound for ??-pseudo starlike functions, Commun. Fac. Sci. Univ. Ank. S ´er. A1 Math. Stat., 68(1)(2019), pp. 538-545 (Web of Science Indexed Journal) (UGC CARE LIST GROUP-I).
  29. Vamshee Krishna, D. & Shalini, Bound on H3(1) Hankel determinant for   Prestarlike functions of order alpha, Proyecciones J. Math., 37(2) (2018), pp. 305–315 (Scopus Indexed Journal).
  30. Vamshee Krishna, D. RamReddy, T. & Shalini, D. Certain Coefficient inequalities for transforms of bounded turning functions, Tamsui Oxf. J. Inf. Math. Sci., 32(1) (2018), pp. 91-101 (Scopus Indexed Journal).
  31. Vamshee Krishna, D. RamReddy, T. Shalini, D. & Venkateswarlu, B., Coefficient inequality for transforms of certain subclass of analytic functions, Acta Comment. Univ. Tartu. Math., 21(2) (2017), pp.185-193 (Scopus Indexed Journal).
  32. Vamshee Krishna, D. &        Shalini, D., Coefficient inequality for transforms of Bounded turning functions, Acta Univ. M. Belii Ser. Math., 25(2017), pp. 73-78 (UGC CARE LIST GROUP-I).
  33. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Hankel determinant for transforms of pre-starlike functions of order alpha, Southeast Asian Bull. Math., 40(1)(2016), pp.131-140 (UGC CARE LIST GROUP-I).
  34. Vamshee Krishna, D. & RamReddy, T. , Coefficient inequality for Multivalent bounded turning functions of order α, Problemy Analiza-Issues of Analysis,5(23)(1) (2016), pp.45–54 (Scopus Indexed Journal).
  35. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Coefficient inequality for certain subclass of p- valent analytic functions whose reciprocal derivative has a positive real part, Mat. Vesnik, 68(2)(2016), pp. 87-92 (Scopus Indexed Journal).
  36. Vamshee Krishna, D. & RamReddy, T. , Coefficient inequality for parabolic starlike functions of order alpha, Afrika Mat., 27(1-2) (2016), pp.121-132. (Scopus Indexed Journal).
  37. Vamshee Krishna, D. & RamReddy, T. , Second Hankel determinant for reciprocal of starlike and convex functions, Ann. Univ. Oradea. Fasc. Mat., 23(2) (2016), pp.131-136.
  38. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T.,Third Hankel determinant for starlike and convex functions with respect to symmetric points, Ann. Univ. Mariae Curie-Sklodowska Sect.A, 70(1)(2016), pp.37-45.
  39. Vamshee Krishna, D. & RamReddy, T., An upper bound to the second Hankel functional for the class of gamma-starlike functions, Bull. Iran. Math. Soc., 41(6)(2015), pp.1327- 1337. (Science Cited & Scopus Indexed Journal).
  40. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Third Hankel determinant for certain subclass of p- valent analytic functions, Complex Var. Elliptic Equ., 60 (9)(2015), pp.1301- 1307 (Science Cited & Scopus Indexed Journal).
  41. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for certain subclasses of Analytic functions associated with Hankel Determinant, Indian J. Pure & Appl. Math., 46(1)(2015), pp. 91-106 (Science Cited & Scopus Indexed Journal).
  42. Vamshee Krishna, D. & RamReddy, T., An upper bound to the second Hankel determinant for pre-starlike functions of order α, Le Matematiche, 70(2)(2015), pp.109-122.
  43. Vamshee Krishna, D. & RamReddy, T., An upper bound to the second Hankel determinant for functions in Mocanu class, Vietnam J. Math., 43 (3)(2015), pp. 541-549 (Scopus Indexed Journal).
  44. Vamshee Krishna, D. & RamReddy, T., Second Hankel determinant for the class of Bazilevic functions, Stud. Univ. Babes-Bolyai Math., 60(3) (2015), pp. 413-420.
  45. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Coefficient inequality for Transforms of Starlike and Convex Functions with Respect to Symmetric Points, Kyungpook Math. J., 55(2)(2015), pp. 429-438 (Scopus Indexed Journal).
  46. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for a function Whose derivative has a positive real part of order alpha, Math.Bohem.,140(1) (2015), pp. 43-52 (Scopus Indexed Journal).
  47. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Coefficient inequality for transforms of starlike and convex functions, Creative Math. & Informatics,24(1)(2015), pp. 69-75 (UGC CARE LIST GROUP-I).
  48. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., On a Subclass of Uniformly Quasi Convex functions of order alpha, Konuralp      J. Math., 3(2)(2015), pp. 33-41.
  49. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Third Hankel determinant for a function whose derivative has a positive real part of order alpha, J. Nigerian Math. Soc., 34(2)(2015), pp. 121-127.
  50. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for certain subclass of p-valent functions, Palestine J. Math., 4(1)(2015), pp. 222-227.
  51. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Coefficient inequality for transforms of reciprocal of bounded turning functions, Annals Univ. Sci. Budapest., Sect. Comp., 44(1)(2015), pp. 69-77.
  52. Vamshee Krishna, D. & RamReddy, T.,Coefficient inequality for certain p- valent analytic functions, Rocky Mont. J. Math., 44(6)(2014), pp.1941- 1959 (Science Cited & Scopus Indexed Journal).
  53. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T. ,Third Hankel determinant for the inverse of a function whose derivative has a positive real part, Mat. Stud., 42 (1)(2014), pp. 54-60. (Scopus Indexed Journal).
  54. Vamshee Krishna, D. & RamReddy, T., An upper bound to the non- linear functional for certain subclasses of analytic functions associated with Hankel determinant, Asian-Eur. J. Math., 7(2) (2014), Article ID 1350042, pp. 1-14 (Scopus Indexed Journal).
  55. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for certain subclass of analytic functions, Bull. Allahabad Math. Soc., 29(1) (2014), pp. 1-14.
  56. Vamshee Krishna, D. & RamReddy, T., An upper bound to the second Hankel determinant for a subclass of analytic functions, Bull. Int. Math. Virtual Inst., 4(1)(2014), pp. 17-26.
  57. Vamshee Krishna, D. Venkateswarlu, B. & RamReddy, T., Coefficient inequality for transforms of parabolic starlike and uniformly convex functions, Annals Math. Blaise Pascal, 21(2) (2014), pp. 39-56 (UGC CARE LIST GROUP-I).
  58. Vamshee Krishna, D. & RamReddy, T., An upper bound to the second Hankel determinant for certain subclass of analytic functions, Proc. Janjgeon Math.Soc.,16(4)(2013), pp.559-568 (Scopus Indexed Journal).
  59. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for uniformly convexfunctions of order alpha, J. Adv. Res. Pure Math., 5(1) (2013), pp. 25-41.
  60. Vamshee Krishna, D. & RamReddy, T., An upper bound to the non-linear functional associated with Hankel determinant for a subclass of analytic functions, Indian J. Math., 54(3)(2012), pp. 343-355 (Scopus Indexed Journal).
  61. Vamshee Krishna, D. & RamReddy, T., An upper bound to the second Hankel functional for non- Bazilevic functions, Far East J. Math. Sci., 67(2)(2012), pp.187-199 (Scopus Indexed Journal).
  62. Vamshee Krishna, D. & RamReddy, T., Hankel determinant for p- valent starlike and convex functions of order alpha, Novi Sad J. Math., 42(2) (2012), pp. 89-102 (Scopus Indexed Journal).
  63. RamReddy, T., & Vamshee Krishna, D., Hankel determinant for starlike and convex functions with respect to symmetric points, J.  Indian Math. Soc. (N. S)., 79(1-4) (2012), pp. 161-171.
  64. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for certain subclass of analytic functions, Armenian. J. Math.,4(2)(2012), pp.98-105.
  65. Vamshee Krishna, D. & RamReddy, T., Coefficient inequality for certain subclasses of analytic functions, New Zealand J. Math., 42 (2012), pp. 217-228 (UGC CARE LIST GROUP-I).
  66. Vamshee Krishna, D. & RamReddy, T., Hankel determinant for starlike and convex functions of order α, Tbilisi Math. J., 5 (1) (2012), pp. 65-76.

Papers presented in Conferences/ Seminars

  1. “Certain coefficient inequalities associated with Parabolic starlike functions” International  Conference on Pure, Applied & Engineering Mathematical Sciences-2024 (ICPAEMS-2024) from 30-03-2024 to 31-03-2024 organized by Uttara Andhra Society for Mathematical Sciences (UASMS) at Department of Mathematics,  Andhra University, Visakhapatnam, India.
  2. ‘Third-order Hankel Determinant for Transforms of Reciprocal of Bounded turning functions’, National Conference on Recent Developments in Mathematics and it’s Applications (RDMA-2018), from 21-12-2018 to 22-12- 2018 at Department of Mathematics, Dr. B. R. Ambedkar  University, Srikakulam, India.
  3. ‘Second Hankel determinant for the class of Bazilevic Functions’, National Conference on Recent Advances in Mathematics and its Applications (RADMAS-2016), from 17-11-2016 to 18-11-2016 at St. Joseph's College for Women (Autonomous), Visakhapatnam, India.
  4. ‘Second Hankel determinant for reciprocal of starlike and convex functions’, National Conference on Recent Developments in Mathematical Sciences and their Applications to Science &Technology, from 11-12-2015 to 13-12-2015 at Vignana Bharathi Institute of Technology, Hyderabad, India.
  5. ‘Third Hankel determinant for certain subclass of p-  valent  analytic functions’ International Conference on Geometric Function Theory and its Application (ICGFTA-2014), from 18-12-2014 to 21-12-2014 at IIT, Kharagpur, India.
  6. ‘An upper bound to the second Hankel functional for the class of Gamma- starlike functions’, International National Conference on Algebra and Applications (ICAA-2014),     from 29-04-2014 to 01-05-2014 at Andhra University, Visakhapatnam, India.
  7.   ‘An application of Toeplitz determinants for an upper bound to the second Hankel functional for the class of Bazilevic functions’, National Conference on Complex Analysis (NCCA-2014), from 08-03-2014 to 09-03-2014 at Central University of Rajasthan, Rajasthan, India.
  8. ‘Hankel Determinant for Transforms of pre-starlike functions of order α’, International Conference on Recent Advances in Mathematical Sciences and Applications (ICRAMSA -2013), from 24-12-2013 to 26- 12-2013, at Rajiv Gandhi Proudyogiki Vishwavidyalaya, Bhopal, Madhya Pradesh, India.
  9. ‘Neighborhoods of functions in S* (α) and its applications to a certain fractional operator’, XV Congress of Andhra Pradesh Society for Mathematical Sciences (APSMS) (National Conference), from 11-08-2006 to 13-08-2006 at Kakatiya University, Warangal, TS, India.

Participated in Conferences/ Seminars/Workshops

  1. Participated workshop on “Pedagogical Knowledge of Mathematics”(Teaching Linear Algebra) held at Kerala School of Mathematics (KSoM), Kozhikode, Kerala, during 24-26 March, 2018.
  2. Participated in Mission 10X WORKSHOP conducted at Swarna Bharathi College of Engineering, during 7-10 March 2012, Khammam, T.S., India.
  3. Attended a Two- day Workshop on “High Impact  Teaching Skills”, attested by Dale Carnegie & Associates. Inc. Trainer and Wipro, from 5-6  March 2012, conducted at Swarna Bharathi College of  Engineering,  Khammam, T.S., India.

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