Dr. Sushil Kumar, Ph.D.

    Dr. Sushil Kumar

   Head, Department of Applied Science

   IQAC and NBA Coordinator

    Bharati Vidyapeeth’s College of Engineering

    A-4, Paschim Vihar

    Delhi- 110063,  BHARAT

    Email: sushilkumar16n@gmail.com / sushil.kumar@bharatividyapeeth.edu           

    Phone: 011-25278444/25278443 (Ext-226), +91-9810928296

   MR Author ID: 1155986

  Education

    Doctor of  Philosophy  (Mathematics)  

    Thesis Title: Coefficient Estimates and Subordination for Univalent Functions  

    Doctoral advisor:  Prof. V.  Ravichandran

    Department of Mathematics,  University of Delhi, Delhi 110007, India

     Additional Qualification

•  CSIR JRF

  Position Held

• Associate Professor (August 1, 2017 – till date),   Assistant Professor  (April 1, 2010 – July 31, 2017), Lecturer   (August 1, 2006 – March 31, 2010),  Visiting Lecturer (September 5, 2005 – November 19, 2005),  Bharati Vidyapeeth’s College of Engineering, New Delhi, India.                                                                                                                                                                                            

  Membership in Professional Bodies

•  Life Member of Indian Mathematical Society (IMS) and  Ramanujan Mathematical Society (RMS)

•  Member of Society for Industrial and Applied Mathematics (SIAM),  Jan 1, 2017–Dec 31, 2017

  Research field --       Complex Analysis ( Geometric Function Theory)

• Special Classes of Univalent  Functions

• Coefficient and Radius  Problems for  Univalent Functions

• Differential Subordinations.

  h-index  

• Google Scholar- 11, Research Gate- 11, Scopus- 8

Best Researcher award

• Received consecutive 7 years (since 2016-17) from the BVCOE, New Delhi.

  Research Publications

1. Sushil Kumar*, R. K. Pandey and Pratima Rai, Certain Sharp Estimates of Ozaki close-toconvex functions, Asian-European Journal of Mathematics , https://doi.org/10.1142/S1793557124500475, Accepted (April 19, 2024). Indexing: SCOPUS, ESCI, zbMATH

2. S. Anand, Pratima Rai and Sushil Kumar*, Close-to-convex functions associated with a rational function, Math. Slovaca 74 (2024), no. 2, 339–354. Indexing: Mathematical Reviews 4749967, SCIE, SCOPUS, zbMATH, Impact factor: 1.6, MCQ=0.37

3. M. Sharma, N. K. Jain and Sushil Kumar*, Starlikeness of analytic functions using special functions and subordination, Bol. Soc. Mat. Mex. 30, 55 (2024). https://doi.org/10.1007/s40590-024-00630-7 Indexing: Mathematical Reviews 4751712, ESCI, SCOPUS, zbMATH, MCQ=0.39

4. Om. P. Ahuja, A. Cetinkaya and Sushil Kumar, Certain properties of starlike functions associated with Hyperbolic Cosine function, Commun. Korean Math. Soc.,  2024; 39(2): 407-420 . Indexing: SCOPUS, ESCI, zbMATH

5. R. M. Ali, Sushil Kumar and V. Ravichandran, The Third Hermitian-Toeplitz and Hankel Determinants for Parabolic Starlike Functions, Bull. Korean Math. Soc. 60 (2023), no.~2, 281--291..  Indexing: SCIE, SCOPUS, zbMATH, UGC-CARE. Impact factor: 0.467.

6. P. Rai and Sushil Kumar*, Coefficient inequalities for a subfamily of Sakaguchi functions, Asian Eur. J. Math. 16 (2023), no. 5, Paper No. 2350084, 15 pp.   Indexing: SCOPUS, ESCI, zbMATH

7. M. Sharma, Sushil Kumar and N. K. Jain, Differential Subordination implications for Certain Caratheodory functions, Studia Universitatis Babe-Bolyai Mathematica, 68(2023), no. 4, 775– 787.  Indexing: SCOPUS, ESCI, zbMATH

8. Sushil Kumar and P. Rai, and A. Cetinkaya, Bound on Hankel determinants H(2)^4 (f) and H(3)^4 (f) for Lemniscate  starlike functions,  Honam Math. J.,  45 (2023),  No. 1,  pp. 92-108. Indexing: ESCI,  zbMATH

9. P. Rai, A. Cetinkaya and Sushil Kumar*, Starlike functions associated with tanh z and Bernardi integral operator, Mathematical Foundations of Computing, 6 (2023), no. 3, 573-585. Indexing: SCOPUS, ESCI, zbMATH

10. S. Anand,  N. K. Jain and Sushil Kumar, Normalized analytic functions with fixed second coefficient, J. Anal.31(2023), no.3, 1917–1938. . https://doi.org/10.1007/s41478-022-00544-5 .   Indexing: SCOPUS, ESCI, zbMATH, UGC-CARE.

11. Sushil Kumar, S. Anand, and N. K. Jain, Hankel and Symmetric Toeplitz determinants for Sakaguchi starlike functions, Stud. Univ. Babes¸-Bolyai Math., Accepted (June 23, 2022). Indexing: SCOPUS, ESCI, zbMATH

12. Sushil Kumar and A. Cetinkaya, Coefficient inequalities for certain starlike and convex functions, Hacet. J. Math. Stat., 51(1) (2022), 156–171. DOI : 10.15672/hujms.778148.    Indexing: SCIE, SCOPUS, zbMATH, Impact factor: 0.929.

13. Sushil Kumar and V. Kumar, Sharp estimates on Hermitian–Toeplitz Determinant for Sakaguchi classes, Commun. Korean Math. Soc., 37 (2022), No. 4, pp. 1041-1053. Indexing: SCOPUS, ESCI, zbMATH

14. H. M. Srivastava, Sushil Kumar, V. Kumar and N. E. Cho, Hermitian-Toeplitz and Hankel determinants for starlike functions associated with a rational function, J. Nonlinear Convex Anal. 23 (2022), no. 12, 2815-2833. Indexing: SCIE, SCOPUS, zbMATH, Impact factor: 1.075.

15. S. Anand, N. K. Jain, and Sushil Kumar, Certain estimates of normalized analytic functions, Math. Slovaca 72 (2022), no. 1, 85–102. DOI: 10.1515/ms-2022-0006.  Indexing: SCIE, SCOPUS, zbMATH, Impact factor: 1.6

16. A. Naz, Sushil Kumar and V. Ravichandran, Coefficient functionals and radius problems of certain starlike functions, Asian-Eur. J. Math. 15 (2022), no. 5, Paper No. 2250089, 19 pp.  Indexing: ESCI, SCOPUS, zbMATH

17. V. Kumar, Sushil Kumar and N. E. Cho, Coefficient functionals for starlike functions of reciprocal order, Thai J. Math. 20 (2022), no. 3, 1183–1197. Indexing: SCOPUS, ESCI, zbMATH

18. N. E. Cho, Sushil Kumar and V. Kumar, Hermitian-Toeplitz and Hankel determinants for certain starlike functions, Asian-Eur. J. Math. 15 (2022), no. 3, Paper No. 2250062, 16 pp. Indexing:  ESCI, SCOPUS, zbMATH  

19. M. Sharma, Sushil Kumar and N. K. Jain, Differential Subordinations for functions with positive real part using Admissibility conditions,  Asian-Eur. J. Math. 15 (2022), no. 4, Paper No. 2250042, 15 pp. Indexing:  ESCI, SCOPUS, zbMATH 

20. Sushil Kumar, P.  Rai and A. Cetinkaya, Radius Estimates of Certain Analytic Functions,  Honam Math. J. 43 (2021), no. 4, 627–639.  Indexing:  ESCI, zbMATH     

21. S. Anand, Sushil Kumar, and V. Ravichandran,  Differential Subordination for Janowski  Functions with Positive Real Part, Studia Universitatis Babeş-Bolyai Mathematica,  66(2021), no. 3, 457–-470. Indexing:  ESCI,   SCOPUS ,  zbMATH                                                                                                                                                  

22. V. Kumar and Sushil Kumar, Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions, Bol. Soc. Mat. Mex. (3) 27 (2021), no. 2, Paper No. 55. Indexing: ESCI, SCOPUS , zbMATH               

23. S. Anand, N. K. Jain, and Sushil Kumar, Sharp Bohr Radius Constants for Certain Analytic Functions, Bull. Malays. Math. Sci. Soc. 44 (2021), no. 3, 1771–1785. Indexing: SCIE, SCOPUS, zbMATH

24. Om P. Ahuja, Sushil Kumar, and A. Cetinkaya, Normalized Multivalent functions involving some entire Functions, Acta Univ. Apulensis Math. Inform. No. 67 (2021), 111–123. Indexing: Mathematical Reviews, zbMATH 

25. N. Bohra, Sushil Kumar and V. Ravichandran, Applications of Briot Bouquet differential subordination,   J.  Class. Anal. 18 (2021), no. 1, 17–28.  Indexing: Mathematical Reviews, zbMATH                                                                                                                                                  

26. Om Ahuja, N. Bohra, A. Cetinkaya and Sushil Kumar, Univalent functions associated with the symmetric points and cardioid-shaped domain involving (p,q)-calculus, Kyungpook Math. J. 61(2021), 75–98. Indexing: ESCI, SCOPUS , zbMATH                                                                                                                                                                                                   

27. V. Kumar, Sushil Kumar and V. Ravichandran, Third Hankel Determinant for Certain Classes of Analytic Functions. In: Deo N., Gupta V., Acu A., Agrawal P. (eds) Mathematical Analysis I: Approximation Theory. ICRAPAM 2018. Springer Proceedings in Mathematics and Statistics, (2020),  vol 306, 22–231, Springer, Singapore.   Indexing:  SCOPUS , zbMATH                                                                                                                        

28. S. Anand, Sushil Kumar and V. Ravichandran(2020), First-Order Differential Subordinations for Janowski Starlikeness. In: Deo N., Gupta V., Acu A., Agrawal P. (eds) Mathematical Analysis I: Approximation Theory. ICRAPAM 2018. Springer Proceedings in  Mathematics and Statistics, (2020),  vol 306, 185–196, Springer, Singapore.   Indexing:  SCOPUS , zbMATH                                                                                              

29. N. Bohra, Sushil Kumar, and V. Ravichandran, Some Special Differential Subordinations, Hacet. J. Math. Stat., 48(4) (2019), 1017–1034. DOI : 10.15672/HJMS.2018.570.   Indexing: SCIE, SCOPUS, zbMATH, Impact factor: 0.929.

30. N. E. Cho, Sushil Kumar, V. Kumar and V. Ravichandran, Convolution and Radius problems of analytic functions associated with the Tilted Carathéodory functions, Mathematical Communications, 24, (2019), 165--179.  Indexing: SCIE, SCOPUS, zbMATH                                                                                                        

31. N. E. Cho,  Sushil Kumar, V. Kumar, V. Ravichandran and H. M. Srivastava, Starlike functions related to the Bell numbers, Symmetry, 11, (2019), no. 2. Article 219, 1--17.  Indexing: SCIE, SCOPUS, zbMATH

32. Om P. Ahuja, Sushil Kumar and V. Ravichandran, Applications of First Order Differential Subordination for Functions with Positive Real Part, Studia Universitatis Babe-Bolyai Mathematica,  63(2018), no. 3, 303–311. Indexing:  ESCI, SCOPUS, zbMATH

33. Sushil Kumar, and V. Ravichandran, Subordinations for Functions with Positive Real Part, Complex Anal. Oper. Theory, 12 (2018), no. 5, 1179–1191. Indexing: SCIE, SCOPUS, zbMATH

34. N. E. Cho, Sushil Kumar, V. Kumar and V. Ravichandran, Differential Subordination and Radius Estimates for starlike functions associated with Booth lemniscate, Turkish J Math., 42 (2018), 1380–1399.  Indexing: SCIE, SCOPUS, zbMATH 

35. S. Gandhi, Sushil Kumar and V. Ravichandran, First Order Differential Subordinations for Caratheodory Functions, Kyungpook Math. J. 58 (2018), 257–270. Indexing: ESCI, SCOPUS, zbMATH

36. Sushil Kumar, V. Ravichandran, and S. Verma, Initial coefficients of starlike functions with real coefficient, Bull. Iranian Math. Soc., 43 (2017), no. 6, 1837–1854. Indexing: SCIE, SCOPUS, zbMATH

37. Sushil Kumar and V. Ravichandran, Functions defined by coefficient inequalities, Malays. J. Math. Sci., 11 (2017) no. 3, 365-375. Indexing: SCOPUS, zbMATH

38. Sushil Kumar, S. Nagpal and V. Ravichandran, Coefficient Inequality for Janowski Starlikeness,  Proc. Jangjeon Math. Soc., 19 (2016), No. 1. pp. 83-100. Indexing: SCOPUS, zbMATH

39. Sushil Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2016) pp.199-212. Indexing: ESCI, zbMATH

Edited Book  and Chapters

• Topics in Mathematical Sciences, (2017), Centre for Professional Development in Higher Education(CPDHE), UGC-HRDC, University of Delhi, Delhi. (ISBN 978-81-93451-96-0).

• Sushil Kumar, and P. Rai, Eigenvalues and Mean of the matrices, Topics in Mathematical Sciences, (2017), Centre for Professional Development in Higher Education(CPDHE), UGC-HRDC, University of Delhi, Delhi.                                                                                

• P. Rai and Sushil Kumar, Matrices: Eigenvalues and its application in Numerical Analysis , Topics in Mathematical Sciences, (2017), Centre for Professional Development in Higher Education(CPDHE), UGC-HRDC, University of Delhi, Delhi.             

 Associate Editor 

• Journal of Multi Disciplinary Engineering Technologies, October 2017--September 2021.

 Talks delivered/ Paper presented

1. Title: Estimates on Hermitian-Toeplitz and Hankel determinants of certain starlike functions, International conference on Analysis and its Applications  (ICAA-24), Department of Mathematics, Jamia Millia Islamia, New Delhi, India, January 19–21, 2024. 

2. Title: Coefficient functionals and subordination properties of certain analytic functions, International Conference on Pure and Applied Mathematics (ICPAM-23), Department of Mathematics, Dr. B.R.Ambedkar NIT Jalandhar and MNIT Jaipur, India, October 26-28, 2023.

3. Title: Starlike functions associated with certain Caratheodory functions, The 2nd (Hybrid) International Conference on Orthogonal Polynomials, Special Functions and Computer Algebra: Applications in Engineering(OPSFCA-22), Department of Mathematics, Anand International College of Engineering, Jaipur, India, October 15-16, 2022.

4. Title: Properties of certain functions associated with the right half plane, its applications and generalizations, VIII International Conference of Mathematics and Computer Science ”Congressio-Mathematica”, Department of Complex Analysis, Faculty of Mathematics and Computer Sciences, University of Warmia and Mazury in Olsztyn, Poland, September 19-25, 2022.

5. Title: Certain starlike functions associated with right half plane, 69th Annual National conference on ”Advances in Mathematics and its Applications”, Bharata Ganita Parisad (BGP) and Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India, September 24-25, 2022.

6. Title: Zeros of Analytic Functions, Complex Integration, Cauchy’s Theorem,   Two Days Workshop on "Recent Trends in Complex Analysis" , Department of Mathematics, J C Bose University of Science and Technology YMCA,  Faridabad , Haryana, India, February 09-10, 2022.

7. Title: Coefficients Estimates of Certain Univalent Functions, International Conference on Recent Advances in Mathematics and Computational Engineering, Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam, Tamil Nadu, India, January 06-07, 2022.

8. Title:  Geometric properties of certain Starlike functions, One Day International Symposium on Mathematical Analysis on National Mathematics Day, Department of Mathematics, ASAS Amity University Haryana (AUH), Gurugram. India, December 22, 2021.

9. Title: Univalent Starlike functions defined by differential subordination, International Conference on Special Functions and Applications (ICSFA-2021), Department of Mathematics, University of Kerala, Kerala, December 22-24, 2021.

10. Title: Certain Estimates of Univalent functions associated with functions with positive real par, The 87th Annual Session of the Indian Mathematical Society -an International Meet,  Department of Applied Sciences, Jawaharlal Nehru Engineering College, MGM University, Aurangabad , Maharashtra, December 04-07, 2021.     

11. Title: Normalized Univalent functions associated with Geometric properties of Cardioid, National conference on New Trends in Applied Mathematics, Department of Mathematics, University Institute of Engineering and Technology, Chhatrapati Shahu Ji Maharaj University, Kanpur, India, October 11-12, 2021.

12. Title: Certain Geometric properties of Starlike functions associated with Cardioid shaped region, Ramanujan Mathematical Society, 36th Annual Conference, Department of Mathematics, Amrita Vishwa Vidyapeetham, Coimbatore, India, August 5-7, 2021.                                    

13. Title: Starlikeness of certain Caratheodory functions using Subordination,  Ramanujan Mathematical Society, 35th Annual Conference,   Department of Mathematics, Central University of Rajasthan, Kishangarh, Ajmer- 305817, India, December 28-30, 2020.                                                                                        

14. Title: (p, q)-starlike and convex functions w.r.t. Symmetric points associated with a rational functions, International Conference on Special functions and Applications, XIX Anual Conference of Society for special functions and their Applications, Department of Mathematics and Computer Sciences, Babu Banarasi Das University, Lucknow, India, December 22-23  2020.                                                                                                                                                

15. Title: Differential subordination for certain Caratheodory functions, The VI Conference of mathematics and computer science CONGRESSIO-MATHEMATICA, Department of Complex Analysis, Faculty of Mathematics and Computer Sciences, University of Warmia and Mazury in Olsztyn, Poland, November 21-22, 28-29– 2020.                                                                                                                   

16. Title: Starlike functions associated with the right half plane, National Conference on Advances in Mathematical Analysis and its Applications, Department of Mathematics, PGDAV College (University of Delhi), Delhi,  November 8-10, 2019.                                                         

17. Title: Radii of convexity and starlikeness of certain functions with positive real part, The 84th Annual Conference of Indian Mathematical Society: An International Meet, School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, November 26-30, 2018.                                                                                                                                                                                                                      

18. Title: Third Hankel Determinant For Certain Classes of Analytic Functions, International Conference on Recent Advances in Pure and Applied Mathematics, Department of Applied Mathematics, Delhi Technological University, Delhi, October 23-25, 2018.

19. Title: Geometric Aspects of Starlike Functions associated with the Bell Numbers, The 33rd Annual Conference of the Ramanujan Mathematical Society, Department of Mathematics, University of Delhi, New Delhi, June 1-3, 2018. 

20. Title: First Order Differential Subordination in the Theory of Univalent Functions, International Conference on Current trends in Theoretical and Computational Differential Equations and Applications, Department of Mathematics, South Asian University, New Delhi, December 1-5, 2017. 

21. Title: Radius Estimates of Starlike Functions with Positive Real Part, International Conference on Differential Geometry, Algebra and Analysis, Department of Mathematics, Jamia-Millia Islamia Central University, New Delhi, November 15-17, 2016.                                        

22. Title: Radius Constants of Analytic Functions with Certain Coefficient Inequalities, National Conference on Algebra, Analysis, Coding and Cryptography, Department of Mathematics, University of Delhi, Delhi, October 14-15, 2016.                                                                          

23. Title: Geometric Constants of Starlike Rational Functions, International Conference on Special Function and Applications, Faculty of Engineering and Technology, Jamia-Millia Islamia Central University, New Delhi, September 9-11, 2016.                                                                   

24. Title: Janowski starlikeness of meromorphic rational functions,South Asian Mathematics Research Scholars Meet, Department of Mathematics, South Asian    University, New Delhi, May 8-9, 2015.                                                                                                                              

25. Title: On Starlikeness of Univalent Rational function, International Conference on Advances in Mathematical Sciences, Khalsa College, Patiala, Panjab, March 19–21, 2015.                                                                                                                                                                             

26. Title: Bounds for the initial coefficients of starlike functions with real coefficient, Research Scholar Seminar, Department of Mathematics, University of Delhi, Delhi, February 24-25, 2015.   

27. Title: On A-Frames, International Workshop on Wavelets and Frames and its Application, Kirorimal College, University of Delhi, Delhi, December 15-21, 2011

28.  Title: On Weak Quasi Differential Maps, International Conference on Analysis and its Application, Department of Mathematics, Aligarh Muslim University, Aligarh, November 19-21, 2011.                                                                                                                               

Workshop Organized

• Convener, One-week Faculty Development Program (Hybrid Mode) on  Importance of Accreditation, Outcome-Based Education (OBE) and NEP-2020 in Higher education, Bharati Vidyapeeth’s College of Engineering, New Delhi,  May 27-31, 2024.

• Co-convener,  One day Research Conclave on Methodology of Research Paper Writing and LaTeX, Bharati Vidyapeeth’s College of Engineering, New Delhi, February 26, 2018.

      Participation in Conferences, Workshops and Instructional Schools of NBHM   =  13

   AT Bharati Vidyapeeth's College of Engineering, New Delhi  

  Courses taught: 

• Engineering Mathematics covers Real Analysis, Calculus, Linear Algebra, Ordinary and Partial Differential Equation,  Linear Programming, Statistics, Fourier Series, Fourier Transforms, Z-transform, Difference Equation, Numerical Analysis,  Engineering Mathematics covers Calculus in R^2, Complex Analysis, Laplace Transform, and  Vector Calculus, Fundamental of Computer Science

  Administrative Responsibilities:

• Head, Department of Applied Science, October 5, 2018–till date.

• Chief Coordinator, College National Board Accreditation(NBA) Since July 2018-to date.

• Head, Academic Accreditation Committee, November 20, 2018–till date.

• Nodal Officer of the College for National Institutional Ranking Framework-2019, 2020, 2021, 2022, 2023, 2024.

• Nodal Officer of  the College for  Atal Ranking of Institutions on Innovation Achievements-2019, 2020.

• Coordinator, College IQAC,  July 2017- February 2019 and July 2021-to date.

• In charge- National Institutional Ranking Framework (NIRF) Cell, December 07, 2015–November 20, 2018.

• In charge- Time-Table and Load Distribution Committee, April 1, 2012–November 11, 2013.

• Executive Member-Library Committee, July 22, 2019-August 31, 2022.