**Uaday Singh**Associate professor uaday.singh@ma.iitr.ac.in 01332285430

## Areas of Interest

- Real Analysis, Complex Analysis, Fourier Approximation, Summability

## Professional Background

From | Period | Position | Organisation |
---|---|---|---|

2015-11-23 | Ongoing | Associate Professor | Department of Mathematics, IIT Roorkee |

2010-11-19 | 5 years 3 days | Assistant Professor | Department of Mathematics, IIT Roorkee |

2006-01-21 | 4 years 9 months 28 days | Assistant Professor | Department of Mathematics, Faculty of Science, Banaras Hindu University |

2003-11-10 | 2 years 2 months 10 days | Lecturer in Mathematics | National Council of Educational Research and Training |

## Multiple Posts

From | Period | Position | Organisation |
---|---|---|---|

2019-07-01 | 1 year 11 months 29 days | Member of Library Advisory Committee | IIT Roorkee |

2018-09-01 | 1 year 11 months 30 days | OC Department Library | IIT Roorkee |

2020-09-01 | 1 year 11 months 30 days | Faculty-in-Charge Administration | IIT Roorkee |

2018-07-09 | 1 year 11 months 29 days | Member of Department Administrative Committee | IIT Roorkee |

2019-06-16 | 2 years 14 days | Member of the Panel SRIC for Recruitment of Project/Research Staff | IIT Roorkee |

2018-09-01 | 1 year 11 months 30 days | Member of Department Research Committee | IIT Roorkee |

2016-09-01 | 1 year 11 months 30 days | Member of IAPC | IIT Roorkee |

2019-07-01 | 11 months 29 days | Coordinator, Preparatory Course | IIT Roorkee |

2019-07-01 | 4 years 11 months 29 days | Faculty Advisor for Int. M. Sc. (Applied Mathematics) | IIT Roorkee |

2019-06-04 | 1 year 6 months | Member of Department Management Space Committee | IIT Roorkee |

2019-01-01 | 11 months 30 days | Member of Departmental Faculty Search Committee | IIT Roorkee |

2018-01-01 | 1 year | Member of Departmental Purchase Committee | IIT Roorkee |

2018-07-01 | 11 months 29 days | Member of Anti-Ragging Committee | IIT Roorkee |

2016-09-01 | 1 year 11 months 30 days | Member of Departmental Academic Program Committee | IIT Roorkee |

2016-07-01 | 11 months 29 days | Member of Anti-Ragging Committee | IIT Roorkee |

2014-04-01 | 1 year 9 months | Member of Department Administrative Committee | IIT Roorkee |

2014-01-01 | 2 years | Member of Department Research Commitee | IIT Roorkee |

2015-01-01 | 1 year | Member of Anti-Ragging Committee | IIT Roorkee |

2014-01-01 | 4 years | OC Time Table | IIT Roorkee |

2014-01-01 | 1 year | Member of Anti-Ragging Committee | IIT Roorkee |

2012-01-01 | 2 years | Member of Departmental Academic Program Committee | IIT Roorkee |

2014-07-01 | 3 years 11 months 29 days | Faculty Advisor for Int. M. Sc. (2013-2018) | IIT Roorkee |

## Educational Details

Degree | Subject | University | Year |
---|---|---|---|

Ph. D | Mathematics | Ch. Charan Singh University Meerut and IIT Roorkee | 2007 |

M. Sc. with I division | Mathematics | Ch. Charan Singh University Meerut | 2001 |

## Sponsored Research Projects

Topic | Funding Agency | Start Date | Period |
---|---|---|---|

Fourier Approximation in Certain Function Spaces | SERB, DST Govt. of India | 2014-08-20 | 3 years 11 months 30 days |

Some Problems on Fourier Approximation in Banach Spaces | National Board For Higher Mathematics | 2014-12-22 | 2 years 11 months 29 days |

Pedagogy Course on Engineering Mathematics | MHRD through IIT Khragpur | 2013-04-01 | 2 years 11 months 30 days |

## Memberships

- Forum D’ Analystes, Institute of Mathematical Science Chennai, Life Member
- Indian Mathematical Society, Life Member
- International Society for Analysis, its Applications and Computation, Life Member
- American Mathematical Society, Regular Member till 2021
- Int. Association of Engineers, Life Member
- The Indian Science Congress Association, Life Member
- Forum For Interdisciplinary Mathematics, Life Member

## Teaching Engagements

Title | Course Code | Class Name | Semester |
---|---|---|---|

Real Analysis - I | MA 104 | Int. M.Sc. - I Year | Autumn |

Mathematics-1 | MAN-001 | B. Tech.-I | Autumn |

Linear Algebra | MAN-102 | Int. M. Sc.- I Year | Autumn |

## Projects and Thesis Supervised

Title of Project | Names of Students |
---|---|

Bounds for Trigonometric Polynomials in Two Variables | Ravi Shankar Shukla |

Trigonometric Approximation in Homogeneous Banach Spaces | Akanksha Verma |

A Study of New Inner Product < , > in Real Lp -Space | Deepika Singh |

A Study of Some Summability Methods and their Equivalence | Rohit Patel |

A Study of Trigonometric Series with General Monotone Coefficients and its Convergence in L1 and Lp Norm | Rajan Saini |

Korovkin-type Theorems and Approximation by Positive Linear Operators | Gaurav Sharma |

A modified Fejer and Jackson summability method with respect to orthogonal polynomials | Ankur Malik |

The Evolution of Isoperimetric Problems | Akshay Kumar Jakhar |

Convergence of numerical series of uncertain variable | Dheeraj Kumar |

Trigonometric Interpolation | Dinesh Kumar |

Study of Almost Periodic Functions | Bharat Raj Bairwa |

A Study of Matrix Means of Mellin -Fourier Series | Birendra Singh |

Corrected Fourier Series and Its Application to Function Approximation | Vinod Kumar |

Trigonometric Approximation for Bessel Functions | Raj Kumar Soni |

Maximum Modulus Principal for Non-Analytic Functions Defined in the Unit Disc | Chandani |

## Research Scholar Groups

Scholar Name | Interest |
---|---|

Birendra Singh | Fourier Approximation |

Abhay Pratap Singh | Fourier Approximation |

## PHDs Supervised

Topic | Scholar Name | Status of PHD | Registration Date |
---|---|---|---|

Approximation Theory | Abhay Pratap Singh | O | 2019-07-01 |

Fourier Approximation in Certain Function Spaces | Birendra Singh | O | 2015-01-01 |

Fourier Series Approximation By Linear Operators in Lp Norm | Mrs. Arti | A | 2015-01-01 |

Fourier Series Approximation of Functions in Lp(p>=1)-Spaces | Ms. Soshal | A | 2012-01 |

Some Problems on Trigonometric Approximation in Lp(p>=1)- Spaces | Shailesh Kumar Srivastava | A | 2012-06-01 |

Some Problems on Fourier Approximation in Lp- Spaces | Smita Sonker | A | 2009-01 |

## Visits to outside institutions

Institute Visited | Purpose of Visit | Date |
---|---|---|

University of Zelona Gora, Poland | It was a one month visit. During this visit I worked on some research problem and write a joint research proposal with Prof. W. Lenski and Prof. B. Szal. | 2019-06-15 |

## Participation in short term courses

Couse Name | Sponsored By | Date |
---|---|---|

One Week Short Term Course on Complex Analysis, Fourier Series and Special Functions (Co-convener) | TEQIP, IIT Roorkee | 2017-03 |

QIP Short Term Course on Soft Computing | ISM Dhanbad | 2008-07 |

## Courses or Conferences Organised

Conference Name | Sponsored By | Date |
---|---|---|

International Workshop on Operator Theory and its Applications | IIT Roorkee | 2017-08 |

International Conference on Mathematical Analysis and Its Applications | NBHM, DST, ISAAC, Forunm D'Analytes | 2016-11 |

One Week Short Term Course on Mathematical Analysis and Applications (Co-Convener) | QIP Centre, IIT Roorkee | 2016-07 |

29th International Conference of The Jangjeon Mathematical Society on Number Theory and Special Func | Project Grant | 2016-08 |

International Conference in Mathematical Sciences | Project Grant | 2015-07 |

Second International Conference on Mathematics and Statistics (AUS-ICMS’15) | IIT Roorkee | 2015-04 |

International Conference on Recent Trends on Mathematical Analysis and Applications(Co-convener) | DST, UCOST, ISAAC, QIP, IIT Roorkee | 2014-12 |

7th Conference on Function Spaces | NBHM | 2014-05 |

World Congress on Engineering (WCE-2013) | DST, Govt. of India | 2013-07 |

International Conference on Mathematical Sciences (ICMS-2012) | IIT Roorkee | 2012-12 |

International Congress in Honour of Professor H. M. Srivastava | IIT Roorkee | 2012-08 |

International Conference on Applied Mathematics and Approximation Theory | UGC, New Delhi | 2012-05 |

International Conference on Mathematical Modelling and Scientific Computation | IIT Roorkee | 2012-03 |

International Conference On ‘Optimization and Its Applications | BHU | 2010-02 |

## Special Lectures Delivered

Title | Place | Date |
---|---|---|

INSPIRE camp for School Students | HNB Garhwal University Srinagar | 2020-01 |

INSPIRE camp for school students | HNB Garhwal University Srinagar | 2014-01 |

INSPIRE camp for school students | HNB Garhwal University | 2014-11 |

## JOURNAL PUBLICATIONS

**List of Selected Journal Publications **** (Web of Science Researcher ID AAY-1275-2020, MATHSCINET MR Author ID: 753824)**

1 Uaday Singh, On the trigonometric approximation of functions in a weighted Lipschitz class, J. Anal. (Accepted)

2 W. Łenski, Uaday Singh, B. SZAL, Trigonometric approximation of functions in seminormed spaces, Math. Equal. Appl. (Accepted)

3 Saini, Soshal; Singh, Uaday, Approximation of , conjugate function of f belonging to a subclass of Lp-space by product means of conjugate Fourier series. J. Anal. 28 (2020), no. 1, 155–167.

4 Rathore, Arti; Singh, Uaday, On the degree of approximation of functions in a weighted Lipschitz class by almost matrix summability method. J. Anal. 28 (2020), no. 1, 21–33.

5 Singh, Birendra; Singh, Uaday, Some characterizations of Hausdorff matrices and their application to Fourier approximation. J. Comput. Appl. Math. 367 (2020), 112450, 8 pp.

6 Srivastava, Shailesh Kumar; Singh, Uaday, On T-strong convergence of numerical sequences and Fourier series. Proc. Nat. Acad. Sci. India Sect. A 88 (2018), no. 4, 571–576.

7 Rathore, Arti; Singh, Uaday, Approximation of certain bivariate functions by almost Euler means of double Fourier series. J. Inequal. Appl. 2018, Paper No. 89, 15 pp.

8 Uaday Singh, Arti Rathore, A note on the degree of approximation of functions belonging to certain Lipschitz class by almost Riesz means, Stud. Univ. Babeş-Bolyai Math. 63(3), (2018), 371–379.

9 Singh, Uaday; Saini, Soshal, Approximation of periodic functions in certain sub-classes of Lp[0,2π]. Asian-Eur. J. Math. 10 (2017), no. 3, 1750046, 12 pp.

10 Saini, Soshal; Singh, Uaday, Degree of approximation of functions belonging to Lip(ω(t),p)-class by linear operators based on Fourier series. Boll. Unione Mat. Ital. 9 (2016), no. 4, 495–504.

11 Soshal, Uaday Singh, Approximation of periodic integrable functions in terms of modulus of continuity, Acta et Commentationes Universitatis Tartuensis de Mathematica, 20(1) (2016), 23-34.

12 Singh, Uaday; Srivastava, Shailesh Kumar, Trigonometric approximation of functions belonging to certain Lipschitz classes by C1.T operator. Asian-Eur. J. Math. 7 (2014), no. 4, 1450064, 13 pp.

13 Srivastava, Shailesh Kumar; Singh, Uaday, Trigonometric approximation of periodic functions belonging to Lip(ω(t),p)-class. J. Comput. Appl. Math. 270 (2014), 223–230.

14 Singh, Uaday; Srivastava, Shailesh Kumar, Approximation of conjugate of functions belonging to weighted Lipschitz class W(Lp, ξ(t)) by Hausdorff means of conjugate Fourier series. J. Comput. Appl. Math. 259 (2014), part B, 633–640.

15 Singh, Uaday; Sonker, Smita, Trigonometric approximation of signals (functions) belonging to weighted (Lp, ξ(t))-class by Hausdorff means. J. Appl. Funct. Anal. 8 (2013), no. 1, 37–44.

16 Singh, Uaday; Srivastava, Shailesh Kumar, Degree of approximation of functions in Lipschitz class with Muckenhoupt weights by matrix means. IAENG Int. J. Appl. Math. 43 (2013), no. 4, 190–194.

17 Sonker, Smita; Singh, Uaday, Degree of approximation of the conjugate of signals (functions) belonging to Lip(α,r)-class by (C,1)(E,q) means of conjugate trigonometric Fourier series. J. Inequal. Appl. 2012, 2012:278, 7 pp.

18 Singh, Uaday; Mittal, M. L.; Sonker, Smita, Trigonometric approximation of signals (functions) belonging to W(Lr, ξ(t)) class by matrix (C1.Np) operator. Int. J. Math. Math. Sci. 2012, Art. ID 964101, 11 pp.

19 Mittal, M. L.; Rhoades, B. E.; Sonker, Smita; Singh, U., Approximation of signals of class Lip(α,p) by linear operators. Appl. Math. Comput. 217 (2011), no. 9, 4483–4489.

20 Mittal, M. L.; Singh, Uaday T.C1 summability of a sequence of Fourier coefficients. Appl. Math. Comput. 204 (2008), no. 2, 702–706.

21 Mittal, Madan Lal; Singh, Uaday; Mishra, Vishnu N., On the strong Nörlund summability of conjugate Fourier series. Appl. Math. Comput. 187 (2007), no. 1, 326–331.

22 Mittal, M. L.; Rhoades, B. E.; Mishra, V. N.; Singh, Uaday, Using infinite matrices to approximate functions of class Lip(α,p) using trigonometric polynomials. J. Math. Anal. Appl. 326 (2007), no. 1, 667–676

23 M. L. Mittal, Uaday Singh, Vishnu N. Mishra, Shalini Priti, Saurabh Shyam Mittal, Approximation of functions (signals) belonging to Lip - class by means of conjugate Fourier series using linear operators, Indian Journal of Mathematics, 47 (2 – 3) (2005), 217-229.

24 Shalini Priti, Saurabh Shyam Mittal, Uaday Singh, Vinay Kumar, Approximation of functions by matrix means of Walsh-Fourier series, Advances in Mathematics Research, 5(2003), 31- 45.

## CONFERENCE PUBLICATIONS

**Research Papers in Conference Proceedings:**

1. Shailesh Kumar Srivastava, Uaday Singh, Trigonometric approximation of periodic functions belonging to weighted Lipschitz class W(Lp, Ψ(t), β), Contemporary Mathematics (CONM) Book Series Published by AMS, Vol. 645 (2015), pp. 283-291 [Proceedings of the 7th Conference on Function Spaces at SIUE 2014, Edwardsville, USA held during May 20-24, 2014].

2. Soshal, Uaday Singh, Degree of approximation of fεL[0, ∞) by means of Laguerre – Fourier series, Mathematical Analysis and Its Applications (Vol. 143), pp. 207-217 [Springer Proceedings of ICRTMAA 2014 held at IIT Roorkee during December 21-23, 2014].

3. Uaday Singh, Shailesh Kumar Srivastava, Fourier Approximation of Functions Conjugate to the Functions Belonging to Weighted Lipschtiz Class, Lecture Notes in Engineering and Computer Science, 1(2013), 236-240. [Proceedings of WCE-2013 held at Imperial College of London, July 3-4, 2013].

4. Metric by Matrix Means, Communications in Computer and Information Sciences (Springer-Verlag), 283 (2012), 1-10. [Proceedings of ICMMSC-2012 held at Gandhigram Tamilnadu during March 16-18, 2012].

5. Smita Sonker, Uaday Singh, Approximation of Signals (Functions) Belonging to - Using Trigonometric Polynomials, Procedia Engineering (Elsevier), 38(2012), 1575-1585. [Proceedings of ICMOC-2012 held at Noorul Islam Centre for Higher Education during April 11-12, 2012].

## Books/Chapters/Monographs

1. Uaday Singh, Shailesh Kr. Srivastava, On the Degree of Approximation of Conjugate Functions in Weighted Lipschitz Class, Book chapter accepted for publication in IAENG Transactions on Engineering Sciences by CRC Press/Balkema, Taylor & Francis Group.

2. Uaday Singh, Fourier Approximation in Lp – Spaces (A monograph), VDM Verlag Dr. Müller Aktiengesellschaft & Co. KG, Germany, ISBN-NR 978-3-639-20410-0 (2009).

3. Reviewed the book “Theory and Problems of Complex Variables, SI (metric edition) by Spiegel” for its 2009 Edition.

4. A Chapter entitled STRAIGHT LINES in Mathematics Textbook for Class XI, published by NCERT, New Delhi (2006).

5. A Chapter entitled COORDINATE GEOMETRY in Mathematics Textbook for Class IX, published by NCERT, New Delhi (2006).