Complex Analysis, Geometric function theory.

1. Assistant Professor in Sambalpur University, Odisha, India with effect from Nov. 2009 – till date.
2. Post-Doctoral Research, University of Pretoria, South Africa, with effect from Aug. 2012– July 2014 (via study leave from Sambalpur University).
3. Assistant Professor of Mathematics, Krupajal Engineering College, Bhubaneswar, Odisha, India, from 4th Aug. 2009 – 15th Nov. 2009.
4. Junior/Senior Research Fellow in a NBHM, DAE, Govt. of India, sponsored research project at Berhampur University, Odisha, India, from Dec. 2007 – Dec. 2008.
5. CSIR Senior Research Fellow, Govt. of India from April 2008 – July 2009.

Post Graduate Level

:

Real Analysis, Complex Analysis, Measure & Integration, Advanced Complex Analysis, Geometric Function Theory, Advanced Analysis, Numerical Analysis, Mathematical Methods

1. Geometric Function Theory, Univalent and Harmonic Univalent Functions, Special Functions, q-Series, Orthogonal Polynomials on the Real Line.

Ph.D. Candidates	:	04 (3awarded + 1 continuing)
M.Tech./M.Phil. Candidates	:	M.Phil. : 12

1. Post-Doctoral Research Fellowship, University of Pretoria, South Africa, with effect from Aug. 2012– July 2014.
2. CSIR Senior Research Fellowship, Govt. of India from April 2008 – July 2009
3. 43rd foundation day award for outstanding research publication in 2008 of the Berhampur University
4. Professor Ghanasyam Samal memorial award for Best Paper Presentations on 34th Annual Conference of Orissa Mathematical Society in 2007
5. 42nd foundation day award for outstanding research publication in 2007 of the Berhampur University
6. Selected for 41st foundation day award for outstanding research publication in 2006 of the Berhampur University

1. Member of Research Group in Mathematical Inequality and Applications (RGMIA), Australia.
2. Life Member of Orissa Mathematical Society, Odisha, India.
3. Life Member of Ramanujan Mathematical Society, India.
4. Life Member of Society for Special Functions and Applications, India.
5. Life Member of Indian Mathematical Society, India (L/2019/17)
6. Annual member of the American Mathematical Society.
7. Annual Member of Allahabad Mathematical Society.

1. Completed the project entitled "Coefficient estimates and raddii related problems in univalent functions theory", funded by Odisha State Higher Education Council, DHE, Govt. of Odisha. (Rs. 3,52,000/-).
2. Completed the project entitled "Studies on univalent and multivalent functions in the context of geometric functions theory", funded by DST, Govt. of India. (Rs. 11,52,000/-)

International Publications

2023
1. P. P. Kar, K. Jordaan and P. Gochhayat, Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences. Numerical Algorithm, 92, 723—746 (2023)
2022
2. P. P. Kar and P. Gochhayat, Zeros of quasi-orthogonal q-Laguerre polynomials. Journal of Mathematical Analysis and Applications, 506(1), 125605, (2022)
3. H. M. Srivastava, A. Prajapati and P. Gochhayat, Integral means and Yamashita’s conjecture associated with the Janowski type (j,k)-symmetric starlike functions. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116: 165; 1–22 (2022).
4. P. Gochhayat and S. Mahata, Geometric properties of certain subclass of close-to-Convex harmonic map pings. Vietnam Journal of Mathematics, (2022).
5. P.P. Kar and P. Gochhayat, Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials. Numerical Algorithm, 93, 1157—1170 (2022).
2021
6. P. Gochhayat, A. Prajapati and A. K. Sahoo, Coefficient estimates of certain subclasses of analytic functions associated with Hohlov operator. Asian-European Journal of Mathematics, 14(2), 2150021 (2021).
7. P. Gochhayat and A. Prajapati, Geometric properties of (j,k)-symmetric functions related to starlike and convex functions. Communication in Korean Mathematical Society, 37(2), 455–472, (2021).
2020
8. A.K. Mishra, A. Prajapati and P. Gochhayat, Third order differential subordination and superordination results associated with Hohlov operator. Tbilisi Mathematical Journal, 13(3), 95–109, (2020).
9. P. P. Kar, K. Jordaan, P. Gochhayat and M.K. Nangho, Quasi-orthogonality and zeros of some ${}_2phi_2$ and ${}_3phi_2$ polynomials. Journal of Computational and Applied Mathematics, 377(15), 112910, (2020).
2019
10. B.K.Chinhara, P. Gochhayat and S. Maharana, On certain harmonic mappings with fixed coefficients, Monatshefte Für Mathematik, 190, 261–280, (2019).
11. B. K. Chinhara, P. Gochhayat and S. Maharana, A subclasses of harmonic univalent mappings with restricted analytic part, Commun. Korean Math. Soc. 34(3), 841–854, (2019).
12. A.Prajapati and P.Gochhayat, Applications of third order differential subordination and superordination results associated with Struve functions, Filomat 33(10), (2019).
2018
13. B. K. Chinhara, P. Gochhayat and A. K. Mishra, Certain subclasses of harmonic multivalent functions involving an integral operator, Int. J. Open Problems Complex Analysis, 10(3), 1–18, (2018).
14. H. M. Srivastava, A. Prajapati, and P. Gochhayat, Applications of third order differential subordination and superordination results associated with Srivastava-Attiya operator. Appl. Math. Inf. Sci. 12(3), 469–481 (2018).
2016
15. P. Gochhayat, K. H. Jordaan, K. Raghavendar and A. Swaminathan, Interlacing properties and bounds for zeros of $_2phi_1$ hypergeometric and little q-Jacobi polynomials. Ramanujan J. 40(1), 45–62, (2016).
2015
16. P. Gochhayat, Inclusion properties of certain subclass of multivalent functions defined by generalized derivative operator, Advances in Mathematics: Scientific Journal, 4(2), 221–227, (2015).
2013
17. P. Gochhayat, Sandwich-type theorem for class of functions defined by generalized differential operator. Math. Vesnik, 64(2), pp 178–186, (2013).
18. P. Gochhayat, Convolution properties of p-valent functions associated with a generalization of the Srivastava-Attiya operator, Journal of Complex Analysis, Volume 2013, Art. ID 676027, (2013).
19. A. K. Mishra and P. Gochhayat, Sandwich-type theorems of some subclasses of multivalent functions defined by an adaptation to Srivastava-Attya operator. PanAmerican Math J, 23(1), 25–43, (2013).
2012
20. P. Gochhayat, Sandwich-type theorems of some subclasses of multivalent functions defined by Dziok Srivastava operator. Acta Universitatis Apulensis, 32, 31–47, (2012).
2011
21. A. K. Mishra and P. Gochhayat, A coefficient inequality for a subclass of the Caratheodory functions defined using conical domains, Computers and Mathematics with Applications, 61(9), 2816–2820, (2011).
2010
22. H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Applied Math. Letters, 23, 1188–1192 (2010).
23. A. K. Mishra and P.Gochhayat, Fekete-Szegö problem for a class defined by an integral operator. Kodai Journal of Mathematics, 33, 310–328, (2010).
24. A.K. Mishra and P.Gochhayat, Invariance of some subclasses of multivalent functions under a differintegral operator. Complex Variables and Elliptic Equations, 55(7), 677–689, (2010).
2008
25. A. K. Mishra and P. Gochhayat, Second Hankel determinant of a class of analytic functions defined by fractional derivative. International Journal of Mathematics and Mathematical Sciences, Volume 2008, Art. ID 153280, 10 pages, (2008).
26. A. K. Mishra and P. Gochhayat, Fekete-Szegö problem for k-uniformly convex functions and for a class defined by the Owa-Srivastava operator. Journal of Mathematical Analysis and Applications, 347, 563–572, (2008).
2006
27. A. K. Mishra and P.Gochhayat, Applications of the Owa-Srivastava operator to the class of k-uniformly convex functions. Fractional Calculus and Applied Analysis; An International Journal for Theory and Applications, 9(4), 323–332, (2006).
28. A. K. Mishra and P. Gochhayat, Coefficient of inverse functions in a nested class of starlike functions of positive order. Journal of Inequalities in Pure and Applied Mathematics, 7(3), Art. 94, (2006).

International Conferences

1. Presented a paper entitled Applications of certain fractional differential operator to a class of k-uniformly convex functions in the International Conference on Geometric Function Theory, Special Functions and Applications, held at Pondicherry during January 02-05, 2006.
2. Presented a paper entitled Fekete-Szegö inequality for a class defined by fractional derivative in the International Conference on Special functions and Applications, held at MNIT, Jaipur, India, during December 15-16, 2007.
3. Presented a paper entitled Sandwich-type theorem for a class of functions defined by generalized differential operator in Pre-ICM International Convention on Mathematical Science, held at University of Delhi, during December 18-20, 2008.
4. Presented a paper entitled Sandwich-type theorems for some subclasses of multivalent functions associated with differential operator in ICM2010, Hyderabad, held, during August 19-27, 2010.
5. Presented a paper entitled Sandwich-type theorems of some subclasses of multivalent functions defined by Dziok-Srivastava operator in the Joint International conference of American and South African Mathematical Society, held at Nelson Mandela Metropolitan University, Port Elizabeth, South Africa during 28th Nov, 2011 to 2nd Dec.2011.
6. Presented a paper entitled Sandwich-type theorems and convolution properties of some subclasses of multivalent functions defined by an adaptation to Srivastava-Attiya operator in the Annual conference of South African Mathematical Society, held at University of Stellenbosch, South Africa during 30th Oct., 2012 to 2nd Nov., 2012.
7. Presented a paper entitled Typically real functions and their connection to Chebyshev polynomials in the Research Seminar: Orthogonal Polynomials and Special Functions a Complex Analytic Perspective, University of Pretoria, South Africa on 12th Nov., 2012.
8. Presented a paper entitled On certain subclasses of multivalent functions in the International conference of Computational Methods and Functions Theory (CMFT2013), held at Shantou University, Shantou, China, during 10-14, June 2013.
9. Presented a paper entitled Inclusion properties of certain subclasses of multivalent functions defined by generalized derivative operator in the International symposium of Geometric function theory and applications (GFTA2015), held at Cr. Cryil Methodius University, Ohrid, Macedonia, during 24-27, August 2015.
10. Presented a paper entitled "On harmonic univalent mappings" in the International Conferences on Mathematical Sciences and Applications (ICMSA2018), held at Guru Ghasidas Vishwavidyalaya, Bilaspur, India during February 23-25, 2018.
11. Invited talk on Partial sum and geometric properties of certain family of harmonic mappings in International Webinar on Recent Trends in Geometric Functions Theory and Applications at KIIT Deemed to be University, Odisha, India during 18-21, September, 2020.

National Conferences

1. Presented a paper entitled Coefficient of inverse functions in a nested class of starlike functions of positive order in the 32nd Annual Conference of Orissa Mathematical Society and National Conference on Mathematical Analysis and Applications, held at NIST, Berhampur, Odisha, India during February 05-06, 2005
2. Presented a paper entitled Coefficient of inverse functions in a nested class of starlike functions of positive order at the XII-Ramanujan Symposium on Recent Trend in Analysis, held at Ramanujan Institute for Advance Study in Mathematics, University of Madras, India during March 02-04, 2005
3. Presented a paper entitled Applications of certain fractional differential operator to a class of k-uniformly con- vex functions in the National Seminar on Analysis and Application, organized by Dept. of Mathematics, Utkal University, Vani Vihar, Odisha, India during March 30-31, 2006.
4. Presented a paper entitled On certain subclass of analytic functions defined by fractional derivatives in the National Conference on Mathematical Analysis and its Applications in Real-World Problems, held at Berhampur University during September, 16-17, 2006.
5. Presented a paper entitled A coefficient inequality for k-uniformly convex functions in the 34th Annual Conference of Orissa Mathematical Society, held at Vyasanagar College, Jajpur, Odisha, India, during January, 28-29, 2007.
6. Presented a paper entitled Certain Subclasses of Bi-univalent functions in the 35th Annual Conference of Orissa Mathematical Society, held at Sailavala Women’s College, Cuttack, Odisha, India during February 02-03, 2008
7. Presented a paper entitled Sandwich-type theorems of some subclasses of multivalent functions defined by Dziok-Srivastava operator in the 36th Annual Conference of Orissa Mathematical Society, held at Institute of Mathematics and Applications, Bhubaneswar, Orissa, India, during February 08-09, 2009.
8. Presented a paper entitled Sandwich-type theorems for some subclasses of multivalent functions associated with Dziok-Srivastava operator in National seminar on Advances in complex analysis and special functions, Central university of Rajasthan, held, during March 12-13, 2011.
9. Invited talk on "An extension of Chebyshev Polynomials" in the Department of Mathematics, Berhampur University, Odisha, India, during 21-22, December, 2012.
10. Invited talk on LaTeX in the National workshop on LaTeX, at Institute of Mathematics and Applications, Bhubaneswar, Odisha, India, during 23-24, March, 2018
11. Invited talk on Harmonic analogue of analytic univalent mappings in a National seminar at CTET, Bhilai, India on Dec. 22, 2018.
12. Delivered series of lectures on Complex Analysis at Department of Mathematics, Central University of Odisha, India during Sept. 2-6, 2019.
13. OURIIP project review presentation On coefficients and radii related problems on certain subclasses of har- monic mappings at Odisha Research Conclave (ORC2021), at Utkal university, Bhubaneswar, Odisha, India during 13-14, November 2021.
14. OURIIP project review presentation on Odisha Research Conclave (ORC2022), at Ravenshaw university, Cuttack, Odisha, India during 16-18, November 2022.

Workshops

1. National Workshop on Graph Theory and Applications, held at NERIST, Nirjuli, Itanager, Arunachal Pradesh during 09-16, October 2006
2. Advanced Training Program for Lecturer in Multivariable Calculus held at University of Pune during November 6-18, 2006
3. CMFT Workshop on Complex Analysis, held at DBI, Kharguli, Guwahati, and Organized by IASST, Guwahati, Assam, during 03-10, Jan. 2008
4. Advanced Instructional School in Complex Analysis held at Bhaskaracharya Pratisthana, Pune, from 5th June 2008 to 2nd July 2008.
5. International workshop on Harmonic Mappings and Hyperbolic Metrics, at IIT Madras, Chennai, during 10–19 Dec. 2009
6. Refresher Course on Mathematics and Statistics, at Sambalpur University, Odisha, India, during 4–24 Feb. 2010.
7. MTTS program at RIE, Mysore as tutor from 17th May 2010 to 12th June 2010.
8. Instructional schools for lecturers on Real analysis and measure theory at University of Delhi, during 26th Mar. 2012 to 7th Apr. 2012
9. School and workshop in Complex Analysis, Geometry and Dynamics, at ICTP, Trieste, Italy, during 21st Sept. 2015 to 3rd Oct. 2015.
10. Orientation Course, at HRDC, Sambalpur University, Odisha, India, during 3rd Nov. 2016 to 30th Nov. 2016.
11. Refresher Course in Mathematics, at HRDC, Devi Ahilya Vishwavidyalaya, Indore, M.P., India, during 27th July 2018 to 16th Aug. 2018.
12. 1st International course on Orthogonal Polynomials and Special Functions: from one to several variables, at Anand-ICE, Jaipur, Rajasthan, India during March 5-7, 2019
13. Participated in TEQIP sponsored workshop on Mathematica as a teaching aid, at IIT Roorkee, India, during June 10–14, 2019
14. Participated in online International Faculty Development Programme on "Recent Trends in Applied Mathematics", organized by SNS College of Technology Coimbatore, India, during June 02–06, 2020
15. Participated in One Week Faculty Development Program on Development and Management of MOOCs and Online Courses using LMS - Moodle, organized by Guru Angad Dev Teaching Learning Centre SGTB Khalsa College, University of Delhi under the Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching (PMMMNMTT) of MHRD, during 30th June 2020 - 4th July 2020.
16. Refresher Course in Mathematics, at UGC-HRDC, University of Jammu, Jammu, India, during 4–17 January 2021.
17. Refresher Course in Applicable Mathematics, at Teaching Learning Centre, Ramanujan College, University of Delhi, India, from 26 July - 08 August, 2022.

1. Assistant Superintendent, 2nd Boys Hostel June 2023 to till date.
2. Member of the board of studies in Mathematics, Rajendra University, Balangir, during 2020-21, 21-22, 22-23
3. Member of the board of studies in Mathematics, Ispat Autonomous College, Rourkela during 2021-22, 22-23.
4. Member of the conducting board of examinations, Sambalpur University during 2018-19, 19-20, 20-21, 21-22.
5. Assistant Superintendent, IB Boy’s Hostel August 2020- May 2022.
6. Acted as a supervisor for Joint Science Academies’ Summer Research Fellowship Programme.
7. Library in charge, Department of Mathematics, Sambalpur University from May 2015 to June 2022.
8. Assistant Teacher-in-charge examinations, Department of Mathematics, Sambalpur University since Aug. 2018 to till date
9. Zone Supervisor, +3 Second university examinations all Arts, Science, and Commerce 2019.
10. Zone Supervisor, +3 Second university examinations Science and Commerce 2018.
11. Coordinator, NSS Bureau, Sambalpur University, from November 2014 to July 2017
12. Deputy center superintendent of PG Entrance Test (Mathematics), 2016.
13. Member of the board of studies in NSS during 2014-15
14. Chairman, Board of study in the course in NSS under CBCS 2015
15. Associate Vice-President of Students’ Aid Fund during 2011-12.
16. Member of the board of studies in Mathematics, Sambalpur University during 2011-12, 16-17,17-18,18-19,19-20, 20-21, 21-22.
17. Member of e-Gov Cell for PG Admission during 2011-12.
18. Assistant Superintendent, 3rd Boys Hostel June 2010-May 2012.
19. Teacher-in-Charge of examinations, Dept. of Mathematics, Sambalpur University, 2010-2012.
20. NSS program officer, PG Boys’ Unit, Sambalpur University during 2010-2011.

Present Address :  Department of Mathematics, Sambalpur University, Jyoti Vihar, 768019, Sambalpur, Odisha, INDIA

Permanent Address :  Barahipur, Adaspur,754011, Cuttack, Odisha, INDIA