Kourosh Nourouzi  Professor

Kourosh Nourouzi
Professor of Mathematics

Faculty of Mathematics,
K. N. Toosi University of Technology,
P.O.box 1676-53681,
Tehran, Iran.
Fax: (+98)21-77125291
Phone number: (+98) 21-77125254  

E-mail: nourouzi@kntu.ac.ir

   

                                   

Field                           Linear and Nonlinear Functional Analysis

Research Interests     Metric Fixed Point Theory,  Hilbert modules over C*-algebras

My research interests are primarily in Metric Fixed Point Theory and Functional Analysis, with particular emphasis on nonexpansive and contractive mappings, fixed point properties, and their generalizations in metric and generalized metric structures. A major part of my research concerns Hilbert C*-modules and their geometric and fixed point properties, including reflexivity, and nonexpansive mappings. I am also interested in C*-algebras, especially the interaction between operator-algebraic structures and fixed point theory. Other areas of interest include Nonlinear analysis.

 

Research Papers

63. An Interpolative Generalization of the Nadler Fixed Point Theorem with Applications to Integral Inclusions and Boundary Value Problems, International Journal of Mathematics and Mathematical Sciences, 2026, (accepted)  (Joint with M. Manavi)

62. Fixed Point Property for Nonexpansive Mappings and Reflexivity: A Hilbert C*-Module Approach, Journal of Function Spaces, 2026, (accepted).

61. Reflexivity of Hilbert K(H)-modules and fixed point property for nonexpansive mappings, Journal of Mathematics, 2026, Paper No. 6311273. (PDF)

60. Frechet universality and completion for F-metric spaces: A generalized metric framework, Journal of Mathematics, 2026, Article ID 7915822, 6 pp. (Joint with N. Norouzi-Chenari and M.H. Zeinali) (PDF)

59. Fixed point property of full Hilbert C*-modules over unital C*-algebras, Fixed Point Theory, 25, (2024), no. 1, 171-178 (Joint with F. Jahangir) (PDF)

58. Unit vectors in Hilbert C(Z)-modules, Operators and Matrices, 16, (2022), no. 2, 349-356 (Joint with Z. Hassanpour) (PDF)

57. Diversity-normed spaces and diversity embeddings, Studia Mathematica,  267, (2022), 19-35 (Joint with P. Haghmaram and Sh. Golpaigani Fard) (PDF)

56. Banach weak topology on Hilbert C*-modules, Operators and Matrices, 15, (2021), no. 4, 1309-1317 (Joint with M. Golabi) (PDF) 

55. A nonlinear F-contraction form of Sadovskii's fixed point theorem and its application to a functional integral equation of Volterra type, Facta Universitatis' series: Mathematics and Informatics, 36, (2021), no. 2, 321-331 (Joint with F. Zahedi and D. O'Regan) (PDF)

54. On F-metric spaces, Journal of Fixed Point Theory and Applications, 23, (2021), no. 1, Paper no. 2, 14 pp. (Joint with F. Jahangir and P. Haghmaram) (PDF)

53. Morita equivalnce and Cauchy extensions of Hilbert  C*-modules, Quaestiones Mathematicae, 44, (2021), no. 3, 379-397 (Joint with A. Reza) (PDF)

52. Ultradiversification of diversities, Analysis and Geometry in Metric Spaces, 2020; 8: 410-417 (Joint with  P. Haghmaram) (PDF)

51. Ultradiversities and their spherical completeness, Journal of Applied Analysis, 26, (2020), no. 2, 231-240 (Joint with G. H. Mehrabani) (PDF)

50. Some pre-C*-algebras generated by a C*-algebra A with completion C([-1,1]), A), Iranian Journal of Science and Technology, Transaction A: Science. 44, (2020), 137-142   (Joint with A. Reza) (PDF)

49. Convolution type C*-algebras, Bull. Iranian Math. Soc.  46, (2020), 777-798  (Joint with A. Reza) (PDF)

48. Fixed point property of Hilbert modules over finite dimensional C*-algebras, Journal of Fixed Point Theory and Applications. 21, (2019), no. 3,  Art. 87, 7 pp. (Joint with M. Golabi) (PDF)

47. Totally bounded subsets and a measure of noncompactness for Schatten class operators, Topology and its Applications. 265 (2019), 106825, 8 pp. (Joint with F. Zahedi and D. O'Regan) (PDF)

46.  Functors induced by Cauchy extension of C*-algebras, Sahand Commun. Math. Anal., 14, (2019), no. 1, 27-53 (Joint with A. Reza) (PDF)

45.  A fixed point theorem in uniform spaces generated by a family of b-pseudometrics,  Fixed Point Theory, 20, (2019),  no.1, 177-184 (Joint with H. Faraji and D. O'Regan) (PDF)

44. Stationary Points of Set-valued Contractive and Nonexpansive Mappings on Ultrametric Spaces, Fixed Point Theory, 19, (2018), no. 2, 587-594 (Joint with M. Hosseini and D. O'Regan) (PDF)

43. A fixed and common fixed points for weakly contractive mappings in b-metric spaces,  Sahand Commun. Math. Anal,  7, (2017), no. 1, 49-62 (Joint with H. Faraji) (PDF)

42.  A generalization of Kannan and Chatterjea fixed point theorems on complete b-metric spaces,  Sahand Commun. Math. Anal., 6, (2017), no. 1, 77-86 (Joint with H. Faraji) (PDF)

41. Probabilistic Normed Groups,  Iranian J. Fuzzy Systems, 14, (2017), no. 1, 99-113. (Joint with A.R. Pourmoslemi) (PDF)

40. Mazur-Ulam Problem in Probabilistic Normed Groups,  Int. J. Nonlinear Anal. Appl., 8, (2017), no. 2,  327-333. (Joint with A.R. Pourmoslemi)  (PDF)

39. On Hukuhara's differentiable iteration semigroups of linear set-valued functions,  Aequationes Mathematicae. 90, (2016),  no. 6, 1129-1145. (Joint with M. Aghajani)  (PDF)

38. Fixed points for Kannan type contractions in uniform spaces with a graph, Nonlinear Analysis: Modelling and Control., 21, (2016), no. 1, 103-113 (Joint with A. Aghanians) (PDF)

37. Vector ultra metric spaces  and a fixed point theorem for correspondences, Int. J. Nonlinear Anal. Appl., 7, (2016), no. 1, 147-153. (PDF)

36. Coincidence point theorems for E-(\psi,\varphi)- and E-\varphi-weak contractions in partially ordered uniform spaces, Journal of  Nonlinear and Convex Analysis,  17, (2016), no. 12, 2535-2549 (Joint with R.P. Agarwal, A. Aghanians, K. Fallahi) (PDF)

35. The role of regularity to reach the vector valued version of Caristi's fixed point theorem, Journal of  Nonlinear and Convex Analysis. 16, (2015), no. 5, 937-942 (Joint with F. Lael) (PDF)

34. On stationary points of nonexpansive set-valued mappings,  Fixed Point Theory and Applications. (2015) 2015:236. (Joint with R. Espinola and M. Hosseini) (PDF)

33.  The Continuity of Q+-Homogenous Superadditive Correspondences, Journal of  Nonlinear and Convex Analysis, 16, (2015), no. 9, 899-1904. (Joint with M. Aghajani) (PDF)

32. Fixed points of integral type contractions in uniform spaces,  Filomat, 29:7, 2015, 1613-1621. (Joint with A. Aghanians)  (PDF)

31. Fixed Points for Ciric-G-Contractions in Uniform Spaces Endowed with a Graph, Publications de l'Institut Mathematique. 97, (2015), no. 111, 211-223. (Joint with A. Aghanians, K. Fallahi, R.U. Verma) (PDF)

30. The Continuity of Linear and Sublinear Correspondences Defined on Cones, Bulletin of Iranian Mathematical Society. 41, (2015), no. 1,  43-55. (Joint with M. Aghajani, D. O'Regan) (PDF)

29. Fixed points for Banach and Kannan contractions in modular spaces with a graph, Int. J. Nonlinear Anal. Appl., 5, (2014), no. 2, 50-60.  (Joint with A. Aghanians) (PDF)

28. Some couple coincidence point theorems in partially ordered uniform spaces,  Cubo,  16, (2014),  no. 2, 115-128. (Joint with A. Aghanians, K. Fallahi, D. O'Regan) (PDF)

27. Minimization problem of a variational inequality on a family of set-valued mappings, Politehnica University of Bucharest. Scientific Bulletin. Series A. Applied Mathematics and Physics. 76, (2014), no. 2, 99-110 (Joint with M. Eslamian)

26. Two order theoretic proofs for a fixed point theorem in partially ordered metric spaces and its application to trace class operators, Fixed Point Theory,  15, (2014), no. 2, 393-398. (Joint with F. Bazazi , D. O'Regan)

25. Fixed points of correspondences  in vector valued  metric spaces and applications in integral equations, Journal of  Nonlinear and Convex Analysis, 15,  (2014), no. 6, 1167-1180 (Joint with R.P. Agarwal, F. Lael, D. O'Regan)

24. An embedding theorem for a class of Convex sets in nonarchimedean normed spaces, Journal of  Nonlinear Analysis and Optimization: Theory & Applications, 4,  (2013), no. 3, 127-130 (Joint with M. Aghajani) (PDF) 

23. An entourage approach to the contraction principle in uniform spaces endowed with a graph, Panamer Math. J., 23,  (2013), 87--102. (Joint with A. Aghanians, K. Fallahi)

22. Fixed points for E-asymptotic contractions and Boyd-Wong type E-contractions in uniform Spaces, Bulletin of Iranian Mathematical Society, 39, (2013), no. 6, 1261-1272. (Joint with A. Aghanians, K. Fallahi) (PDF)

21. Fixed points of G-contractions on uniforms spaces endowed with a graph, Fixed Point Theory and Applications, 2012, 2012:182.  (Joint with A. Aghanians, K. Fallahi) (PDF)

20. Fixed points of mappings defined on probabilistic modular spaces, Bulletin of Mathematical Analysis and Applications,  4, (2012), no. 3, 23-28.  (Joint with F. Lael) (PDF)

19. On the regular cosine family of linear correspondences, Aequationes Mathematicae ,  83, (2012), no. 3, 215-221. ( Joint with M. Aghajani) (PDF)

18. Modular locally constant mappings in vector ultrametric spaces, Abstract and Applied Analysis, Vol. 2011 (2011), Article ID 574756, 8 pages, doi: 10.1155/2011/574765 (Joint with K. Fallahi) (PDF).

17. On the fixed points of correspondences in modular spaces, ISRN Geometry, vol. 2011,  2011. doi:10.5402/2011/530254. (Joint with F. Lael) (PDF)

16. Fixed points of correspondences defined on cone metric spaces, Computer and Mathematics with Applications. 60, (2010), no. 3, 653-659. (Joint with Z. Izadi). (PDF)

15. A note on the paper: Charactrerizatios on 2-Isometries, Int. J. Open Problems Compt. Math., 2, (2009), no. 4, 572-573 (Joint with H. Abbassi).

14. Compact operators defined on 2-normed and 2-probabilistic normed spaces, Mathematical Problems in Engineering, Volume 2009, Article ID 950234, 17 pages. Doi:10.1155/2009/950234. ( Joint with F. Lael) (PDF)

13. On the convexity of fuzzy nets. Chaos, Solitons & Fractals, 40, (2009), 1356-1360. (PDF)

12. Operators defined on n-modular spaces, Mediterranean Journal of Mathematics, 6, (2009), 431-446. (Joint with S. Shabanian) (PDF)

11. Probabilistic modular spaces and linear operators, Acta Applicanda Mathematicae, 105, (2009), 123-140. (Joint with K. Fallahi) (PDF)

10.  Probabilistic modular spaces, WSPC Proceedings, December (2008), 814- 818.

9. Baire's Theorem in  probabilistic modular spaces, Lecture Notes in Engineering and Computer Science, WCE 2008, Vol. II, 916-917.

8. Compact operators between probabilistic normed spaces, Operator Theory: Advances and Applications, 181, (2008), 347-354.

7. Some results on IF-normed spaces, Chaos, Solitons & Fractals, 37, (2008), no. 3, 931-939. (Joint with F. Lael) (PDF)

6. Convex sets in probabilistic normed spaces, Chaos, Solitons & Fractals, 36, (2008), no. 2, 322-328. (Joint with A. Aghajani).  (PDF)

5. Convexity in traingular norm of fuzzy sets, Chaos, Solitons & Fractals, 36,  (2008), no. 4, 883-889. (Joint with A. Aghajani) (PDF)

4. The Geometry of the Unit Ball of Some Tensor Product Spaces, Applied Mathematics Letters, 20, 2007, no. 4, 401-404. (PDF)

3. Fuzzy compact linear operators, Chaos, Solitons & Fractals.  34 (2007) 1584-1589.(Joint with F. Lael) (PDF)

2. On the state space of C*-algebras, Journal of Mathematical Analysis  and Applications. 275, (2002), no. 1, 161-164. (PDF)

1. Strongly exposed points in the unit ball of trace class operators, International  Journal of Mathematics and Mathematical Sciences. 30, (2002), no. 7, 393-397. (PDF)

 

Book

Metric Spaces (in persian) (Selected as distinguished book by K. N. Toosi university, 2017)

 

Selected Conferences

  • Fixed point property in Hilbert C*-modules, International Conference on Operators on Banach Algebras and Related Topics, Tarbiat Modares University, Tehran, Iran, Aug. 16-17, 2022. (Invited)

  • Cauchy extension of Hilbert C*-modules. International Congress of Mathematicians (ICM2018), Rio De Janeiro, Brazil, Aug. 1-9, 2018.

  • Diversity normed spaces. International Conference on Mathematical Modeling in Applied Sciences. Saint Petersburg, Russia, Jul. 24-28, 2017.

  • Fixed point property for nonexpansive mappings in C*-algebras. The 8th International ISAAC Congress, Moscow, Russia,  Aug. 22- 27 , 2011.

  • An order theoretic approach to modular fixed point theorems. International Conference on Mathematical Analysis 2010(ICMA 2010),  Bangkok, Thiland, December 7--9, 2010.

  • Ultrametric fixed point theory. The first workshop in fixed point theory and applications.  Amirkabir University, Tehran, Iran, June 9-10 (2010).

  • Baire's Theorem in  probabilisticc modular spaces. The world congress on engineering and applied mathematics.  Imperial College, London, U.K., July 2--4, 2008.  

  • The probabilistic modular spaces. 6th ISAAC Congress. Middle East Technical University, Ankara, Turkey. August 13--18, 2007.

  •  Barcelona Analysis Conference. University of Barcelona, Barcelona, Spain. September 4--8, 2006.

  • Compact operators in probabilistic normed spaces. Operator Algebras, Operator Theory and Applications.  Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Lisbon, Portugal. September 1--5, 2006.

  • Exposed points in the set of completely positive maps.  Bordeaux, France. July 3--13, 2005..

  • On the completely positive maps. 35th Annual Iranian Mathematics Conference.  Ahvaz. January 26-- 29, 2005.

  •  Exposed points and completely positive maps. Third Seminar on Linear Algebra and its Applications.   Kerman. December 28--29, 2004.

  • The geometric properties in the set of completely positive maps. International Conference in Analysis and its Applications. Nanjing University, China. July 20--24, 2004.

  •  On the geometric properties of completely positive maps. 4th European Congress of Mathematics. Stockholm, Sweden. June 27--July 2, 2004.

  •  The geometry of some tensor product spaces. Canadian Operator Algebra Symposium.  University of New Brunswick, Canada. May 21--24, 2003.

  • Extreme and exposed points in the unit balls. 33th Annual Iranian Mathematics  Conference, Ferdowsi University of Mashhad, Mashad. Aug. 30--Sep. 2, 2002.


Graduate Students

MSc:     F. Lael,  (Sep.2006)

S. Vaezzadeh, (Sep. 2007)

K. Fallahi,  (Nov. 2007)

S. Jahani,  (Feb. 2008)

S. Shabanian,  (Oct. 2008)

B. Hedayatfar, (Nov. 2008)

H. Adman, (Mar. 2009)

H. Abbasi, (Feb. 2009)

N. Rezabandehloo, (Sep. 2009)

E. Jafari, (Oct. 2009)

Z. Izadi, (Oct. 2009) 

             A. Aghanians, (Sep. 2010)

             R. Mokhtar, (Feb. 2011)     

             I. Mehrabinejad, (Mar. 2011)

            M. M. Khatibi, (Feb.2011)

 

 

 

M. Manavi, (Nov. 2011)

S. Abdoli, (Jan. 2012)

N. Ashghaei, (Jan. 2012)

K. Shamsolkottabi (Feb. 2012)

F. Ghasemi, (Feb. 2013)

M. Dinarvand, (Sep. 2012)

A. Broumandnia, (Sep. 2012)

M. Hosseini, (Sep. 2013)

N. Salehabadi, (Oct. 2013)

M. Taghavi, (Sep. 2014)

M. Ramzi Iraqi, (Sep. 2014)

S. Alian, (Dec. 2014)

P. Bigdeli, (May, 2015)

E. Rostami, (Dec. 2015)

M. Alimohammadi, (Dec. 2015)

 

 

L. Michani, (Jan. 2016)

M. Farahi, (May, 2016)

N. Ahmadi,  (Oct. 2016)

F. Aloustani,  (Feb. 2017)

Sh. Golpaiganifard,  (Sep. 2017)

H. Chalak,  (Sep. 2017)

S. Pourya (Feb.  2019)

M. Ghaffari (Feb.  2019)

Z. Lak (Joint supervised with Dr. Masiha) (Sep., 2019)

M. Servati (Joint supervised with Dr. Hosseini) (Sep., 2019)

F. Jafari Shahneshin (Apr., 2024)

S. Mohammadsalahi Tohidi (Sep. 2024) 

F. Hashemi (Sep. 2025)

Z. Shahadat (Oct. 2026)

 

 

  

 

PhD:    M. Aghajani, (Aug. 2012)

F. Lael, (Oct. 2012)

K. Fallahi, (Feb. 2013)

A. Aghanians, (Sep. 2014)

A.R.  Pourmoslemi, (Sep., 2016)

H. Faraji, (Sep., 2017)

A. Reza, (Sep. 2019)

F. Jahangir (Mar., 2022)

P. Haghmaram (Mar. 2023)

F. Zahedi (Feb. 2025)

M. Manavi (in progress)

 

 

  

 

 

 

 

Postdoctoral Researchers

 

 


Teaching Schedule

 

Semester I,  2026-27 (1405) 

Basics of Mathematical Analysis (BSc), Sunday and Tuesday mornings (10:30--12:00)  

Convex Analysis (MSc & PhD), Sunday and Tuesday mornings (9:00--10:30)

 

 

 

Semester II,  2025-26 (1404) 

Basics of Mathematical Analysis (BSc), Saturday and Monday afternoons (13:30--15:00--17:00)  

Seminar (MSc), Monday mornings (15:30--17:00)

 

 

Semester I,  2025-26 (1404)

Topology (BSc), Saturday and Monday mornings (10:30--12:00)

Matrix Analysis (MSc & PhD), Saturday and Monday afternoons  (13:30--15:00)

 

 

                    
 Courses Taught

 Matrix Analysis, Nonlinear Analysis, Topology, Mathematical Analysis I-II-III, Calculus I-II, Ordinary Differential Equations, Real Analysis,

Complex Analysis, Functional Analysis I-II, Operator Theory I-II, C*-Algebras I-II, Applied Functional Analysis, Banach Algebras, Fixed point theory.

 

Occupations 

  • Dean of the Faculty of Mathematics (2016-2020, 2023)

  • Member of Scientific Audit Board (Heyatte Momayyazeh) of KNTU (2016-2018, 2020- 2022)

  • Member of Expert Committee for Basic Sciences, KNTU (2010-2011, 2016-2024)

  • Member of Expert Committee for Nonlinear Analysis, Iranian Mathematical Society (2013-present)

  • Research Deputy, Faculty of Science, KNTU (2012-2014)

  • Sabbatical, University of Seville, Spain (2014)

  • Reviewer of MathScinet (American Mathematical Society), (2014)

  • Reviewer of zbMATH (European Mathematical Society), (2022)

  • Director of IT Center, KNTU (2008-2011)

  • Associate Researcher: Institute for Studies in Theoretical Physics and Mathematics (IPM),  Tehran (2006-2012)

  • Leader of Mathematical Competitions and Olympiad Team, KNTU (2005-2009)

  • Representative of Talented Students and Entrepreneurship, Faculty of Science, KNTU (2004-2008)

  • Visiting Researcher, University of Regina, Canada (2000-2001)

 

                                     


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