University of Mohaghegh Ardabili
Dr Mohammadreza Abdollahpour - Full CV
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Full name Dr. Mohammadreza Abdollahpour
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Department Department of Mathematics and Applications
Academic degree
Associate Professor
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City Ardabil
Country ایران
Educational records

1996-2000- B. Sc. : Pure Mathematics, University of Tabriz, Tabriz, Iran.

2000-2002- M. Sc. in Pure Mathematics- Analysis, University of Tabriz, Tabriz, Iran.

Title of thesis : Extremal vectors and invariant subspaces

Supervisor: Dr. Y.  Nejad Dehghan

2002-2007- Ph.D. in Pure Mathematics- Analysis, University of Tabriz, Tabriz, Iran.

Title of thesis : Frames theory and their properties in Banach spaces

 Supervisors : Dr. M. H. Faroughi 

Research projects
  1. Properties of g-frames
  2. Stability of differential equations
  3. Disjointness and strongly disjointness of generalized frames
  4. Investigation of properties of pg-frames and qg-Riesz bases
  5. Ultra Bessel sequences of subspaces in Hilbert spaces
  6.  Hyers- Ulam stability of differential equations
  7.  Investigation of stability of differntial equations by series method 
Theses supervised
  1.   K. Safari Shiran, Fusion frames and distributed processing, defence date September 2010.
  2. A. Irani Lahroudlou, Minimizing fusion frame potential, defence date June 2011.
  3. S. Abdollahnajad, Stability of g-frames and excess of a class of them, defence date July 2011.
  4. K. Ebadi, q-Bessalian frames in Banach spaces, defence date  August  2011. 
  5. F. Fouladi, Sums of Hilbert space frames and their expansion to tight frames, defence date July 2011.
  6. S. Mohammadbagherzadeh, (P,Y)-Operator frames and stability of Banach frames in Banach Spaces, defence date September 2012.
  7. P. Nazari, Bessel fusion multipliers and robustness of fusion frames under erasures of subspaces and of local frame vectors, defence date September 2012.
  8. Z. Jahangiri, g-frame sequences and g-Besselian frames in Hilbert spaces, defence date September 2012.
Published articles

1.  Abdollahpour, M. R.; Bagarello, F.; Triolo, S. An invariant analytic orthonormalization procedure with applications. J. Math. Phys. 48 (2007), no. 10, 103513, 15 pp. (ISI)

2.  Abdollahpour, M. R.; Faroughi, M. H. Continuous G-frames in Hilbert spaces. Southeast Asian Bull. Math. 32 (2008), no. 1, 1--19.

3. Abdollahpour, M. R.; Faroughi, M. H.; Rahimi, A. pg-frames in Banach spaces. Methods Funct. Anal. Topology 13 (2007), no. 3, 201--210.

4. Abdollahpour, M. R.; Bagarello, F.; On some properties of g-frames and g-coherent states. Il Nuovo Cimento B, 125 no. 11 (2010), DOI 10.1393/ncb/i2010-10929-8. (ISI)

5. Abdollahpour, M. R.; Najati, A.; Approximation of the inverse g-frame operators. Proc. Indian Acad. Sci. (Math. Sci.) Vol. 121, No. 2, May 2011, pp. 143–154. (ISI)

6. Abdollahpour, M. R., Najati, A.; Stability of linear differential equations of third order, Appl. Math. Lett. 24 (2011) 1827-1830. (ISI)

7. Abdollahpour, M. R.; Najati, A.; Besselian g-frames and near g-Riesz bases, Applicable Analysis and Discrete Mathematics, 5 (2011), 259–270. (ISI)

8. Najati, A., Abdollahpour, M. R., and G. H. Kim; On Pexider Differences in topological vector spaces, Abstract and Applied Analysis, vol. 2011, Article ID 370104, 10 pages, 2011. doi:10.1155/2011/370104. (ISI)
9. Abdollahpour, M. R.; Najati, A.; G-frames and Hilbert Schmidt operators. Bull. Iranian Math. Soci., vol. 37 no. 4 (2011), pp. 141-155. (ISI)    

10. Abdollahpour, M. R.; Najati, A.;  Park, C.; Rassias, T. M.; Shin, D. Y., Approximate perfect differential equations of second order, Advances in Difference Eqations 2012, 2012: 225. (ISI)   

11. Abdollahpour, M. R., Najati, A.; G-frames as sums of g-orthonormal bases, Kyungpook Math. J., 53 (2013), 135-141. 

12. Najati, A.,  Abdollahpour, M.R., Osgooei, E., Saem, M.M.; More on sums of Hilbert space frames,  Bull. Korean Math. Soc. 50 (2013), No. 6, pp. 1841–1846. (ISI)

13. Abdollahpour, M.R., Shekari, A.: Frameness bound for frame of subspaces, Sahand Commun. Math. Anal. 1 (2014), No. 1, pp. 1-8.

14.  Abdollahpour, M. R., Najati, A.; Ultra g-Bessel sequences in Hilber spaces, Kyungpook Math. J., 54 (2014), 87-94. 

15.  Abdollahpour, M. R.,  Park, C.; Hyers-Ulam Stability of a class of differential equations of second order, J. Comput. Anal. Appl. 18 (2015), No. 5, pp. 899-903.   (ISI)

16. Abdollahpour, M. R.;  Dilation of dual g-frames to dual g-frames, Banach J. Math Anal. 9 (2015), No. 1, pp. 54-66. (ISI)

17. Abdollahpour, M. R.: Dilation of a family of g-frames, Wavelets and linear Algebra, 1 (2014), 9-18.

18. . Abdollahpour, M. R., Shekari, A., Park, C., Shin, D. Y.; Ultra Bessel sequences of subspaces in Hilbert spaces,  J. Comput. Anal. Appl. 19 (2015), No. 5, pp. 874-882.  (ISI)

19.  Abdollahpour, M. R., Najati, A.; On approximate Euler differential equations of third order, Mathematica Pannonica,  24 no. 2  (2013), 1-10.

20. Abdollahpour, M. R., Najati, A.; Hyers-Ulam Stability of a differential equation of third order, submitted.

21. Abdollahpour, M. R., Najati, A., Gavruta, P.; Multipliers of pg-bessel sequences in Banach spapces, submitted.

22. Abbas Najatia,, Mohammad Reza Abdollahpoura, Choonkil Parkb, On the stability of linear di erential equations of second order, Int. J. Nonlinear Anal. Appl. 8 (2017) No. 2, 65-70. (ISI)

23. M. R. Abdollahpoura,, A. Rahimib, Ultra Bessel sequences in direct sums of Hilbert spaces, Wavelets and Linear Algebra 2 (1) (2015) 55 - 64.

24. M.R.Abdollahpour, R.Aghayari, M.Th.Rassias, Hyers–Ulam stability of associated Laguerre differential equations in a subclass of analytic functions, J. Math.Anal.Appl.437(2016)605–612. (ISI)

25. M. R. ABDOLLAHPOUR AND Y. ALIZADEH, MULTIPLIERS OF CONTINUOUS G-FRAMES IN HILBERT SPACES, Bull. Iranian Math. Soc., Vol. 43 (2017), No. 2, pp. 291-305. (ISI)


27. M. R. ABDOLLAHPOUR and and M. Rassias, Hyers–Ulam stability of hypergeometric differential equations, Aequat. Math. (2018), DOI: 10.1007/s00010-018-0602-3 (ISI)

28. M. R. ABDOLLAHPOUR and Y. Khedmati, G-Duals of Continuous G-Frames and Their Perturbations, Results in Mathematics,  (2018) 73:152. (ISI)

29. A. YOUSEFZADEHEYNI and  M. R. ABDOLLAHPOUR, 𝑮-FRAMES POTENTIAL IN HILBERT SPACES, U.P.B. Sci. Bull., Series A,  81(1) (2019), 197-208. (ISI) 

Presented articles
  1. Abdollahpour, M. R.; Generalized frames indexed by measurable spaces. 18th Sem. on Analysis, (2009), TMU, Iran.
  2. Abdollahpour, M. R.; Riesz-type continuous g-frames. 40 th anu. Iranian math. conf., (2009), Sharif University of Technology, Iran.
  3. Abdollahpour, M. R.; Operator valued p-frames. 41 th anu. Iranian math. conf., (2010), Urmia University ,Urmia, Iran.
  4. Abdollahpour, M. R.; Relation between analysis operator and duals of a g-frame, 20th Sem. on Analysis, (2012), University of Maragheh, Maragheh, Iran.  
  5. Abdollahpour, M. R.; Some results on g-Banach frames and g-frame, 20th Sem. on Analysis, (2012), University of Maragheh, Maragheh, Iran. 
  6. Abdollahpour, M. R.; Generalized frames containing a g-Riesz basis, 43 th anu. Iranian Mat. Conf., (2012), Tabriz University, Tabriz Iran.
conference reviewer
Reviwer of 43th Annual Iranian Mathematics Conference
Journal Referee

Reviewer of papers in

  1.  Abstract and Applied Analysis
  2.  Bulletin of the Malaysian Mathematical Sciences Society
  3.  Advances in Difference Equations
  4.  Wavelets and Linear Algebra
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