Hichem Ben-El-Mechaiekh

Professor of Mathematics

Office: MacKenzie Chown J419
Telephone: + 1 (905) 688 5550 Ext 3758
E-mail: hmechaie@brocku.ca, hbenelmechaiekh@brocku.ca

I have been at Brock University since 1988, after a one-year (1987-88) visiting assistant professor appointment at the Technical University of Nova Scotia (now part of Dalhousie University). I have also held visiting scholar positions at the Université Paris I, Panthéon-La Sorbonne, the American University of Sharjah, The University of Sharjah (while I founded the UAE Mathematics Day in 2003, this year in its 15th edition) and the Canadian University Dubai. I hold a B.Sc., M.Sc. and Ph.D. in mathematics from the Université de Montréal. I have been Head of Department for a total of 8 years and Associate Dean for 6 years.

My broad research interest is in Nonlinear Functional Analysis and its applications to various areas of mathematics and sciences. I am associate editor for leading journals in nonlinear functional analysis, including fixed point theory and its applications as well as in convex analysis and optimization.

While a “pure mathematician” by training, I very much value a mathematical education grounded in the utilitarian value of mathematics as Queen of the Sciences and integrating state-of-the-art computational technologies; so much so, that I am currently driving our faculty’s effort in building a unique cross-disciplinary program in big data science here at Brock (to hopefully start in September 2019 – stay tuned).

To Prospective Graduate Students:

You are welcome to apply for admission to work under my supervision if you are interested in working in Mathematical Economics, Optimization and its applications to data science or game theory, Functional Analysis, Nonlinear Analysis, Topology, Topological and Variational Methods in Differential Equations and Inclusions. Make sure to indicate your choice of supervisor on your graduate admission form.

Prospective M.Sc. students would have completed undergraduate courses in Real Analysis. Completion of undergraduate courses in Functional Analysis and/or Topology a bonus.

Research Interests

  • Nonlinear Functional Analysis
  • Mathematical Economics
  • Analytical and Topological Methods in Game Theory
  • Nonsmooth and Convex Optimization and Applications
  • Fixed Point Theory and Applications to Nonlinear Analysis
  • Set-Valued Analysis
  • Differential Equations and Inclusions
  • Noncompact and Nonconvex Problems in Nonlinear Functional Analysis
  • Point Set and Combinatorial Topology

Publications and collections

Books or Chapters Contributed to Refereed Books

    1. Ben-El-Mechaiekh Hichem, Some fundamental topological fixed point theorems for set-valued maps, in Topics in Fixed Point Theory, Almezel Saleh, Ansari Qamrul Hasan, and Khamsi, Mohamed Amine Eds., Springer, (2014) 237-272.
    2. Mohammed A. Khamsi, Hichem Ben-El-Mechaiekh, and Bernd Schroeder, Guest Editors, Recent Contributions to Fixed Point Theory and Its Applications, Abstract and Applied Analysis, Volume 2014, Hindawi Publishing Corp., 2014.
    3. Ben-El-Mechaiekh Hichem, Approximations and Selections Methods for Set-Valued Maps and fixed point theory,in Fixed Point Theory, Variational Analysis, and Optimization, Saleh Abdullah R. Al-Mezel, Falleh Rajallah M. Al-Solamy, and Qamrul Hasan Ansari Eds., CRC Press, pp. 78-136, 2014.
    4. Ben-El-Mechaiekh Hichem, Intersection and Fixed Point Theorems in Set-Valued Analysis, in Topics in Nonlinear Analysis, Q. H. Ansari Ed., World Education,World Education, pp. 159-183, 2011.
    5. Ben‑El‑Mechaiekh H. and G. Isac, Generalized multivalued variational inequalities, in Topology and Analysis, Volume dedicated to Professor S. Stoilow, C. Andreian‑Cazacu, O. Letho and T.M. Rassias, Eds., World Scientific Publishing Co. (1998), 115-142.
    6. Ben-El-Mechaiekh Hichem and Robert Dimand, “Mathematical economics,” in William A. Darity, Jr., ed., International Encyclopedia of the Social Sciences, 2nd. edition, Detroit: Macmillan Reference, 2008.

Articles in Refereed Journal

    1. Ben-El-Mechaiekh Hichem and Robert W. Dimand, Louis Bachelier’s 1938 Monograph on the Calculus of Speculation: Mathematical Finance and Randomness of Asset Prices in Bachelier’s Later Work, Revue d’Histoire des Mathématiques, Société Mathématique de France, To Appear (2018).
    2. Abdul Latif and Hichem Ben-El-Mechaiekh, Topological Fixed Point Theory and Applications to Variational Inequalities, Fixed Point Theory and Applications 85 (2015) 1-26.
    3. Ben-El-Mechaiekh H., Intersection Theorems for Closed Convex Sets and Applications, Missouri J. Math. Sc., 27, No.1 (2015) 47-63.
    4. Ben-El-Mechaiekh H., The Ran-Reurings Fixed Point Theorem Without Partial Order: A Simple Proof, J. Fixed Point Theory and Applications, Springer Basel, 16 (1-2) (2015) 373-383. DOI 10.1007/s11784-015-0218-3.
    5. Ben-El-Mechaiekh H., On the Convex Hull of Closed Convex Sets in Locally Convex Spaces, British J. Math & Comp. Sc. 4, No. 10 (2014) 1351-1355.
    6. Ben-El-Mechaiekh H. and F. B. Saidi, On the Continuous Approximation of Upper Semicontinuous Set-Valued Maps, Questions and Answers in General Topology 31 (2013) 71-78.
    7. Ben-El-Mechaiekh H., On Nonlinear Inclusions in Non-Smooth Domains, Arab J. Math. 1 No. 4 (2012) 395-416.
    8. Ben-El-Mechaiekh Hichem and Robert Dimand, How General Equilibrium Came to North America: Irving Fisher’s Mathematical Investigations in the Theory of Value and Prices (1891), Journal of Economic and Social Measurement, Vol. 37 (2012) 97-118.
    9. Ben-El-Mechaiekh H. and R. Dimand, A Simpler Proof of the von Neumann Minimax theorem, American Mathematical Monthly 118 (2011) 636-641.
    10. Ben-El-Mechaiekh and R. Dimand, Von Neumann, Ville, and the Minimax Theorem, International Game Theory Review 12 No. 2 (2010), 1-23.
    11. Ben-El-Mechaiekh H., P. Bich, and M. Florenzano, General equilibrium and fixed point theory: a partial survey, Journal of Fixed Point Theory and Application 6 (2009) 207-226.
    12. Ben-El-Mechaiekh H., Equilibria for Set-valued Maps on Nonsmooth Domains, J. Fixed Point Theory and Applications 4 (2008) 177-182.
    13. H. Ben-El-Mechaiekh H., Strong Approximation for Nonconvex Set-valued Maps, of Nonlinear and Convex Analysis 9  (2008) 65-70.
    14. Ben-El-Mechaiekh H. and R. Dimand, The von Neumann Minimax Principle Revisited, Fixed Point Theory and Its Applications, Banach Center Publications, Vol. 77, Inst. of Mathematics, Polish Academy of Sciences (2007) 23-34.
    15. Dimand R. W. and H. Ben-El-Mechaiekh, Louis Bachelier, in Geoffrey Poitras Ed., Pioneers of Financial Economics, Volume 1: Contributions Prior to Irving Fisher, Cheltenham, U.K.,and Northampton, maine: Edward Elgar Publishing, (2006) 225-237.
    16. Ben-El-Mechaiekh H., The Ky Fan Fixed Point Theorem on Star-Shaped Domains, Math. Reports. Acad. Sc. Canada, 27 (4) (2005) 97-100.
    17. Ben-El-Mechaiekh H., S. Chebbi, M. Florenzano, A generalized KKMF Principle and Applications, J. Math. Anal. Appl 309 (2005) 583-590.
    18. Ben-El-Mechaiekh H., Spaces and Maps Approximations and Fixed Points,Special issue on Fixed Point Theory and Applications, Journal of Computational and Applied Mathematics 113 (2000) 283-308.
    19. H. Ben‑El‑Mechaiekh H., S. Chebbi and M. Florenzano, A nonlinear alternative for approximable maps: a simple proof, Proceedings of the American Math. Soc. 126 (1998) 2345-2349.
    20. Ben-El-Mechaiekh H., S. Chebbi, M. Florenzano and J-V. Llinares, Abstract convexity and fixed points, Journal of Math. Analysis and Applications 222 (1998) 138-150.
    21. Ben‑El‑Mechaiekh H. and G. Isac, Some geometric solvability theorems in topological vector spaces, Bulletin of the Korean Math. Soc. 34 (1997), 273-285.
    22. H. Ben‑El‑Mechaiekh H. and W. Kryszewski, Equilibria for set‑valued maps on nonconvex domains, Transactions of the American Math. Soc. 349 (1997) 4159-4179.
    23. Ben‑El‑Mechaiekh H. and W. Kryszewski, Equilibria for perturbations of upper semicontinuous set‑valued maps by convex processes, Georgian Journal of Math. 3 (1996) 201‑215.
    24. Ben‑El‑Mechaiekh H. and A. Idzik, Ky Fan type coincidence theorems I, Bulletin of the Polish Academy of Science 122 (1994) 105-109.
    25. Ben‑El‑Mechaiekh H. and W. Kryszewski, Equilibres dans les ensembles non‑convexes, Comptes Rendus de l’Académie des Sciences de Paris 320, Série 1 (1995) 573‑576.
    26. Ben‑El‑Mechaiekh H. and M. Oudadess, Some selection theorems without convexity, Journal of Math. Analysis and Applications 195 (1995) 614‑618.
    27. Ben‑El‑Mechaiekh H. and P. Deguire, Equilibrium for abstract nonconvex games, Mathematical Reports of the Academy of Science of Canada XVII (1995) 1‑6.
    28. Ben‑El‑Mechaiekh H. and G. Isac, A general variational inequality with application, Mathematical Reports of the Academy of Science of Canada XVII (1994) 235‑240.
    29. Ben‑El‑Mechaiekh H. and A. ldzik, A Leray‑Schauder theorem for approximable set-valued maps, Proceedings of the American Mathematical Society 122 (1994) 105-109.
    30. Ben‑El‑Mechaiekh H., Fixed points for compact set‑valued maps, Questions and Answers in General Topology 10 (1992) 153‑156.
    31. Ben‑El‑Mechaiekh H. and P. Deguire, Approachability and fixed points for nonconvex set‑valued maps, Journal of Mathematical Analysis and Applications 170 (1992) 477‑500.
    32. Ben‑El‑Mechaiekh H., General fixed point and coincidence theorems for set-valued maps, Mathematical Reports of the Academy of Science of Canada XIII (1991) 237‑242.
    33. Ben‑El‑Mechaiekh H. and P. Deguire, Approximation of non‑convex set‑valued maps Comptes Rendus de l’Académie des Sciences de Paris 312 Série 1 (1991) 379‑384.
    34. Ben‑El‑Mechaiekh H. and P. Deguire ,General fixed point theorems for non‑convex set‑valued maps, Comptes Rendus de l’Académie des Sciences de Paris 312 Série 1 (1991) 433‑438.
    35. Ben‑El‑Mechaiekh H., The coincidence problem for compositions of set‑valued maps Bulletin of the Australian Math. Society 41 (1990) 421‑434.
    36. Ben‑El‑Mechaiekh H., Zeros for set‑valued maps with non‑compact domains, Mathematical Reports of the Academy of Science of Canada XII (1990) 125‑130.
    37. Ben‑El‑Mechaiekh H., A remark concerning a matching theorem of Ky Fan, Chinese Journal of Mathematics 17 (1989), 309‑314.
    38. Ben‑El‑Mechaiekh H., Fixed points for compositions of set‑valued maps, Extracta Mathematicae 4 (1989), 93‑95.
    39. Ben‑El‑Mechaiekh H., P. Deguire, and A. Granas, Points fixes et coincidences pour les applications multivoques III. Applications M et M* , Comptes Rendus de l’Académie des Sciences de Paris 305 Série 1 (1987) 381‑384.
    40. Ben‑El‑Mechaiekh H., P. Deguire, and A. Granas, Points fixes et coincidences pour les applications multivoques II. Applications de type F et F* , Comptes Rendus de l’Académie des Sciences de Paris 295 Série 1 (1982) 381‑384.
    41. Ben‑El‑Mechaiekh H., P. Deguire, and A. Granas, Points fixes et coincidences pour les applications multivoques I.‑ Applications de Ky Fan, Comptes Rendus de l’Académie des Sciences de Paris 295 Série 1 (1982) 337‑340.
    42. Ben‑EI‑Mechaiekh H., P. Deguire, and A. Granas,Une alternative non‑linéaire en analyse convexe et applications, Comptes Rendus de l’Académie des Sciences de Paris 295, Série 1 (1982) 257‑259.

Refereed Conference Proceedings

  1. Ben-El-Mechaiekh H., On the solvability of nonlinear inclusions in infinite dimensions, in Yeol Je Cho (Ed.), Proceedings of the International Conference on Mathematical Analysis and Applications, 1-A (2000), 69-89.
  2. Ben-El-Mechaiekh H., Fixed points for set-valued maps: a topological approach, in Wataru Takahashi and Tamaki Tanaka (Eds.), Nonlinear Analysis and Convex Analysis, Proceedings of the International Conference, Niigata University and The Tokyo Institute of Technology, (1999), 118-125.
  3. Ben‑El‑Mechaiekh H. and W. Kryszewski, Equilibria for set‑valued maps without compactness or convexity, Proceedings of the “Troisième Colloque de la Société Tunisienne de Mathématiques”, Hammamet, Tunisia, April 1995.
  4. Ben‑El‑Mechaiekh H., Continuous approximation of set‑valued maps, fixed points and coincidences, Proceedings of the Second International Conference on Approximation and Optimization, Havana University, September 1993, M. Florenzano et al. Eds., Peter Lang Verlag, Frankfurt, 1995, 69‑97.
  5. Ben‑El‑Mechaiekh H., M. Oudadess and J. Tounkara, Approximation of multifunctions on uniform spaces and fixed points, in Topological Vector Spaces, Algebras and Related Areas, A.T‑L. Lau and I. Tweddle, Eds., Pitman Research Notes in Mathematics Series, 316, Longman, New York, 1994, 239‑250.
  6. Ben‑El‑Mechaiekh H., Note On a class of set‑valued maps having continuous selections, Fixed Point Theory and Applications, M.A. Théra. and J.B. Baillon Eds, Proceedings of the “Colloque International sur la Théorie du Point Fixe et Applications”, France, 1989, Pitman Research Notes in Math. Series, 252, 1991, 33‑43.

Selected Research Reports

  1.  Ben‑El‑Mechaiekh H., Continuous approximations of set‑valued maps and fixed points, Rapport de recherche du Centre de Recherches Mathématiques 1820, Université de Montréal, 1992, 46 pages.
  2. Ben‑El‑Mechaiekh H., A remark concerning a matching theorem of Ky Fan, Publications Mathématiques, Ecole Normale Supérieure de Rabat, 1989, (reviewed by Zentralblatt fur Mat.), 5 pages.
  3. Ben‑El‑Mechaiekh H., The coincidence problem for compositions of set‑valued maps Publications Mathématiques, Ecole Normale Supérieure de Rabat, 1989, (reviewed by Zentralblatt fur Mat.), 10 pages.
  4. Ben‑El‑Mechaiekh H., Principes Topologiques en Analyse Convexe, Partie I. Résultats Géométriques, Université de Montréal, 1988, 50 pages.
  5. Ben‑El‑Mechaiekh H., Principes Topologiques en Analyse Convexe, Partie II. Formulations Analytiques, Théorèmes de Minimax et Inégalités Variationnelles, Université de Montréal, 1988, 40 pages.
  6. Ben‑El‑Mechaiekh H. and P. Deguire, Approximation and fixed points for non‑convex set‑valued maps, Rapport de recherche Math‑ 17, Université de Moncton, 1990, 40 pages.
  7. Ben‑El‑Mechaiekh H., P. Deguire, and A. Granas, Analyse Fonctionnelle Non-Linéaire: Points Fixes et Coincidences pour les Applications Multivoques, Parties I & II, Université de Montréal, 1982, 20 pages.
  8. Ben‑El‑Mechaiekh H., P. Deguire, and A. Granas, Une Alternative Non‑Linéaire en Analyse Convexe, Université de Montréal, 1982,7 pages.

Theses

Ben‑El‑Mechaiekh, Quelques Principes Topologiques en Analyse Convexe, Ph.D. Thesis, Université de Montréal, 1987.

Ben‑El‑Mechaiekh, Points Fixes et Coincidences pour les Applications Multivoques, M.Sc. Thesis, Université de Montréal, 1982.

Other

(i) Redaction of Lecture Notes:

Méthodes Topologiques en Analyse Convexe by A. Granas, NATO Advanced Studies Institute, Séminaire de Mathématiques Supérieures, Presses de l’Université de Montréal, 1990.

(ii) Translation

Translation from English into French of “Non‑linear Boundary Value Problems for Certain Classes of Ordinary Differential Equations”, by R.B. Guenther, NATO Advanced Studies Institute, Séminaires de Mathématiques Supérieures, Presses de I’Université de Montréal, 1985.

Experience

Membership on Editorial Boards:

  • Journal of Fixed Point Theory and Applications, Birkhauser, Berlin (http://www.springer.com/birkhauser/mathematics/journal/11784)
  • Arabian Journal of Mathematics, SpringerOpen (http://www.springer.com/mathematics/journal/40065)
  • Palestinian Journal of Mathematics (http://pjm.ppu.edu/)
  • Gulf Journal of Mathematics (http://gjom.org/)
  • Journal of Fixed Point Theory (Working Group on Nonlinear Analysis and Computation; http://jfpt.scik.org/)
  • Advances in Fixed Point Theory (http://scik.org/index.php/afpt/index)
  • Guest Editor: Recent Contributions to Fixed Point Theory and Its Applications, Special Issue of Abstract and Applied Analysis (www.hindawi.com/journals/aaa/si/781509/
  • Guest Lead Editor: Proceeding of the 1st UICPAS 2016 International Conference, University of Management and Technology, Lahore (Special Issue of Journal of Basic and Applied Sciences, in process)

Research Expertise:

  • Mathematical Economic
  • Game Theory
  • Nonsmooth Optimization and Optimal Control
  • Topological and Metric Fixed Point Theory
  • Set-Valued Analysis
  • Differential Equations and Inclusions
  • Point Set and Combinatorial Topology
  • Topological and Variational methods for the solvability of problems lacking compactness and/or convexity in nonlinear functional analysis

Courses Taught in The Past 5 Years

  • MATH 1P01 Calculus Concepts I
  • MATH 1P02 Calculus Concepts II
  • MATH 2P03 Calculus III (Multivariate Calculus)
  • MATH 2P04 Basic Concepts in Analysis
  • MATH 2P08 Ordinary Differential Equations
  • MATH 3P03 Real Analysis
  • MATH 3P97 Introductory Topology
  • MATH 3P98 Functional Analysis (Undergraduate)
  • MATH 4P03 Advanced Real Analysis (Lebesgue Theory)
  • MATH 5P40 Functional Analysis (Graduate)
  • MATH 5P41 Nonlinear Functional Analysis I(Graduate)
  • MATH 5P70  Topology (Graduate)