Publications

Department of Mathematics




Publications


1) Books or Chapters Contributed to Refereed Books

H. Ben-El-Mechaiekh, Approximations and Selections Methods for Set-Valued Maps, in Fixed Point Theory, Variational Analysis, and Optimization, Taylor and Francis (2014) 77-138.

H. Ben-El-Mechaiekh, Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps, in Topics in Fixed Point Theory, Springer International Publishing, Switzerland (2013) 245-282.

H. Ben-El-Mechaiekh, Intersection and Fixed Point Theorems in Set-Valued Analysis, in Topics in Nonlinear Analysis, Q. H. Ansari ed., World Education (2011) 159-183. 

H. Ben-El-Mechaiekh, 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.

H. Ben‑El‑Mechaiekh 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 (invited contribution).

H. Ben-El-Mechaiekh and Robert Dimand, "Mathematical economics," in William A. Darity, Jr., ed., International Encyclopedia of the Social Sciences, 2nd. edition, Detroit: Macmillan Reference, 2008 (invited contribution).

2) Articles in Refereed Journal

H. Ben-El-Mechaiekh, On the Convex Hull of Closed Convex Sets in Locally Convex Spaces, British J. Math & Comp. Sc. 4 (10), 1351-1355, 2014.

H. Ben-El-Mechaiekh and F. B. Saidi, On the Continuous Approximation of Upper Semicontinuous Set-Valued Maps, Questions and Answers in General Topology 31, 71-78, 2013.

H. Ben-El-Mechaiekh, On Nonlinear Inclusions in Non-Smooth Domains, Arab J. Math. 1 No. 4, 395-416 (2012).

R. Dimand and H. Ben-El-Mechaiekh, Louis Bachelier’s 1938 Monograph on the Calculus of Speculation: Mathematical Finance and Randomness of Asset Prices in Bachelier’s Later Work, Electronic Journal for the History of Probability and Statistics (Accepted).

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, pp. 97-118 (2012).

H. Ben-El-Mechaiekh, Intersection Theorems for Closed Convex Sets and Applications, Missouri J. Math. Sc., 17 pages, 2012 (in print).

H. Ben-El-Mechaiekh and R. Dimand, A Simpler Proof of the von Neumann Minimax theorem, American Mathematical Monthly 118 (2011), 636-641.

H. Ben-El-Mechaiekh and R. Dimand, Von Neumann, Ville, and the Minimax Theorem, International Game Theory Review 12 No. 2 (2010), 1-23.

H. Ben-El-Mechaiekh, 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.

H. Ben-El-Mechaiekh, Equilibria for Set-valued Maps on Nonsmooth Domains, J. Fixed Point Theory and Applications 4 (2008) 177-182.

H. Ben-El-Mechaiekh, Strong Approximation for Nonconvex Set-valued Maps, J. of Nonlinear and Convex Analysis  9  (2008) 65-70.

H. Ben-El-Mechaiekh 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.

R. Dimand 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, 225-237 (2006).

H. Ben-El-Mechaiekh, The Ky Fan Fixed Point Theorem on Star-Shaped Domains, Math. Reports. Acad. Sc. Canada, 27 (4) (2005) 97-100.

H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano, A generalized KKMF Principle and Applications, J. Math. Anal. Appl 309 (2005) 583-590.

H. Ben‑El‑Mechaiekh, S. Chebbi and M. Florenzano, A nonlinear alternative for approximable maps: a simple proof, Proceedings of the American Math. Soc. 126 (1998) 2345-2349.

H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano and J-V. Llinares, Abstract convexity and fixed points, Journal of Math. Analysis and Applications 222 (1998) 138-150.

H. Ben‑El‑Mechaiekh and G. Isac, Some geometric solvability theorems in topological vector spaces, Bulletin of the Korean Math. Soc. 34 (1997), 273-285.

H. Ben‑El‑Mechaiekh and W. Kryszewski, Equilibria for set‑valued maps on nonconvex domains, Transactions of the American Math. Soc. 349 (1997) 4159-4179.

H. Ben‑El‑Mechaiekh and W. Kryszewski, Equilibria for perturbations of upper semicontinuous set‑valued maps by convex processes, Georgian Journal of Math. 3 (1996) 201‑215.

H. Ben‑El‑Mechaiekh and A. Idzik, Ky Fan type coincidence theorems I, Bulletin of the Polish Academy of Science 122 (1994) 105-109.

H. Ben‑El‑Mechaiekh and W. Kryszewski, Equilibres dans les ensembles non‑convexes, Comptes Rendus de l’Académie des Sciences de Paris 320, Série 1 (1995) 573‑576.

H. Ben‑El‑Mechaiekh and M. Oudadess, Some selection theorems without convexity, Journal of Math. Analysis and Applications 195 (1995) 614‑618.

H. Ben‑El‑Mechaiekh and P. Deguire, Equilibrium for abstract nonconvex games, Mathematical Reports of the Academy of Science of Canada XVII (1995) 1‑6.

H. Ben‑El‑Mechaiekh and G. Isac, A general variational inequality with application, Mathematical Reports of the Academy of Science of Canada XVII (1994) 235‑240.

H. Ben‑El‑Mechaiekh and A. ldzik, A Leray‑Schauder theorem for approximable set-valued maps, Proceedings of the American Mathematical Society 122 (1994) 105-109.

H. Ben‑El‑Mechaiekh, Fixed points for compact set‑valued maps, Questions and Answers in General Topology 10 (1992) 153‑156.

H. Ben‑El‑Mechaiekh and P. Deguire, Approachability and fixed points for nonconvex set‑valued maps, Journal of Mathematical Analysis and Applications 170 (1992) 477‑500.

H. Ben‑El‑Mechaiekh, General fixed point and coincidence theorems for set-valued maps, Mathematical Reports of the Academy of Science of Canada XIII (1991) 237‑242.

H. Ben‑El‑Mechaickh 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.

H. Ben‑El‑Mechaiekh 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.

H. Ben‑El‑Mechaiekh, The coincidence problem for compositions of set‑valued maps Bulletin of the Australian Math. Society 41 (1990) 421‑434.

H. Ben‑El‑Mechaiekh, Zeros for set‑valued maps with non‑compact domains, Mathematical Reports of the Academy of Science of Canada XII (1990) 125‑130.

H. Ben‑El‑Mechaiekh, A remark concerning a matching theorem of Ky Fan, Chinese Journal of Mathematics 17 (1989), 309‑314.

H. Ben‑El‑Mechaiekh, Fixed points for compositions of set‑valued maps, Extracta Mathematicae 4 (1989), 93‑95.

H. Ben‑El‑Mechaiekh, 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.

H. Ben‑El‑Mechaiekh, 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.

H. Ben‑El‑Mechaiekh, 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.

H. Ben‑EI‑Mechaiekh, 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.


3) Refereed Conference Proceedings

H. Ben-El-Mechaiekh, 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.

H. Ben-El-Mechaiekh, 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.

H. Ben‑El‑Mechaiekh 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.

H. Ben‑El‑Mechaiekh, Continuous approximation o 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.

H. Ben‑El‑Mechaiekh, 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.

H. Ben‑El‑Mechaiekh, 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.

 

4) Selected Research Reports

 

H. Ben‑El‑Mechaiekh, Continuous approximations of set‑valued maps and fixed points, Rapport de recherche du Centre de Recherches Mathématiques 1820, Université de Montréal, 1992, 46 pages.

H. Ben‑El‑Mechaiekh, A remark concerning a matching theorem of Ky Fan,  Publications Mathématiques, Ecole Normale Supérieure de Rabat, 1989, (reviewed by Zentralblatt fur Mat.), 5 pages.

H. Ben‑El‑Mechaiekh, The coincidence problem for compositions of set‑valued maps Publications Mathématiques, Ecole Normale Supérieure de Rabat, 1989, (reviewed by Zentralblatt fur Mat.), 10 pages.

H. Ben‑El‑Mechaiekh, Principes Topologiques en Analyse Convexe, Partie I. Résultats Géométriques, Université de Montréal, 1988, 50 pages.

H. Ben‑El‑Mechaiekh, Principes Topologiques en Analyse Convexe, Partie II. Formulations Analytiques, Théorèmes de Minimax et Inégalités Variationnelles, Université de Montréal, 1988, 40 pages.

H. Ben‑El‑Mechaiekh and P. Deguire, Approximation and fixed points for non‑convex set‑valued maps, Rapport de recherche Math‑ 17, Université de Moncton, 1990, 40 pages.

H. Ben‑El‑Mechaiekh, 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.

H. Ben‑El‑Mechaiekh, P. Deguire, and A. Granas, Une Alternative Non‑Linéaire en Analyse Convexe, Université de Montréal, 1982,7 pages.

 

5) Theses

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

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

 

6) 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.