Last Updated: February 14, 2010
A: CONTACT INFORMATION
Mehdi Roohi
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar, 47416-1468
Iran
http://mehdi-roohi.page.tl
m.roohi@umz.ac.ir
mehdi.roohi@gmail.com
B : PERSONAL INFORMATION
Date of Birth : 1977
Place of Birth : Amol, Mazandaran, Iran
Sex : male
Status : married, one children, (
Fatima, 29 Jan 2010)
C : EDUCATION
Ph.D. : Geometry of Banach Spaces and Nonlinear Functional Analysis,
University of Mazandarn, 2010.
M.Sc: Functional Analysis,
University of Mazandaran, January, 2005.
B.Sc: Pure Mathematics,
Amir Kabir University of Technology (Tehran Polytechnic), September, 2002.
Dissertation title:
Ph.D: Maximal monotone operators and variational inclusions.
Supervisor: Dr. Mohsen Alimohammay (University of
Mazandaran, Babolsar, Iran)
Advisor 1: Dr. Jafar Zafarani (University of Isfahan, Isfahan, Iran)
Advisor 2: Dr. Javad Mashreghi (University of Laval, Quebec, Canada)
Abstract of Ph.D thesis: This thesis is devoted to generalize maximal monotone operators and variational inclusions theory. Indeed, this thesis is organized as follows. In chapter 1 some preliminary results of topology, functional analysis, set valued analysis and convex analysis which are used in other chapters are gathered. Chapter 2 is devoted to introduce and to investigate monotone and maximal monotone operators, their some generalized versions such as $varepsilon$-monotone, $H$-monotone and $(H,eta)$-monotone operators and also an introduction to variational inequalities and variational inclusions. In this chapter we remember some known properties of monotone operators which we shall generalize most of them in the future chapters. The concepts of premonotone operators and premonotone bifunctions are introduced and considered in chapter 3. In this chapter we will prove many properties of monotone operators (bifunctions) for the larger class of premonotone operators (bifunctions). Indeed, we show that local boundedness in the interior of their domain and some surjectivity properties for operators whose domain is the whole space, remain valid for the larger class of premonotone operators. We will also show a generalization of the Libor Vesely theorem. In chapter 4 a generalized type of monotone operators and their associated resolvent operators are introduced. It is shown that these generalized resolvent operators are single valued and also are Lipschitz continuous under weak assumptions. A new system of nonlinear implicit variational-like inclusions is introduced and by using Lipschitz continuity of the generalized resolvent operator, existence and uniqueness of the solution of this new variational inclusions system is proved. Moreover, a type of variational convergence of operators for generalized monotone operators is established and so by applying this result, stability and convergence analysis for a perturbed three step iterative algorithm are given. Chapter 5 is devoted to introduce and investigate some classes of generalized nonconvex set-valued variational inequalities and general Wiener-Hopf inclusions are introduced. By using the projection technique, equivalence between the generalized nonconvex set-valued variational inequalities and the fixed point problems as well as the generalized nonconvex Wiener-Hopf inclusions are proved. Then by this equivalent formulation, we discuss the existence of solutions of the generalized nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the generalized nonconvex set-valued variational inequalities and their convergence analysis. Chapter 6 deals with some basic notions of convex analysis and convex optimization via convex semi closed functions. A decoupling-type result and also a sandwich theorem are proved. As a consequence of the sandwich theorem, we get a convex subdifferential sum rule and two separation results. Finally, the derived convex subdifferential sum rule is applied to solving the convex programming problem.
M.Sc thesis: Pelczynski's classical properties in Banach spaces.
Supervisor: Dr. Mohsen Alimohammay (University of
Mazandaran, Babolsar, Iran)
Advisor: Dr. Ali Taghavi (University of
Mazandaran, Babolsar, Iran)
Abstract of M.Sc thesis: In this thesis the concepts of property $V$ and $V^*$ introduced by A. Pelczynski are considered and Banach spaces which satisfy these properties are characterized and some conclusions are gathering. In chapter 1 basic preliminaries of Functional Analysis which are used in other chapters are collecting. In the next chapter we consider the notion $V$-sets and Pelczynski's property $V$ and we show as an example that all reflexive Banach spaces have this property. Moreover, the Banach spaces which satisfy it will be characterized. In fact, a Banach space $X$ has the property $V$ if and only if for any Banach space $Y$, any unconditionally converging operator from $X$ to $Y$ is a weakly precompact operator. As a dual of $V$-sets and Pelczynski's property $V$ the concepts $V^*$-sets and Pelczynski's property $V^*$ in chapter 3 are introduced and some important results in these regards investigated. Some characterization of this property are given. For example a Banach space $X$ has property $V^*$ if and only if for any Banach space $Y$, any unconditionally converging adjoint operator from $X^*$ to $Y^*$ is a weakly precompact operator. Finally the properties $wV$ and $wV^*$ introduced by E. Saab and P. Saab in chapter 4 are considered and some results in this connections are studied. The main part of this chapter is a joint work with my supervisor Dr. Mohsen Alimohammady. In this chapter we improve a well known result in Functional Analysis. In fact, we prove that a Banach space contains a copy of $l_1$ if and only if contains a copy of $c_0$ where $X$ has the property $wV^*$.
D : RESEARCH AREAS
Convex Analysis
Variational Analysis
Monotonic Analysis
Fixed Point Theory
Geometry of Banach spaces
General Topology
Algebraic Hyper Structure
Fuzzy Mathematics.
E : TEACHING EXPERIENCE
Foundations of Mathematics (for several various groups of students in Mazandaran University and
Payame Noor University)
Calculus I (for several various groups of students in universities of Mazandaran State)
Calculus II (for several various groups of students in universities of Mazandaran State)
Calculus III for Math students
Ordinary Differential Equations (for several various groups of students in universities of Mazandaran State)
General Mathematics (for several groups of students in Agriculture and Natural Resources )
Mathematics and introduction of Statistics (for several groups of students in Art and Architecture)
Pre-Mathematics (for several various groups of students in universities of Mazandaran State)
Mathematics and its applications in Management (I)
Mathematics and its applications in Management (II)
Statistics and its applications in Management (I)
Operations research (I)
Operations research (II)
F : RESEARCH PROJECTS
[1] M. Alimohammady and M. Roohi, Considering Functional Analysis in View of Fuzzy Theory and Fuzzy Duality, Islamic Azad University, Noor Branch, completed in 2005.
[2] M. Alimohammady and M. Roohi, Topics on Maximal Monotone Operators and Their Applications, Islamic Azad University, Noor Branch, completed in 2008.
[3] M. J. Nematollahi and M. Roohi, On Topological Groups and Fuzzy Minimal Structures, Islamic Azad University, Arsanjan Branch, completed in 2009.
[4] A. Dabbaghian, R. Darzi and M. Roohi,Kinds of Compactness in Fuzzy Topological Spaces, Islamic Azad University, Neka Branch, completed in 2009.
[5] V. Dadashi, A. Dabbaghian and M. Roohi, Variational Inclusion Problems and Resolvent Mappings of Set Valued Monotone Operators, Islamic Azad University,
Sari Branch, to be completed.
[6] Sh. Akbarpour, A. Dabbaghian and M. Roohi, Iterative Algorithm for Solving Variational Inclusions with Monotone Operators, Islamic Azad University, Jouybar Branch, to be completed.
[7] R. Darzi, M. Roohi and S. Mousazadeh, Perturbed Iterative Algorithm for Variational Inclusions with Nonlinear Set Valued Relaxed Co-coercive Operators
in Uniformly smooth Banach Spaces, Islamic Azad University, Neka Branch, to be completed.
[8] M. Salehi, V. Dadashi and M. Roohi, Generalized Hybrid Method for Common Fixed Points of Family of Mappings with Applications in Convex Analysis,
Islamic Azad University, Savadkooh Branch, to be completed.
[9] V. Dadashi, M. Roohi and S. A. Mohammadzadeh, Generalizations of Sandwich and Separation Theorems with Applications in Convex Optimization in Frechet Spaces, Islamic Azad University, Sari Branch, to be completed.
G : PAPERS
[1] M. Alimohammady and M. Roohi, Fixed point in minimal spaces, Nonlinear Anal. Model. Control, 10(4)(2005), 305--314.
[2] M. Alimohammady and M. Roohi, On the weakly precompact and unconditionally converging operators, Glasgow Math. J. 48(2006), 29--35.
[3] M. Alimohammady and M. Roohi, Fuzzy minimal structure and fuzzy minimal vector spaces, Chaos, Solitons & Fractals, 27(3)(2006), 599--605.
[4] M. Alimohammady and M. Roohi, Fuzzy $U_m$-sets and fuzzy $(U,m)$-continuous functions, Chaos, Solitons & Fractals, 28(1)(2006), 10--25.
[5] M. Alimohammady and M. Roohi, On fuzzy $varphipsi$-continuous multifunction, J. Appl. Math. Stoch. Anal. 2006(2006), 1--7.
[6] M. Alimohammady and M. Roohi, Compactness in fuzzy minimal spaces, Chaos, Solitons & Fractals 28(4)(2006), 906--912.
[7] M. Alimohammady and M. Roohi, $Lambda_m$-set in fuzzy minimal space, Journal of Basic
Science 3(2)(2006), 11--17.
[8] M. Alimohammady and M. Roohi, Separation of fuzzy sets in fuzzy minimal spaces, Chaos, Solitons & Fractals 31(1)(2007), 155--161.
[9] M. Alimohammady and M. Roohi, Linear minimal space, Chaos, Solitons & Fractals 33(4)(2007), 1348--1354.
[10] M. Alimohammady and M. Roohi, Fuzzy transfer minimal closed multifunctions, Ital. J. Pure Appl. Math. 22(2007), 67--74.
[11] M. Alimohammady and M. Roohi, Minimal $H_v$-vector spaces, Ital. J. Pure Appl. Math. 22(2007), 177--184.
[12] M. Alimohammady and M. Roohi, Hyper semi-normed spaces, Int. J. Mod. Math. 3(1)(2008), 1--10.
[13] M. Alimohammady and M. Roohi, Remarks on the fixed points on star-shaped sets, Kochi Journal of Mathematics 3(2008), 109--116.
[14] M. Alimohammady, S. Jafari and M. Roohi, Fuzzy minimal connected sets, Bull. Kerala Math. Assoc. 5(1)(2008), 1--15.
[15] M. Alimohammady, M. Roohi and M. R. Delavar, Knaster-Kuratowski-Mazurkiewicz theorem in minimal generalized convex spaces, Nonlinear Funct. Anal. Appl. 13(3)(2008), 483--492.
[16] M. Alimohammady and M. Roohi, Implicit variational-like inclusions involving general (H, eta)-monotone operators, J. Nonlinear Sci. Appl. 1(3)(2008), 145--154.
[17] M. Alimohammady, M. Roohi and V. Dadashi, Baire category theorem in hyper metric space, Int. J. Mod. Math. 3(3)(2008), 337--344.
[18] M. Alimohammady, Kh. Pourbarat, S. A. Mohammadzadeh and M. Roohi, Maximal element theorems in finite continuous spaces, International Journal of Mathematical Sciences 7(3-4)(2008), 215--224.
[19] M. Alimohammady, M. Roohi and M. R. Delavar, Transfer closed multimaps and Fan-KKM principle, Nonlinear Funct. Anal. Appl. 13(4)(2008), 597--611.
[20] M. Alimohammady and M. Roohi, Extreme points in minimal spaces, Chaos, Solitons & Fractals 39(3)(2009), 1480--1485. Fulltext
[21] M. Alimohammady, M. Roohi and M. R. Delavar, Transfer closed and transfer open multimaps in minimal spaces, Chaos, Solitons & Fractals 40(3)(2009), 1162--1168. Fulltext
[22] M. Alimohammady, J. Balooee and M. Roohi, Fixed point theorems for multivalued contractions by altering distance in complete metric spaces, Journal of Advanced Research in Pure Mathematics 1(2)(2009), 1--17.
[23] M. Alimohammady and M. Roohi, A system of generalized variational inckusion problems involving $(A, eta)$-monotone mappings, FILOMAT 23(1)(2009), 13--20.
[24] M. Alimohammady, L. Gholizadeh and M. Roohi, On the markov-Kakutani's fixed point theorem, in press in STUDII SI CERCETARI STIINTIFICE Seria: MATHEMATIC
19(2009).
[25] M. J. Nematollahi and M. Roohi, Fuzzy minimal structures and fuzzy minimal subspaces, accepyed by Ital. J. Pure Appl. Math.
[26] M. Alimohammady and M. Roohi, On the general proximal mappings, Accepted by international Journal of Mathematical Sciences 9(3--4)(2010), 361--367.
[27] M.Alimohammady and M. Roohi, A system of generalized variational inclusions involving G-eta-monotone mappings, accepted by Bull. Iranian Math. Soc.
[28] M. Alimohammady, J. Balooee, Y. J. Cho and M. Roohi, A new system of nonlinear fuzzy variational inclusions involving $(A,eta)$-accretive mappings in uniformly smooth Banach spaces, J. Inequali. Appl. 2009(2009), doi:10.1155/2009/806727.
[29] Sh. Akbarpoor and M. Roohi, Existence, uniqueness and iterative algorithm for variational inclusion problems involving $H$-maximal $m$-relaxed $eta$-monotone
operators, J. Adv. Res. Pure Math. 2(2)(2010), 68--79.
[30] V. Dadashi and M. Roohi, Variational-like inclusion systems via general monotone operators
with convergence analysis, East Asian Math. J. 26(1)(2010), 95--103.
[31] M. Alimohammady, J. Balooee, Y. J. Cho and M. Roohi, An iterative algorithm for solving the generalized nonlinear random $A$-maximal $m$-relaxed $eta$-accretive equations with random fuzzy mappings and relaxed cocoercive mappings in Banach spaces, Adv. Nonlinear Var. Inequal. 13(2)(2010), 37--58.
[32] M. Alimohammady, E. Ekici, S. Jafari and M. Roohi, Fuzzy minimal separation axioms, accepted by The Journal of Nonlinear Sciences and Applications.
[33] M. Alimohammady, V. Dadshi, M. Roohi and Mr M. Salehi, Hybrid method for a family of mappings with applications in zero of maximal monotone operators, accepted by Nonlinear Funct. Anal. Appl.
[34] M. Alimohammady, E. Ekici, S. Jafari and M. Roohi, On fuzzy upper and lower contra-continuous multifunctions, accepted by Iranian Journal of Fuzzy Systems.
[35] M. Alimohammady, J. Balooee, Y. J. Cho and M. Roohi, New perturbed finite step iterative algorithm for a system of extended generalized nonlinear mixed-quasi variational inclusions, accepted by Comput. Math. Appl.
[36] M. Alimohammady, J. Balooee, Y. J. Cho and M. Roohi, Iterative algorithms for a new class of extended general nonconvex set-valued variational inequalities, Nonlinear Anal. 73(2010), 3907--3923.
G: COLLABORATORS
I have had the pleasure to write papers with:
Ms. Shahrbanoo Akbarpoor Kiasari
Islamic Azad University
Jouybar Branch,
Jouybar, Iran,
sh.akbarpoor@math.com
Dr. Mohsen Alimohammady
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar 47416-1468
Iran
E-mail: amohsen@umz.ac.ir
Mr. Javad Balooee
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar 47416-1468
Iran
E-mail: Javad.Balooee@gmail.com
Prof. Yeol Je Cho
Department of Mathematics Education and the RINS,
Gyeongsang National University,
Chinju 660-701, Korea,
E-mail: yjcho@gsnu.ac.kr
Mr. Vahid Dadashi
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar 47416-1468
Iran
E-mail: v.dadashi@gmail.com
Mr. Mohsen Rostamian Delavar
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar 47416-1468
Iran
E-mail: m.rostamian@umz.ac.ir
Dr. Erdal Ekici
Department of Mathematics
Canakkale Onsekiz Mart University
Terzioglu Campus
17020 Canakkale
Turkey
E-mail: eekici@comu.edu.tr
Ms. Leila Gholizadeh
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar 47416-1468
Iran
E-mail: l.gholizade@gmail.com
Professor Saeid Jafari
College of Vestsjaelland South
Herrestraede 11
4200 Slagelse
Denmark
E-mail: jafari@stofanet.dk
Mr. Morteza Koozehgar Kallegi
Department of Mathematics
Faculty of Basic Sciences
University of Mazandaran
Babolsar 47416-1468
Iran
E-mail: m.kallegi@gmail.com
Mr. Seyyed Asghar Mohammadzadeh
Department of Mathematics
Faculty of Sciences
University of Kashan
Kashan
Iran
E-mail: asghar.mohammadzadeh@gmail.com
Dr. Khyrollah Pourbarat
Department of Mathematics
Faculty of Sciences
University of Kashan
Kashan
Iran
E-mail: pourbara@kashan.ac.ir
I: PRESENTATIONS
[1] On fuzzy $varphipsi$-continuous multifunctions, 35^th Annual Iranian Mathematics Conference, January 26--29, 2005, Ahvaz, Iran.
[2] $wV$ and $wV^*$ Property, 15'th Iranian Seminar of Mathematical Analysis and its Applications, March 9--10, 2005, Zahedan, Iran .
[3] Minimal $H_v$-vector spaces, 9_th International Conference in Algebraic Hyperstructures & its Applications [AHA 2005], 1--7 September 2005, University of Mazandaran, Babolsar, Iran.
[4] Some results on fixed points, 36^th Annual Iranian Mathematics Conference, September 10--13, 2005, Yazd, Iran.
[5] Transfer open multimaps and minimal spaces, 37^th Annual Iranian Mathematics Conference, September 2--5, 2006, Tabriz, Iran.
[6] KKM maps and fixed point theorems in $MG$-convex spaces, Symposium of Mathematics, Islamic Azad University--Noor Branch with association Babol Branch, October 6--7, 2006, Noor, Iran.
[7] On the minimal generalized convex spaces, International Conference on Nonlinear Analysis and Optimization, April 25-27, 2007 Isfahan, Iran.
[8] Fuzzy $U_m$-set in Sostak sense, First Joint Congress on Fuzzy and Intelligent Systems, 7^th International Conference on Fuzzy Systems and 8^th Conference on Intelligent Systems, August 29--31, 2007, Mashhad, Iran.
[9] KKM-property via abstract convexity, 38^th Annual Iranian Mathematics Conference, September 3--6, 2007, Zanjan, Iran.
[10] Thychonoff, Himmelberg and Fan-Glicksberg's fixed point theorems in locally $p$-convex spaces, 38^th Annual Iranian Mathematics Conference,
September 3--6, 2007, Zanjan, Iran.
[11] On two functions minimax inequalities in $MG$-convex spaces, The 1st National Conference of Mathematics and its Applications, March 5--6, 2008, Lahijan, Iran.
[12] Lipschitz continuity of resolvent operators associated to a generalized type of monotone operators, 17^th Seminar of Mathematical Analysis and its Applications, April 24--25, 2008, Arak, Iran.
[13] On fuzzy minimal groups, 2^{nd} Workshop on Hyperalgebraic Structures and Fuzzy Mathematics, June 12--13, 2008, Babolsar, Iran.
[14] A system of generalized variational inclusions involving $G$-$eta$-monotone mappings, 8th Seminar of Differential Equations, Dynamical Systems and Their Applications, Isfahan University of Technology, July 19--21, 2008, Isfahan, Iran.
[15] Fuzzy Compactness in fuzzy topological spaces, 2nd Joint Congress on Fuzzy and Intelligent Systems, 8th International Conference on Fuzzy Systems and 9th Conference on Intelligent Systems, October 28--30, 2008, Malek Ashtar University of Technology, Tehran, Iran.
J: MEMBERSHIPS
Iranian Mathematical Society,
IMS.
Working Group on Generalized Convexity,
WGGC.
Research Group in Mathematical Inequalities and Applications,
RGMIA.
EURO Working Group on Continuous Optimization,
EUROPT.
Society for Industrial and Applied Mathematics,
SIAM.
Pacific Optimization Research Activity Group,
POP.