Department of Mathematics
Islamic Azad Univerity
1 Personal Data
Date of Birth:September 19, 1979
Place of Birth:Neyriz, Fars, Iran
Mother Tongue:Persian (Farsi)
1998–2006: Bachelor, Pure Mathematics, Shiraz University, Shiraz, Iran
2006–2008: M.Sc, Analysis, Shiraz University, Shiraz, Iran
2008–2012: PhD, Analysis, Shiraz University, Shiraz, Iran
2.2 Grade Point Averages (GPA) (out of 20)
M.ScWithout thesis: 17.63, With thesis: 17.75, Thesis: 18.25 (Excellent)
PhD in Analysis: 17.89 (without thesis), Thesis evaluated as: Excellent, defence date: July 18, 2012
2.3 Master thesis
title:Moduli of Continuity supervisor:Bahram Khani Robati evaluated as:excellent
description:The theory of continuous selections of multivalued mappings is an interesting research area in general topology. In this thesis we study an application of this theory to the modulus of continuity. The main result asserts that if and are metrisable spaces, then there exists a continuous function such that for each in and for each if , then , where and denote the spaces of all metrics compatible with the topologies of and , respectively. Among various applications, we show that the group of all homeomorphisms of a topological space endowed with the majorant topology is a topological group.
2.4 Doctoral thesis
title:On Some Properties of the Iteration of Functions supervisor:Bahram Khani Robati evaluated as:Evaluated as excellent
description:First, we discuss necessary and sufficient conditions for the continuous solutions of a simultaneous system of Abel equations. In the study of such equations the iteration of functions plays an essential role. Moreover, we describe such solutions and investigate the relationship between any two continuous solutions of the same system. Second, we determine the structure of disjoint groups of continuous self functions on an open interval. Since the operation of such groups is understood to be the composition of functions, this subject also deals with the iteration of functions. Since disjoint iteration groups are special cases of disjoint groups of continuous functions, our work generalizes the previous ones. The results on simultaneous Abel equations is used as an important tool for this purpose.
3 Professional Employment
Feb.2009–present: Lecturer, Department of Mathematics, Shiraz Branch, Islamic Azad University,
Jul.2012–present: Assistant Professor, Department of Mathematics, Shiraz Branch, Islamic Azad University,
Sep.2017–Jan.2018: Research Fellow, Institute of Mathematics, Polish Academy of Sciences, Supervisor: Andrzej Schinzel
4 Research Interests
4.1 Number Theory
Analytic Number Theory Algebraic Number Theory Arithmetic Number Theory
4.2 Iteration Theory
Characterizing Real Functions Iteration Groups and Semigroups Regular Iterations The Schröder Functional Equation The Abel Functional Equation
5 Teaching Experience
Analysis I, II, III Foundations of Mathematics General Topology Calculus I, II Differential Equations Functional Analysis Measure Theory I, II
1.Member of the mathematics competition team of Shiraz University: 2004 and 2005 2.Member of the Olympiad Team of Shiraz University: 2005 3.Member of Yound Researchers and Elite club, Islamic Azad University: 2017–present
7.1 Published Papers
1. Simultaneous Abel equations, Aequationes Mathematicae, 83:3 (2012), 283–294. (joint work with B. Khani Robati)
2. The structure of disjoint groups of continuous functions, Abstr. Appl. Anal., 2012, Article ID 790758, 14 pages. (joint work with B. Khani Robati)
3. Simultaneous Schröder/Abel equations on the topological spaces, Journal of Difference Equations and Applications, 21:11 (2015), 1119–1145.
4. The structure of regular disjoint groups of real homeomorphisms, Aequationes Mathematicae, 90:3 (2016), 661–670.
5. On a limit formula for regular iterations, Journal of Mathematical Analysis and Applications, 443:2 (2016), 947–958. (joint work with Professor Marek Cezary Zdun)
6. The Schröder equation and its solutions of uniformly regular variation with respect to a given function, Journal of Difference Equations and Applications 24:5 (2017), 784-796
7. Bi-iterative limits used to the theory of the Schröder equation, Journal of Mathematical Analysis and Applications, 456:1 (2017), 608–615.
1. 21st European Conference on Iteration Theory, Innsbruck, Austria, September 4–10, 2016. Title: A Classification of Regularly Varying Functions
2. 17th International Conference on Functional Equations and Inequalities, Bedlwo, Poland, July 9–15, 2017. Title: Precinct Theory: A Useful Tool for Iteration Theory