Welcome to website of  professor abdul rahim khan

 

Academic Resume of Dr. Abdul  Rahim  Khan

 
   
Nationality Pakistani
 
Date of Birth

January 1, 1953
Present Address Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, (KFUPM), Dhahran 31261, Saudi Arabia
 

Academic Record
Ph.D. University of Wales, UK, 1983
M.Sc. University of the Punjab, Lahore, Pakistan, 1974
B.Sc.(Hons.) University of the Punjab, Lahore, Pakistan, 1973
Major Field Nonlinear Functional Analysis
Areas of Research Interest Fixed Point Theory and its Applications, Approximation Theory, Operator Theory, Iterative Methods, Measure Theory and Integration.
 

Professional  Experience

Professor

Department of Mathematics and Statistics, KFUPM, Dhahran , Saudi Arabia. July 2008 to date.
Associate Prof.

Department of Mathematics and  Statistics, KFUPM, Dhahran , Saudi Arabia. September 1997  -June 2008 .
Professor Center for Advanced  Studies in Pure and Applied Mathematics (CASPAM),Bahauddin Zakariya University (BZU) ,Multan , Pakistan .January 1996 –August 1997.
Associate Prof. CASPAM, B.Z. University, Multan, Pakistan. May 1988 - December 1995.
Assistant Prof. CASPAM, B.Z. University, Multan, Pakistan.August 1984 -  May 1988.
Lecturer Department of Mathematics, University of Multan, Pakistan.October 1976 -  August 1984.
 

Administrative Experience
Director CASPAM, B.Z. University, Multan, Pakistan. September 1995 -  December 1996.
President Bahauddin Zakariya University Teachers Association.1991 - 1997.
Students Advisor CASPAM ,B.Z.University ,Multan,1983-1992 .
Treasurer Pakistan Teachers Forum.1991-1997.
Secretary

Pakistan Association for the Advancement of Science, Multan Local Chapter 1987-1992
Chief Organizer Zakarian Mathematical Society.
Coordinator Math Education Seminar, KFUPM, 2002- to date
Coordinator Text book, Department of Mathematics & Statistics, KFUPM, 2006---to date
 

Member of Professional Societies
Member American Mathematical Society (1990-91, 1994-95 and 2000-2011).
Member Japanese Association of Mathematical Sciences (2000-2001).
Life Member

Punjab Mathematical Society.
Life Member Zakariyan Mathematical Society.
Member All Pakistan Mathematical Society.
Member Pakistan Association for the Advancement of Science
 

Awards of Scholarship
 

Merit Scholarship in B.Sc. Hons. (1970-73)

Merit Scholarship in M.Sc.  (1974)

Central Overseas   Training Scholarship, Govt. of  Pakistan (1979-1983 ).

Post Doctoral Fellowship ,  British Council (August1994 –January 1995 )
 

Awards Won
  Excellence in  Research Award, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 2010
  Best Research Project Award, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 2012
 

Research Activity

  
 

Thesis Supervision

  
  Ph.D.Thesis supervised at KFUPM
 

A. A. Domlo (ID #200652)  Fixed points of some nonlinear maps with applications, 2006

 

Sami Shukri   (ID #  201106910201106910201106910 )  Common Fixed Point Problem and Iterativ  Methods   [ In progress]. 

 
 

Ph.D. Thesis supervised at University of Sargodha, Pakistan

 
 
  1. Farhana Akbar , Fixed point and best approximation results in certain topological vector spaces, 2011.
 
 

 Theses supervised at B. Z. University, Multan, Pakistan

 
 

(a)   Ph.D. Theses Supervised

 

(1) Nawab Hussain                    Some  types of best approximation and their applications, 2002.

 

           (2) Arjamand Bano           Fixed points for multivalued maps, 2004.

 

           (3 ) M.Arif Rafiq                Fixed point  theorems in generalized metric and

                                                           Banach  spaces ,2004  .

                                                          

(b)         M. Phil. Thesis Supervised

 

1.

Attiya Qaseem Siddiqui

The strict convexity and fixed point theorems, 1987.

2.

M. K. Mehmood

The fixed points of non-expansive mappings,1988 (Review).

3.

Naseem Gul

The Hewitt-Yosida decomposition, 1988 (Review).

4.

Safeer Hussain

Group-valued order continuous submeasures, 1990.

5.

Mujahid Abbas

Multifunctions and the existence of best approximation, 1992.

6.

M. Shahid Ashraf

Strongly unique best approximation in metrizable topological vector spaces, 1993.

7.

M. Aslam

Best approximation and fixed point theorems in locally

convex spaces, 1995.

8.

Hamid Ayaz

Some aspects of strong uniqueness, 1995.

9.

Gulam Mustafa

Fixed point theorems for multivalued mappings, 1996.

10.

M. Akram

Some studies in open mapping and closed graph theorems, 1996.

 
 

.Theses  reviewed and examined

 Theses  reviewed and examined

Ph. D. Theses

    1.        Mujahid Abbas ,  Solution of random operator equations   and   inclusions, 2005

           ( written under the supervision of Professor I.Beg  , LUMS,  Lahore   ,Pakistan).

 

2.   Afrah A.N.Abdou, Generalized distance with application to fixed point theory, 2010

           (written under the supervision of Professor A.Latif, KAU, Jeddah, Saudi Arabia) .

 

3        Zahra Al-Rumaih, Analytic and iterative methods for fixed points and equlibria,2013.

( written under the supervision of Dr. Souhail Chebbi, KSU, Riyad, Saudi Arabia)

 

 
 

 M. Phil. Theses , Quaid-e-Azam University, Islamabad, Pakistan.

 

1.  Fixed point theorems, 1986.

2.  Integral representation of linear operators, 1987.

3.  Decompositional properties of Banach spaces, 1988.

4.  Best approximation in function spaces, 1990.

5.  P. Commutative topological algebras, 1991.

6.      Compact and precompact operators on topological vector spaces, 1991.

7.  Gelfand representation theory of topological algebras, 1991.

8.  Fixed point theorems in probabilistic spaces, 1991.

9.  Decomposition of C*-algebras relative to a functional equation, 1991.

10.  Weak resolvents of operators, 1992.

 

M.S. Theses, King Abdulaziz University, Jeddah, Saudi Arabia

1.  

On coincidence points for hybrid contraction maps, 2001.

2.  

Derivations on Banach and   topological   algebras, 2003.

3.  

Multipliers and   Aren   product on topological   algebras, 2003.

4.  

Fixed points for  nonexpansive maps in locally convex spaces, 2005

5.  

Continuity of algebra homomorphisms  on topological algebras, 2006 .

6.  

Best approximation in nonA-rchmidean vector-valued function spaces, 2008 .

7.  

On some classes of statistical convergence,2009.

8

 Topological  Modules of Multipliers, 2010

 

Refereed Papers for:

1.  

Applicable Analysis

2.  

Applied Mathematics Letters

3.  

Taiwaneese Journal of  Mathematics

4.  

Journal of Applied Mathematics and Stochastic Analysis

5.  

International Journal of Mathematics and Mathematical sciences,

6.  

Journal Natural Science & Mathematics

7.  

Arabian Journal  for Science and  Engineering

8.  

Carpathian Journal of  Mathematics

9.  

Indian  Journal of Mathematics

10.   

The Science Journal of King Abdulaziz University

11.   

Punjab University  Journal of Mathematics

12.   

Computers & Mathematics with Applications

13.   

Bulletin of the Belgian Mathematical  Society

14.   

Tamkang Journal of Mathematics

15.   

Turkish Journal of Mathematics

16.   

Fixed point theory  and applications

17.   

Journal of inequalities and applications

18.   

Demonstratio Mathematica

19.   

Numerical Functional Analysis and optimization

20.   

Thai Journal of Mathematics

21.   

Opuscula Mathematica

22.   

Nonlinear Analysis, Theory ,Methods, Applications

23.   

An. St. Univ. Ovidius, Constanta, Seria Matematica

24.   

Journal of Applied Mathematics and Computing

25.   

Hacettepe Journal of Mathematics and Statistics

26.   

Mathematical and Computer Modelling

27.   

Applied Mathematics and Computation

28.

29.

30.

31.

32.

33.

Journal of Optimization Theory and Applications

Abstract Applied Analysis

Arab Journal of Mathematical Sciences

 Journal of Mathematical Analysis and Applications

 Kragujevac Journal of Mathematics

 Acta Math Sinica, China

34. Journal of Applied Analysis and Computation (JAAC), Shinghai  Normal University & Wilmington scientific Publisher

35. Filomat

36. Kochi Journal of Mathematics

37. Advances in Pure and Applied Mathematics(APAM)

38. Dynamics of continuous, discrete and impulsive systems

      ------ Applications and Algorithms

 

 

 

 Papers Reviewed for the Mathematical Reviews

 

1-O,Regan, Donal, Learay- Schauder and  Krasnoselskii fixed point theory in Frechet spaces for Urysohn type operators, Advances in nonlinear analysis: theory methods and applications, 149-163 , Math Probl. Eng. Aerosp. Sci.,3,Camb. Sci. Publ., Cambrdige,2009.
 

2-MR2790449 Açikgöz, M.; Karakuş, Y.; Aslan, N.; Araci, S. Some results on approximations in 2-Banach spaces. Proc. Jangjeon Math. Soc. 14 (2011), no. 1, 173–181.
 

3-MR2656001 de Blasi,F.S. Semifixed sets of maps and Rådström embedding in locally convex topological linear spaces. Fixed Point Theory 11 (2010), no. 1, 11–28.
 

4-MR2532752  Singh, S. L.; Mishra, S. N.; Pant, Rajendra New fixed point theorems for asymptotically regular multi-valued maps. Nonlinear Anal. 71 (2009), no. 7-8, 3299–3304.

 

5-MR2655484  Antony, Jessy A minimal point theorem in product spaces. J. Pure Math. 25 (2008), 95–100.
 

6-MR2445704  Nashine, H. K.; Dewangan, C. L. Existence results on best proximity pair for multifunction. Focus on African diaspora mathematics, 167–177, Nova Sci. Publ., New York, 2008.
 

7-MR2436164  Li, S. J.; Zhang, W. Y. A minimization theorem for a set-valued mapping. Appl. Math. Lett. 21 (2008), no. 8, 769–773
 

8-MR2290051 (2008d:49012) Hai, N. X.; Khanh, P. Q. The solution existence of general variational inclusion problems. J. Math. Anal. Appl. 328 (2007), no. 2, 1268--1277.
 

9-MR2355768 (2008k:47130) Žikić-Došenović, Tatjana Probabilistic contractor and nonlinear operator equations with set-valued operator in probabilistic normed spaces. Fixed point theory and applications. Vol. 7, 189--199, Nova Sci. Publ., New York, 2007.
 

10-MR2172319 (2006i:41029) O'Regan, Donal; Shahzad, Naseer Invariant approximations for generalized  I -contractions. Numer. Funct. Anal. Optim. 26 (2005), no. 4-5, 565--575.

11-MR2147613 (2006f:49015) Kimura, Yasunori On Mosco convergence for a sequence of closed convex subsets of Banach spaces. Banach and function spaces, 291--300, Yokohama Publ., Yokohama, 2004.

 

12-MR2128782 (2006b:41051) Narayana, Darapaneni; Rao, T. S. S. R. K. Proximinality in generalized direct sums. Int. J. Math. Math. Sci. 2004, no. 65-68, 3663-----
 

13-MR1997786 (2004i:49024) Zhang, H.-L. On maximal element problem and quasi-variational inequality problem in l.c. metric spaces. J. Appl. Anal. 9 (2003), no. 1, 131--138.

 

14-MR1929430 (2003j:47071) Frigon, M.; O'Regan, D. A Leray-Schauder alternative for Mönch maps on closed subsets of Fréchet spaces. Z. Anal. Anwendungen 21 (2002), no. 3, 753--760.

 

15-MR2043195 (2005c:49048) Zhu, Jiang Locally variational principle and surjective mapping theorems of set-valued mappings. Fixed point theory and applications. Vol. 2 (Chinju/Masan, 2000), 185--200, Nova Sci. Publ., Huntington, NY, 2001.
 

16-MR1892912 (2003d:49010) Naselli, Ornella A class of functionals on a Banach space for which strong and weak local minima do coincide. Optimization 50 (2001), no. 5-6, 407--411.
 

17-MR1867790 (2003a:41035) Li, Chong; Ni, Renxing; Watson, G. A. On nonlinear coapproximation in Banach spaces. Approx. Theory Appl. (N.S.) 17 (2001), no. 2, 54--63.

 

18-MR1814140 (2002b:47108) Agarwal, Ravi P.; O'Regan, Donal Essentiality for Mönch type maps. Proc. Amer. Math. Soc. 129 (2001), no. 4, 1015--1020 (electronic)
 

19-MR1812588 (2002c:47126) Kim, In-Sook Fixed point theorems of quasicompact multivalued mappings in general topological vector spaces. Bull. Korean Math. Soc. 38 (2001), no. 1, 113—120 .
 

20-MR1810576 (2002b:41021) Dinh Dung On asymptotic orders of n-term approximations and non-linear n-width, Vietnam J. Math.27 (1999), no. 4, 363-367.
 

 

PARTICIPATION   IN   SHORT   COURSES

 

1)   Nonstandard Analysis, University College of Wales, Aberystwyth ,UK (1980)

2)   British Mathematical Colloquium (1981 and 1982.)

3)   Recent Developments in Mathematics and Computer Science and their Applications, ICTP, Trieste, Italy (May-June, 1990).

4)   Topics in Nonlinear   Analysis with Applications to Differential   Equations, KFUPM(2003) . 

5)   Sobolev Spaces, KFUPM(2004 ) .

6)   Mathematical Economics (2009).

7)   Wavelets and Frames

 

 Note: These programmes were offered by prominent faculty members from various British and   American   Universities and KFUPM.

 

Editor

 

1-    Carpathian Journal of Mathematics, Romania, ISI journal

2-   Arab Journal of Mathematics ,King Fahd Univ. of Petroleum & Minerals, Dhahran, Saudi Arabia

 
   
   
 

Number of Citations on Google Scholar  959
 
 

Non-Self Citations [Incomplete] 435
 
 

Number of citations (Web of Knowledge) 326

 

Conference publications

                        

1.      A. R. Khan ,N. Hussain and M. Aslam ,Fixed point theorems for the sum of two maps in locally convex spaces, Proc. All Pakistan Mathematical Conference, 1997, 15-20.

 

2.      A. R. Khan ,Common fixed points from best approximation, Proc. 26th Summer Symposium in Real Analysis (Washington and Lee University), Real Analysis Exchange, 2002, 189- 196.

 

3.      A. R. Khan , Random  coincidence points of multivalued contractive random Operators ,Proc. International Conference on Nonlinear Analysis and Convex        Analysis, Okinawa ,    2005,215-226

 

4.      A. R. Khan, Best approximation operator and  fixed points of  multivalued mappings ,Modern Mathematical Models, Methods and  Algorithms for Real World Problems, Anamaya Publishers ,New Delhi,2007.

5.      A.R.Khan , Common fixed point iterations of a finite family of quasi-nonexpansive maps,  Proceedings of the World Congress on Engineering 2009 vol.II( WCE 2009),London ,2009, 1219-1223.

6.      A. R. Khan and H.Fukhar-ud-din, "Weak Convergence of Ishikawa Iterates for Nonexpansive Maps," in Proceedings of the World Congress on Engineering and Computer Science WCECS 2010, October 20-22, 2010, San Francisco, USA, 2010, pp. 1026-1029.

7.      A. R.Khan and A.A.Domlo, "Random Ishikawa iteration scheme of two random operators"," in Proc. 2011 Int.Conf. Appl. Engin. Math.,Imperial,College,London., 2011, pp. 165-169.

8.      A. K.Katsaras, L.A,Khan, and A.R.Khan, "On maximal closed ideals in topological algebras of continuous vector -valued functions over non-Archimedean valued fields," in Contemporary Mathematics Vol. 551 ;Proc. 11th International conference on P-adic Functional Analysis, 2011, pp. 135-141.

9.      H. Fukharuddin, A. R. Khan, and M. A. A. Khan, A new implicit algorithm of asymptotically quasi-nonexpansive maps in uniformly convex Banach spaces, IAENG International Journal of Applied Mathematics, 42, No. 3( 2012), 171-175.

10.   A.R. Khan and H. Fukhar-ud-din, A unified approach to iterative construction of  common fixed points in nonlinear domains, Proceedings of the 10th IC-FPTA, 143 – 156,July 9-18, 2012, Cluj-Napoca, Romania.

 

Papers Under Review for Publication in Refereed Journals
  1.  

A. R. Khan, Random coincidence points of contractive multivalued mappings.

 

      

  1.  

H.Fukhar-ud-din and A. R. Khan , Implicit iteration  process for a finite family of asymptotically quasi-nonexpansive maps without rate of convergence condition .

 

 

Other Publications

  

            1. A. R. Khan, "On group-valued measures and submeasures and locally solid topological l-groups," Ph.D. Dissertation, Department of Pure Mathematics, University of Wales, Aberystwyth, Wales, U. K., 1983. 

 

            2. Introduction to Lebesgue Integration , Ilmi Kitab Khana, Lahore, Pakistan, 1993 (M.Sc. Level Book).

 

 Seminars / Invited Lectures

 

 

1.      A measure-theoretic proof of the uniform boundedness principle, Department of Pure Mathematics, University College of Wales, Aberystwyth, UK (1979).

 

2.      On the generalization of exhaustion principle for submeasures, Conference Scientific Society of Pakistan, University of Karachi, Pakistan (1983).

 

3.      On a theorem of Danes and the principle of equicontinity for topological groups, All Pakistan Mathematical Conference, Quaid-e-Azam University, Islamabad, Pakistan (1985).

 

4.      On locally solid topological l-groups, accepted for presentation at International Congress of Mathematicians, Berkeley, California, USA (1986).

 

5.      Decomposition theorems for group-valued submeasures, under the auspices of Research and Planners Group, B.Z. University, Multan, Pakistan (1986).

 

6.      Some recent developments in functional analysis, Department of Mathematics, Govt. F.C. College, Lahore, Pakistan (1989).

 

7.      Mathematical logic and reasoning, Summer School in science for talented students of Intermediate classes from all Boards of Education from the Punjab province arranged by the Board of Intermediate and Secondary Education Multan at Khanaspur, Pakistan (1991).

 

8.      Fixed point theorems for set-valued mappings in a Semi-Convex setting, Manila International Conference on Functional analysis and Global analysis (1992).

 

9.      Some aspects of Ky Fan best approximation theorem, Department of Mathematical Sciences, KFUPM, Dhahran, Saudi Arabia (1998).

 

10.  Random fixed point results for *-nonexpansive operators and their applications, Department of Mathematical Sciences, KFUPM, Dhahran, Saudi Arabia (2000).

 

11.  Common fixed points form best approximation, 26th Summer symposium in Real Analysis, Washington and Lee University ,Lexington,U.S.A. (2002).

 

12.    Noncommuting maps, Coincidence points and invariant approximation, Lahore University of Management Sciences (LUMS), Lahore, Pakistan, 2002.

 

13.    Coincidence point theory: Existence and Applications, Department of Mathematical Sciences, KFUPM, Dhahran, Saudi Arabia (2003).

 

 

14.  Applications of best approximation operator, Poster  presentation , Fifth International Congress       on Industrial  and     Applied Mathematics, Sydney, Australia (2003) .

 

15.  Random coincidence point of random multivalued operators,  The    fourth international conference on   Nonlinear Analysis and   Convex   Analysis   , Okinawa, Japan, 2005.

 

16.     Coincidences and a general  scheme for non-commuting maps ,Ist Mathematics Conference ,Bahauddin Zakariya University, Multan , Pakistan 2007 .

 

17.  An iterative scheme of a   nonexpansive map and its applications , Summer conference in mathematics ,LUMS ,Lahore, PAKISTAN, 2007 .

 

18.  Fixed point iteration process of nonexpansive mappings---A unified  approach , Engineering Mathematics and Applications Conference ,University of Tasmania , Hobart , Australia ,2007.

 

19.  Ishikawa Iteration Process for Nonself Nonexpansive Maps in Banach Spaces , International Conference of Applied and Engineering Mathematics,
 Imperial College ,London ,England,2008.

20.  Common fixed point iterations of a finite family of quasi-nonexpansive  maps, International Conference of Applied and Engineering Mathematics,
 Imperial College ,London ,England,2009.

21.  Weak Convergence of Ishikawa Iterates for Nonexpansive Maps , International Conference of Applied and Engineering Mathematics,
 Imperial College ,London ,England,2010.

22.  Convergence of Implicit Iterations without Fast Rate of Convergence Condition, 11th International Conference on P-Adic Functional Analysis, Université Blaise Pascal, Clermont-Ferrand, France, 2010.

23.  Convergence of an implicit algorithm for  a finite family of asymptotically quasi- nonexpansive maps, Numerical Analysis Conference 2011,University of Strathclyde, Glasgow, UK,2011.

24.  Random Ishikawa iteration scheme of two random operators, International Conference of Applied and Engineering Mathematics,
 Imperial College, London England, 2011.

25.   A unified approach to iterative construction of common fixed points in nonlinear domains, 10th International Conference on Fixed Point Theory and Applications, Babes-Bolyai University, Cluj-Napoca, Romania, 2012.

26.  Nonlinear functional equations and common fixed point, International Conference on the Theory, Methods and Applications of Nonlinear Equations, Texas A & M University -Kingsville, USA.,2012.

27.  Well-Posedness of common fixed point problem in vector lattices, International Conference on Mathematical Sciences and Statistics, ICMSS2013, Kuala Lumpur, Malaysia, 2013.

28.Common Fixed Point Iterations of Generalized Asymptotically   Quasi-Nonexpansive Mappings in Hyperbolic Spaces” Applied Mathematics Section(AEM-S), 2014 Spring World Congress on Engineering and Technology(SCET 2014),Shanghai, China[April 16-18,2014].

          29- Iterative Methods for Common Fixed Point Problem, 5th