Research Activities



Selected Research Publications (In refereed Journals)


1.       A.R. Khan (with K. Rowlands), A decomposition theorem for submeasures, Glasgow  Math. J. 26, no.1, 1985, 67-74. PDF


2.       A.R. Khan, On group-valued sbmeasures, Punjab Univ. J. Math. VXII-VXIII, 1984-85, 11-22.


3.       A.R. Khan, A note on semigroup-valued measures, Math. Japonica, 30, no.3, 1986, 399-403.


4.       A.R. Khan (with K. Rowlands), On a theorem of Danes and the principle of equicontinuity, Bolletino UMI (6) 5-A, 1986, 211-215. PDF


5.       A.R. Khan, On the theorem of Helson and the principle of equicontinuity, J.  Natural Sci. and Math. 27, no.1, 1987, 15-19.


6.       A.R. Khan (with A.Q. Siddiqui) Fixed points in metrizable topological vector spaces, Math. Japonica, 36, no.6, 1991, 1129-1134.


7.       A.R. Khan (with S.H. Khan), Principle of equicontinuity for topological groups, Matema. Bech. 44, 1992, 7-10.


8.       A.R. Khan (with Zahida and M. Abbas), Fixed point theorems for set-valued mappings in a semi-convex setting, Southeast Asian Bull. Math.,

      World Scientific Publishing Co., special issue 1993, 43-47.


9.       A.R. Khan (with M.A. Shahid and N.Hussain), Strong uniqueness in metrizable topological vector spaces, Bull. Malaysian Math. Soc. (Second series) 17, 1994, 21-27.


10.   A.R. Khan (with L.A. Khan), An extension of Brosowski-Meinardus theorem on invariant approximation, Approximation Theory and its Applications 11, no.4, 1995, 1-5.


11.   A.R. Khan (with M. Aslam & N. Hussain), Some best approximation results in locally convex spaces, Approximation Theory and its Applications 12, no.3, 1996, 29-36.


12.   A.R. khan (with N. Hussain), Mann iterative construction of fixed points in locally convex spaces, J. Natural Sci. and Math. 26, no.2, 1996, 155-159.


13. A.R. Khan (with N. Hussain & L.A. Khan), A note on Kakutani type fixed point theorems, Internat. J. Math. & Math. Sci. 24, no.4, 2000, 231-235.

14. A.R. khan (with N.Hussain), Best approximation and fixed point results, Indian J. Pure Appl. Math. 31(8), 2000, 983-987. PDF


15.        A.R. Khan (with N. Hussain & A.B. Thaheem), Applications of fixed point theorems to invariant approximation, Approximation Theory and its Applications 16, no. 3, 2000, 48-55.


16.    A.R. Khan (with N. Hussain), Fixed point and best approximation theorems for *-nonexpansive maps, Punjab Univ. J. Math. XXXIII, 2000, 135-144.


17. A. R. Khan (with N. Hussain), Random fixed points for *-nonexpansive random operators, J. Appl. Math.  Stoch. Anal. 14, no.4. 2001, 341-349.


18. A.R. Khan (with N. Hussain), Iterative approximation of fixed points of nonexpansive maps,  Sci. Math. Japon. 54, no.3, 2001, 503-511.


19.    A.R. Khan (with A.B. Thaheem), On some properties of Banach operators, Internat. J. Math & Math. Sci. 27, no.3, 2001, 149-153.


20.    A.R. Khan (with S.H. Khan), Group-valued submeasures and the range of measures, Scientific Annals, of “A1. I. Cuza”, University of Iasi, XLVII, Mate., 2001, 35-42.


21.    A.R. Khan (with N. Hussain), An extension of a theorem of Sahab, Khan and Sessa, Internat J. Math. & Math. Sci. 27, no.11, 2001, 701-706.


22.    A.R. Khan (with A. Latif and A. Bano), Some results on multivalued s-nonexpansive maps, Radovi Mat. 10, no.1, 2001, 195-201.


23.    A.R. Khan (with N. Hussain), Random fixed point theorems for *-nonexpansive operators in Frechet spaces, J. Korean, Math. Soc. 39, no.1, 2002, 51-60. PDF


24.    A.R. Khan (with A.B. Thaheem and N. Hussain), Random fixed points and random approximations in nonconvex domains, J. Appl. Math. Stoch. Anal., 15, no.3, 2002, 263-270.


25.    A.R. Khan (with A. Bano and N. Hussain), Common fixed points in best approximation theory, Internat. J. Pure and Applied Math., 2, no.4, 2002, 411-426.


26.   A.R. Khan (with N. Hussain), Random approximations and random fixed points for

*-nonexpansive maps, Math. Sci. Res. J., 6, no.4, 2002, 174-182.


27.    A.R. Khan (with A. Latif, A. Bano and N. Hussain), Coincidence point results in locally convex spaces, Internat, J. Pure and Applied Math. 3, no.4, 2002, 413-423.


28.    A.R. Khan (with N. Hussain), Common fixed point results in best approximation theory, Applied Mathematics Letters, 16, no.4, 2003, 575-580.


29.    A.R. Khan (with I. Beg and N. Hussain), Fixed point, almost fixed point and best approximation of nonexpansive multivalued mappings in Banach Spaces, Adv. Math. Sci. Appl. 13, no.1, 2003, 83-111.


30.   A.R. Khan (with N. Hussain), Random fixed points of multivalued *-nonexpansive maps, Random Operators and Stochastic Equations, 11, no.3, 2003.


31.   A.R. Khan (with N. Hussain), Applications of the best approximation operator to *-nonexpansive maps in Hilbert spaces, Numer. Funct. Anal. and Optimiz. 24,no.3& 4,327-338. PDF


32.   A.R. Khan (with I. Beg and N. Hussain), Approximation of *-nonexpansive random multivalued operators on Banach Spaces, J. Australian Math. Soc. 76,2004,51-66. PDF


33.   A.R. Khan (with N. Hussain), Common fixed point and best approximation in P-normed spaces, Demonstratio Mathematica 36,no.3,2003,675-681.


34.   A.R. Khan (with N. Hussain and A.B. Thaheem), Random fixed points and random approximations, Southeast Asian Bull. Math.27,2003,1-6.


35.   A.R. Khan (with N. Hussain), Random Coincidence point theorem in Frechet spaces with applications, Stoch. Anal. Appl.22,no.1,2004,155-168. PDF Full File PDF


 36.  A.R.Khan   (with N.Hussain and A.B.Thaheem ) , Some generalizations of Ky Fan,s  best

       approximation theorem, Analysis in  theory and Applications 20 ,no.2,2004,189-198.


 37.  A.R.Khan ( with A.B.Thaheem ) , On some properties of Banach operators II,Inter. J.Math.&

       Math. Sc.47 ,2004,2513-2515.


38.  A.R.Khan (with H.Fukhar-ud-din ),Convergence of implicit iterates with errors for mappings with  unbounded domain in Banach spaces ,Inter.J.Math.&Math. Sc. 10,2005,1643-1653.


 39.  A.R.Khan ( with A.Latif and N.Hussain), Some results on  common fixed points and best approximation,Tamkang J.Math ,36,no.1,2005,33-38.


40.  A.R.Khan ,Properties of fixed point set of a multivalued map,J.Appl.Math. Stoch. Anal.2005:3,2005,323-331.


41. A.R.Khan( with A.A. Domlo ),Common fixed points of compatible maps on balls and eigenvalue problems, Nonlinear Analysis Forum 11,no1,2006,15-21.


 42. A.R. Khan (with F.Akbar,N.Sultana and N.Hussain) ,Coincidence and invariant approximation theorems for generalized f- nonexpansive multivalued mappings, Internat. J. Math. Math. Sci.,2006 ( 2006),1-18.


43.  A.R.Khan ( with A.A. Domlo ) ,Random fixed points of multivalued inward  random operators, J.Appl.Math Stoch. Anal. Volume 2006,Article ID19428,pages1-8 .


44 . A.R. Khan ( with K.Rowlands ) , On locally solid  topological lattice groups, Czechoslovak  Mathematical  Journal ,  57(123), 2007 ,963-9739. PDF Full File PDF


45.  A.R.Khan , On principle of equicontinuity, Engineering  Modelling  ,( National  Academy of Sciences , Ukraine ) 29,no.5,2007,23-32 . PDF  (full file) PDF 


46.  A.R. Khan (with H.Fukhar-ud-din ), Approximating common fixed points of asymptotically nonexpansive maps in uniformly  convex Banach spaces,Compt Math Appl. . 53,no. 9, 2007, 1349-1360. PDF Submitted File PDF


47.    A.R.Khan , (A.A Domlo, H. Fukhar-ud-din) , Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces, J.Math. Anal. Appl. 341 (2008) 1-11. PDF - Submitted File PDF


48.    A.R.Khan (  L. C. Ceng, Q.H.Ansari and J.C.Yao) , Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces , Nonlinear Analysis, in press.PDF

49 .      A. R. Khan ( F. Akbar), Common fixed points from simultaneous best approximations, Taiwanese
Journal of  Mathematics ( Accepted). PDF

50. A. R. Khan( A.A.Domlo, and N.Hussain) "Coincidences of Lipschitz type hybrid maps and invariant approximation," Numerical Functional Analysis and Optimization,  vol.28 , no.9-10,pp. 1165-1177,2007. PDF Submitted File PDF

51.  A. R. Khan (A.A.Domlo), "Coincidence and fixed point of nonself contractive maps with applications," Indian Journal of Mathematics, vol. 49, no. 1, pp. 17-30, 2007. PDF 


Other Publications


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


  1. Fixed point theorems for the sum of two maps in locally convex spaces, Proc. All Pakistan Mathematical Conference, 1997, 15-20.


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



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).





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