Dr. Liaqat
Ali Khan (CV & Publications)
Personal data:
Name: Liaqat Ali Khan
Date & Place of
Birth: July 29, 1947 (Jhelum,
Nationality: Pakistani
Permanent Address: House
No. 468, Street No. 74,
Present Address: Department of Mathematics, Faculty of Science,
Jeddah-21589,
E-Mail: akliaqat@gmail.com
; lkhan@kau.edu.sa
URL: http://liaqat.adtime.co.uk
; http://lkhan.kau.edu.sa
Education:
1. B.A. (1964-66) Mathematics
1. M.A. (1966-68) Mathematics
3. Ph.D. (1974-77) Mathematics
Ph.D. Thesis: "The Strict Topology and its
Generalizations" (1977)
(supervised by Dr. K. Rowlands,
Field of Research: Functional Analysis and Topology
(i) Spaces of continuous
vector-valued functions (with various linear topologies);
(ii) Stone-Weierstrass
and Arzela-Ascoli type theorems (for vector-valued
continuous functions);
(iii) Vector-valued measures
and integration;
(iv) Fixed point theorems and Best Approximation;
(v) General strict topology on
topological Algebras and modules;
(vi)
Multipliers and
Quasi-multipliers on topological Algebras and modules;
(vii) Differentiation and Mean
Value Theorems in TVSs;
(viii) Almost periodicity of functions with
values in a TVS.
Courses Taught: (B.Sc./M.Sc./M.Phil. Levels)
(i) Calculus and Analytic
Geometry, Engineering Mathematics, Differential Equations;
(ii) Linear Algebra, Abstract
Algebra;
(iii) Real Analysis, Complex
Analysis, Functional Analysis;
(iv) General Topology;
(v) Measure and Integration
Theory;
(vi)
Topological Vector
Spaces, Topological Algebras, Ordered Topological Vector Spaces, Non-archimedean Functional Analysis;
(vii) Fixed Point Theory,
Approximation Theory.
Teaching positions:
1968-1971: Lecturer
1971-1973: Lecturer Federal Government College, Islamabad
(1974-1977: Ph. D. student
1977-1981: (i) Lecturer Federal Government College, Islamabad
(ii)
1981-1986: Assistant Professor Garyounis
University, Benghazi
1986-1988: Assistant Professor Federal Government College, Islamabad
1988-1991: Assistant Professor
Quaid-i-Azam
University, Islamabad
1991-1996: Associate Professor
Quaid-i-Azam
University, Islamabad
1996-2003: Associate Professor
King Abdulaziz
University, Jeddah
2003-todate: Professor King Abdulaziz
University, Jeddah
Theses Supervised (M.
Phil, M.Sc. and Ph.D.):
(I) M.
Phil Theses (supervised at QAU, Islamabad)
1.
On a
class of ordered topological vector spaces (Farhad
Ali, 1981).
2.
Theory
of double centralizer algebras (Akhtar Hussain, 1981).
3.
Best
approximation in function spaces (Muhammad Ali, 1990)
4.
Compact
and precompact operators on topological vector spaces
(Muhammad Akram, 1991).
5.
Fixed
point theorems and applications (Muhammad Iqbal,
1991).
6.
Locally
m-convex and A-convex algebras (Arshad Imam, 1991).
7.
Optimization
in ordered topological vector spaces (Muhammad Arif,
1991).
8.
Metric
projections in best approximation theory (Zafar Iqbal, 1993).
9.
Approximation
in non-archimedean function space (Khalil Ahmad,
1994).
10.
Topologies
on function spaces (Ali Muhammad, 1996).
11.
Fuzzy
topological vector spaces (Zafar Hussain,
1996).
12.
Vector-valued
measures and integration (Mohammad Sagheer, 1997).
13.
Weighted
approximation in vector-valued function spaces
(Khalida Parveen,
1997).
14.
Fixed points and best approximation theorems
in convex and H-spaces (Fazeelat Sultana, 1998).
(II) M. Sc.
Theses (supervised at KAU, Jeddah)
1.
Multipliers on commutative Frechet
algebras (Areej Al-harbi,
KAU, 2003).
2. Multipliers
and Arens product in topological algebras(Maha Saeed, KAU, 2003).
3. Derivations
on Banach and Topological algebras (Abeer Badgaish, KAU, 2003).
4. Stone-Weierstrass type theorems for non-archimedean
vector-valued function spaces
(Lujain Abulhamayel,
KAU, 2006).
5. Continuity
of algebra homomorphisms on topological algebras
(Enaam Alidaroos, KAU, 2006).
6. Non-archimedean Approximation in Weighted Spaces of Continuous
Vector-valued Functions (Amer Hassan Al-bargi, 2007)
7. Best
Approximation in Non-archimedean Vector-valued
Function Spaces (Khayriah Awad
Al-ahmri, 2008)
8.
Topological Modules of Multipliers (Muneerah Omar Al-ansari, 2010)
9.
Quasi-multipliers on A*-algebras (Sultan Usman Al-Ghamdi, 2012)
10.
Various Properties of Spaces of Continuous and
Bounded Functions (Asma Thabit
Ahmed Al-Hamidi, 2012)
11.
Convex Metric Spaces and their Applications (Riham Alattas, in progress)
(III) Ph.D theses
co-supervised:
1.
Random
Fixed Points and Approximations (Naseer Shahzad, QAU, 1995).
2.
Some
Types of Best Approximations and their Applications
(Nawab Hussain, BZU (
Research Publications
(L.A. Khan)
1. L. A. Khan, The strict dual of C(X,En), Punjab Univ. J. Math. (
2. L. A. Khan, The
strict topology on a space of vector-valued functions, Proc. Edinburgh Math.
Soc. 22(1) (1979), 35-41. (MR 80f: 46042)
3. L. A. Khan, On the
Stone-Weierstrass theorem for vector-valued
functions, Punjab Univ. J. Math. (
4. L. A. Khan (with K.
Rowlands): On the representation of strictly
continuous linear functionals, Proc. Edinburgh Math.
Soc. 24(1981), 123-130. (MR 83b: 46050)
5. L. A. Khan,
Characterizations of maximal closed submodules in
vector-valued function spaces, Kobe J. Math. 1(1984), 153-156. (MR 87h: 46067)
6. L. A. Khan, Separability in the uniform topology, Studia
Sci. Math. Hungarica 20(1985), 407-409. (MR 88g:
46055)
7. L. A. Khan,
Weighted topology in the non-locally convex setting, Matematicki
Vesnik 37(1985), 189-195. (MR 87k: 46081)
8. L. A. Khan, The
countable-open topology in the locally convex setting, Kobe J. Math. 3(1986),
47-50. (MR 87k: 46052)
9. L. A. Khan, On the
convergence of Mann iterates to a common fixed point of two mappings, J. Pure
and Applied Sci., 5(1986), 57-58.
10. L. A. Khan, A
characterizations of strictly closed ideals in vector-valued function algebras,
Math. Japonica 31(1986), 45-49. (MR 87f: 46082)
11. L. A. Khan, Separability in function spaces, J. Math. Anal. Appl. 113(1986), 88-92. (MR 87f: 46061)
12. L. A. Khan, On approximation in weighted spaces of continuous
vector-valued functions, Glasgow Math. J. 29(1987), 65-68. (MR 88c: 41056)
13. L. A. Khan, On a
fixed point theorem for iterates in locally convex spaces, J. Natural Sciences
and Mathematics 27(1)(1987), 1-5. (MR 88g: 47111)
14. L. A. Khan, Mackey
space problem for double centralizer algebras, Punjab Univ. J. Math. 20(1987),
7-12. (MR 89f: 46109)
15. L. A. Khan, Fixed
point theorems for Mann iterates in metrizable linear
topological spaces, Math. Japonica 33(2)(1988),
247-251. (MR 89g: 47079)
16. L. A. Khan, On seminorm separability
for vector-valued function spaces, Studia Sci. Math. Hungarica 24(1989), 43-45. (MR 89m: 46073)
17. L. A. Khan, Fixed
points by Ishikawaa iterates in metric linear spaces,
Math. Reports Toyama Univ. 12(1989), 57-63. (MR 90j: 47075)
18. L. A. Khan, Some
fixed point theorems for involutory mappings in
complete metrizable linear topological spaces, J.
Natural Sciences and Mathematics, 30(1990), 45-50.
19. L. A. Khan, Common
fixed point results by iterations using linear mappings, J. Pure and Applied
Sci., 39(1990), 43-45.
20. L. A. Khan,
Extensions of some fixed point theorems of Kannan and
Wong to paranormed spaces, Punjab Univ. J. Math.
323(1990), 77-82. (MR 92e: 47106)
21. L. A. Khan (with
K. Rowlands): The σ-compact-open topology and
its relatives on a space of vector-valued functions, Boll. Unione
Mat. Italiana (7) 5-B (1991), 727-739. (MR 92k:
46057).
22. L. A. Khan, On the
Stone-Weierstrass theorem for scalar and
vector-valued functions, ICTP (
23. L. A. Khan, Theory
of fuzzy sets and its applications, Proc. Second Regional Conf. on Applications
of Mathematics (UNESCO),
24. L. A. Khan, Seminorm separability in function
spaces, Math. Japonica 37 (1992), 687-689. (MR 93f: 46053)
25. L. A. Khan, Common
fixed point results for iterations in metric linear spaces, Studia
Sci. Math. Hungarica, 27(1992), 143-146.(MR 94d:47H10)
26. L. A. Khan,
Integration of vector-valued continuous functions and the Riesz
representation theorem, Studia Sci. Math. Hungarica 28(1993), 71-77. (MR 94k: 46071)
27. L. A. Khan,
Multiplication operators on weighted spaces in the non-locally convex setting,
Abstracts, International Congress of Mathematicians, Zurich, 3-11 August 1994,
page 70.
28. L. A. Khan, Metrization and separation axioms for finite topological
spaces, (Classroom Note),Int. J. Math. Edu. in Science and Technology(U.K) 25(1994), 473-474.
29. L. A. Khan, Riesz representation theorem for the dual of a space of
vector-valued functions, Boll. Unione Mat. Italiana (7) 8-A (1994), 391-396. (MR 95k: 46055)
30. L. A. Khan, Some
approximation results for the compact-open topology, Periodica
Math. Hungarica 30(1995), 81-86. (MR 96b: 46056)
31. L. A. Khan (with
A.R. Khan): An extension of Brosowski-Meinardus
theorem on invariant approximation, Approximation Theory and its Applications
11(4) (Dec. 1995), 1-5. (MR 97h: 41065)
32. L. A. Khan (with
K. Morishita): The minimum support for a functional
on Cb(X), Topology and its Applications 73(1996),
285-294. (MR 97j: 54017)
33. L. A. Khan (with A.B. Thaheem): On automorphisms of prime
rings with involution, Demonstratio Math. 30(1997),
307-311.
34. L. A. Khan (with A.B. Thaheem): Multiplication operators on weighted spaces in
the non-locally convex framework, Internat. J. Math. & Math. Sci. 20(1997), 75-80. (MR 98b: 47042)
Publications
during work at KAU, Jeddah (1997-present)
35. L. A. Khan, Mean value theorem in
topological vector spaces, C. R. Math. Rep. Acad. Sci. Canada 19(1997), 24-27.
(MR 98k: 58023)
36. L. A. Khan, (with N. Mohammad and A.B. Thaheem): Double multipliers on topological algebras, Internat. J. Math. & Math.
Sci. 22(1999), 629-636. (MR 2000m: 46100).
37. L. A. Khan (with N. Shahzad):
Random fixed points of 1-set contractive random maps in Frechet
spaces, J. Math. Anal. Appl. 231(1999), 68-75. (MR
2000b: 47135).
38. L. A. Khan (with N. Shahzad):
Some random fixed points in Frechet spaces, New
Zealand J. Math. 28(1999), 107-110. (MR 2000b: 47136).
39. L. A. Khan (with N. Shahzad):
Random fixed point theorems for multivalued acyclic random maps, Stochastic
Analysis and Applications 17(5) (1999), 835-840. (MR 2000e: 47100).
40. L. A. Khan, Generalized separability in vector-valued function spaces, Annales Univ. Sci. Budapst,
42(1999), 3-8. (MR 2001f: 54018)
41. L. A. Khan (with H.A.S. Abujabal and M.A. Alghamdi): On
the Riesz representation theorem in topological
vector spaces Studia Sci. Math. Hungarica, 36(2000), 347- 352.
(MR 2001k: 46058).
42. L. A. Khan (with A.R. Khan and N. Hussain): A note on Kakutani type
fixed point theorem, Internat. J. Math. & Math. Sci., 24(2000), 231-235. (MR 2003g: 46053)
43. L. A. Khan, A note on the Stone-Weierstrass theorem, Internat. J.
Math. Game Theory and Algebra 10(2000), 325-326. (MR 2001d: 46079)
44. L. A. Khan (with A.B. Thaheem): On the equivalence of the Heine-Borel theorem and the Bolzano-Weierstrass
Theorem, Int. J. Math. Edu. in Science and Technology (U.K)
31(2001), 620-622. (MR 1-777-775)
45. L. A. Khan (with N. Mohammad and A.B. Thaheem): On the closed range multipliers on topological
algebras, Scientiae Math. Japonica, 53(2001), 89-96. (MR 2003g: 46053)
46. L. A. Khan, Random fixed point theorems
for composites of acyclic multifunctions, Stochastic
Analysis Appl., 19(2001), 925-930. (MR 2002h: 47086)
47. L. A. Khan (with A. Latif):
Some results on common fixed poits and best
approximation in p-normed spaces, Demonstratio Math.
34(2001), (MR 2002i: 47074)
48. L. A. Khan (with N. Mohammad and A.B. Thaheem): Inner derivations on locally C*-algebras, Far
East J. Math., Special Volume (2001), Part I (Functional Analysis and its
Applications), 101-108. (MR 2002c: 46018)
49. L. A. Khan (with A.B. Thaheem): Operator-valued multiplication operators on
weighted function spaces, Demonstratio Math.
35(2002), 599-605. (MR 2003e: 47058)
50. L. A. Khan (with A.O. Badghaish and M.M. Saeed):
Automatic continuity of multipliers and derivations, (Survey), Proc. 4th
International Pure Math. Conf. (Islamabad, 2003), 36-65.
51. L. A. Khan, Trans-separability
in spaces of continuous vector-valued functions, Demonstratio
Math. 37(2004), 611-617. (MR 2005g: 46074)
52. L. A. Khan (with N. Mohammad and A.B. Thaheem): The strict topology on topological algebras, Demonstratio Math 38(2005), 883-894. (MR 2006m:46061)
53. L. A. Khan (with L. Oubbi):
Arzela -Ascoli theorem for non-locally convex
weighted function spaces, Revista Real Academia de Ciencias (Spain) (2) 60 (2005), 107-115. (MR 2006k:46055)
54. L.A. Khan, Some generalizations of the
mean value theorem to topological vector spaces, Proc. 6th International Pure
Math. Conf. (Islamabad, 2005), pp. 1-10.
55. L. A. Khan, The general strict topology
on topological modules, Contemporary Math. 435(2007), 253-263. MR2359434
(2009a:46086)
56. L. A. Khan, Topological modules of
continuous homomorphisms, J. Math. Anal.
Appl. 343(2008), 141-150. (MR2409463; 2009a:46087)
57. L. A. Khan, Trans-separability
in the strict and compact-open topologies, Bull. Korean Math. Soc. 45(2008),
681-687. (MR2463144 (2009j:46089)
58.
L. A. Khan (with Saud M. Alsulami and Hamed H. Alsulami),
Multiplication operators on non-locally convex weighted function spaces, Acta Universitatis Apulensis (Mathematics and Informatics), 18(2009), 35-50.
(MR2554314 (2010h:47048)
59. L. A. Khan (with Saud M. Alsulami and Hamed H. Alsulami), On precompact
multiplication operators on weighted function spaces, Acta
Universitatis Apulensis
(Mathematics and Informatics), 19(2009), 125-137. (MR2629797 (2011i:47041)
60. L. A. Khan (with A.K. Katsaras and A.R. Khan), On
maximal closed ideals in topological algebras of continuous vector-valued
functions over non-Archimedean valued fields, Contemporary Math. (AMS)
551(2011), 135-141.
61. L. A. Khan (with Marjan
Adib and A.H. Riazi),
Quasi-multipliers on F-algebras, Abstract and Applied Analysis, Volume 2011,
Article ID 235273, 30 pages. MR2784382 (2012d:46111)
62. L. A. Khan (with A. K. Katsaras and Hamed H. Alsulami), On the Weighted Function Space CVo(X,E) in the Non-Archimedean
Setting, Indagationes Mathematicae,
Indag. Math. 23(2012),
571-588.
63. L. A. Khan (with Asma
T. Al-Hamidi), On a Stone-Weierstrass
type theorem for C(X), Internat. J. Pure and Applied
Math. 80(3) (2012), 357-361.
64. L. A. Khan (with Saud M. Alsulami), Almost periodicity in linear topological spaces
– Revisited, Commun. Math. Anal. 13 (2012), No. 1, pp. 54-63.
65. L. A. Khan (with Saud M. Alsulami), Multipliers of commutative F-algebras of
continuous vector-valued functions, Bull. Malaysian Math. Sci.
Soc. (to appear).
Monograph:
“Linear Topological Spaces of
Continuous Vector-valued Functions”, (submitted).
Research Award:
1. Awarded by the National Book Council
(Ministry of Education of Pakistan) under the scheme “Incentive for publication
of Articles in International Journals” in Mathematics (1990).
2. Awarded by Deanship of Scientific
Research, King Abdulaziz University, Jeddah, for
publication of Articles in ISI Journals (2008).
Membership of
Mathematical Societies:
1.
2. American
Mathematical Society (1984-86,
96-todate).
3.
Professional Services:
1.
Incharge, Mathematics Department,
2.
Referee
to various journals.
3.
Reviewer:
American Mathematical Society, Zbl.
4.
Seminar
Co-ordinator:
Co-Author of the Book:
"Business
Mathematics and Statistics", (with S. Ibrar Hussain and others) (published as a text-book for B.A.
course by Allama Iqbal Open
University, Islambad, 1982).
Participation in
Mathematical Conferences / Seminars:
1.
British
Mathematical Colloquium,
2.
Gregynog Symposium,
3.
British
Mathematical Colloquium, Univeristy of
4.
All
5.
All
1978.
6.
Seminars
held at
7.
Workshop
on Recent Developments in Mathematics and Computer Science, ICTP,
8.
Visiting
Mathematician, ICTP,
9.
Second
Regional Workshop on Applications of Mathematics (Under UNESCO), Islamia University,
10. Visiting
Associate, ICTP,
11. All
12. International
Pure Mathematical Conference (IPMC, held Annually),
13.
International Conference on Theory, Methods
and Applications of Nonlinear Equations, Texas A&M University, Kingsville
(USA, Dec 17-21, 2012)