Liaqat Ali Khan (mathematician)
For other people with the same or similar name, see Liaqat Ali (disambiguation)
|Liaqat Ali Khan|
July 29, 1947|
Jhelum, Punjab, British India
|Residence||Jeddah, Saudi Arabia|
|Institutions||Municipal College, Pattoki
Federal Government College, Islamabad
University of Wales
Quaid-i-Azam University, Islamabad
Garyounis University, Benghazi
King Abdulaziz University, Jeddah
International Centre for Theoretical Physics, Trieste
|Alma mater||University of Wales at Aberystwyth
University of the Punjab, Lahore
|Doctoral advisor||Dr. Keith Rowlands|
|Doctoral students||Naseer Shahzad and Nawab Hussain|
|Other notable students||Farhad Ali
|Known for||his work on Functional analysis, Vector-valued function spaces, Stone–Weierstrass theorem, Riesz representation theorem, Fixed-point theorem, and Topological algebra|
|Notable awards||National Book Council of Pakistan (1990)|
Liaqat Ali Khan or L.A. Khan is a Pakistani mathematician and academic who has carried out research in the fields of functional analysis, linear topology, and topological algebra. He has supervised two doctoral students, fourteen M.Phil. students at the Quaid-i-Azam University and six M.Sc. students at King Abdulaziz University, Jeddah. As of 2012[update] he was professor of mathematics at the King Abdulaziz University, Jeddah.
Born in Jhelum, Punjab, Khan received his intermediate education from there and attended University of the Punjab in 1964. He received his B.A. in mathematics in 1966. The same year, he was admitted to the graduate school of the Punjab University, and did his M.A. in mathematics in 1968. With a scholarship awarded in 1974 he traveled to Great Britain to pursue doctoral studies in mathematics. He attended University of Wales at Aberystwyth where, in 1977, he wrote his doctoral thesis on "The Strict Topology and its Generalizations", supervised by K. Rowlands. Following his thesis, he is awarded his Ph.D. in mathematics in 1977.
He joined Government College, Pattoki in 1968 where he served as a lecturer. In 1971, he moved to Islamabad and joined Federal Government College as a lecturer. After his Ph.D. in 1977, he again joined Federal Government College, Islamabad as a lecturer, and was a visiting professor at the Quaid-i-Azam University Islamabad. In 1981 he went to Libya where he joined Garyounis University Benghazi as an assistant professor. After spending five years there, he returned to Pakistan and re-joined Federal Government College Islamabad in 1986. In 1991, he joined Qaid-i-Azam University as an associate professor. In 1996, he went to Saudi Arabia where he joined King Abdulaziz University Jeddah, as an associate professor. In 2003 became a full professor of mathematics at there.
He has published a monograph on "Topological Vector Spaces of Continuous Vector-valued Functions". He joined International Centre for Theoretical Physics (ICTP) as a visiting mathematician in 1990s. He has taught undergraduate and post-graduate mathematics. He has been engaged in research on linear topologies on spaces of continuous vector-valued functions, Stone-Weierstrass approximation theorem, best approximation, vector-valued measures and integration, fixed-point theorems, topologies on topological algebras and topological modules, multipliers, derivations and homomorphisms.
Association and fellowships
- Pakistan Mathematical Society (from 1977)
- American Mathematical Society (1984–1986, from 1996).
- London Mathematical Society (1985–2010).
- Topological Vector Spaces of Continuous Vector-valued Functions.
- L. A. Khan, The strict topology on a space of vector-valued functions, Proc. Edinburgh Math. Soc. 22(1) (1979), 35-41
- L. A. Khan, (with K. Rowlands): On the representation of strictly continuous linear functionals, Proc. Edinburgh Math. Soc. 24(1981), 123-130
- L. A. Khan, Separability in the uniform topology, Studia Sci. Math. Hungarica 20(1985), 407-409
- L. A. Khan, Weighted topology in the non-locally convex setting, Matematicki Vesnik 37(1985), 189-195
- L. A. Khan, Separability in function spaces, J. Math. Anal. Appl. 113(1986), 88-92
- L. A. Khan, On approximation in weighted spaces of continuous vector-valued functions, Glasgow Math. J. 29(1987), 65-68
- 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
- L. A. Khan, Common fixed point results for iterations in metric linear spaces, Studia Sci. Math. Hungarica, 27(1992), 143-146
- L. A. Khan, Integration of vector-valued continuous functions and the Riesz representation theorem, Studia Sci. Math. Hungarica 28(1993), 71-77
- L. A. Khan, Some approximation results for the compact-open topology, Periodica Math. Hungarica 30(1995), 81-86
- L. A. Khan, (with K. Morishita): The minimum support for a functional on Cb(X), Topology and its Applications 73(1996), 285-294
- 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
- L. A. Khan, Mean value theorem in topological vector spaces, C. R. Math. Rep. Acad. Sci. Canada 19(1997), 24-27
- L. A. Khan, (with N. Mohammad and A.B. Thaheem): Double multipliers on topological algebras, Internat. J. Math. & Math. Sci. 22(1999), 629-636
- 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
- L. A. Khan, (with N. Shahzad): Random fixed point theorems for multivalued acyclic random maps, Stochastic Analysis and Applications 17(5) (1999), 835-840
- L. A. Khan, Random fixed point theorems for composites of acyclic multifunctions, Stochastic Analysis Appl., 19(2001), 925-930
- L. A. Khan, (with A.B. Thaheem): Operator-valued multiplication operators on weighted function spaces, Demonstratio Math. 35(2002), 599-605
- L. A. Khan, Trans- separability in spaces of continuous vector-valued functions, Demonstratio Math. 37(2004), 611-617
- L. A. Khan, (with N. Mohammad and A.B. Thaheem): The strict topology on topological algebras, Demonstratio Math 38(2005), 883-894
- 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
- L. A. Khan, The general strict topology on topological modules, Contemporary Math. 435(2006), 253-263
- L. A. Khan, Trans-separability in the strict and compact-open topologies, Bull. Korean Math. Soc. 45(2008), 681-687
- L. A. Khan, Topological modules of continuous homomorphisms, J. Math. Anal. Appl. 343(2008), 141-150
- L. A. Khan, (with Saud M. Alsulami and Hamed H. Alsulami), Multiplication operators on non-locally convex weighted func tion spaces, Acta Universitatis Apulensis (Mathematics and Informatics), 18(2009), 35-50
- 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