Liaqat Ali Khan (mathematician)

For other people with the same or similar name, see Liaqat Ali (disambiguation) Dr. Prof. Liaqat Ali Khan or L.A. Khan is a Pakistani mathematician and an academic who has been a noted researcher to 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 the King Fahd University of Petroleum and Minerals. Currently, he is serving professor of engineering mathematics at the King Fahd University of Petroleum and Minerals.

Education

Born in Jhelum, Punjab, Khan recieved his intermediate education from there and attended University of the Punjab in 1964. He recieved 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 an awarded scholarship in 1974, he traveled to Great Britain to pursue doctoral studies in mathematics. He attended University of Wales at the Aberystwyth where, in 1977, he wrote his doctoral thesis on "The Strict Topology and its Generalizations" which was supervised by the Dr. K. Rowlands. Following his thesis, he was awarded his Ph.D. in mathematics in 1977

Academic Career

He joined Government College, Pattoki in 1968 where he served as a lecturer. In 1967, he moved to Islamabad and joined Urdu University as a lecturar. After his Ph.D, he then joined Federal Urdu University as a full professor, and a visiting professor at the Quaid-i-Azam University. In 1981, he went to Lybia where he joined Garyounis University as an associate professor. After spending short time there, he came back to Pakistan and re-joined Federal Urdu University in 1986. In 1991, he joined Qaid-i-Azam University as an associate professor. In 1996, he went to Saudia Arabia where he joined King Fahd University of Petroluem and Minerals as an associate professor. In 2003, he was upgraded to his position and serving as a full professor of mathematics at there.

Academic Research

He is a noted researcher and has published monograph on "Topological Vector Spaces of Continuous Vector-valued Functions". He joined International Center for Theoretical Physics (ICTP) in 1980s. He has been a noted professor of mathematics and has taught undergraduate and post graduate mathematics. He has been engaged in the research to the fields of 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.

Awards

• Pride of Performance Award (2008)
• Gold Medal, University of the Punjab (1968)

Association and Fellowships

• Pakistan Mathematical Society (1977-present)
• American Mathematical Society (1984-1986, 1996-todate).
• London Mathematical Society (1985-todate).

Publications

Monograph

• Topological Vector Spaces of Continuous Vector-valued Functions.

Conference Papers

• On the Stone-Weierstrass theorem for scalar and vector-valued functions,L. A. Khan, ICTP (Trieste, Italy), Preprint No: IC/91/257 (1991), pp. 1-5.
• Theory of fuzzy sets and its applications, L. A. Khan, Proc. Second Regional Conf. on Applications of Mathematics (UNESCO), Islamia University, Bahawalpur, Pakistan (Jan. 10-14, 1992), pp.1-27.
• Multiplication operators on weighted spaces in the non-locally convex setting, L. A. Khan, Abstracts, International Congress of Mathematicians, Zurich, 3-11 August 1994, page 70.
• Automatic continuity of multipliers and derivations, (Survey), L. A. Khan, (with A.O. Badghaish and M.M. Saeed): Proc. 4th International Pure Math. Conf. (Islamabad, 2003), 36-65.
• Some generalizations of the mean value Theorem to topological vector spaces, L.A. Khan, Proc. 6th International Pure Math. Conf. (Islamabad, 2005), pp. 1-10.

Research Papers

• On the representation of strictly continuous linear functionals, L.A. Khan, (with K. Rowlands), Proc. Edinburgh Math. Soc. 24(1981), 123-130. (MR 83b: 46050)
• Characterizations of maximal closed submodules in vector-valued function spaces, L.A. Khan, Kobe J. Math. 1(1984), 153-156. (MR 87h: 46067)
• Separability in the uniform topology, L.A. Khan,Studia Sci. Math. Hungarica 20(1985), 407-409. (MR 88g: 46055)
• Weighted topology in the non-locally convex setting, L.A. Khan, Matematicki Vesnik 37(1985), 189-195. (MR 87k: 46081)
• The countable-open topology in the locally convex setting, L.A. Khan, Kobe J. Math. 3(1986), 47-50. (MR 87k: 46052)
• On the convergence of Mann iterates to a common fixed point of two mappings, L.A. Khan, J. Pure and Applied Sci., 5(1986), 57-58.
• A characterizations of strictly closed ideals in vector-valued function algebras, L.A. Khan, Math. Japonica 31(1986), 45-49. (MR87f:46082)
• Separability in function spaces, L.A. Khan, J. Math. Anal. Appl. 113(1986), 88-92. (MR 87f: 46061)
• On approximation in weighted spaces of continuous vector- valued functions, L.A. Khan, Glasgow Math. J. 29(1987), 65-68. (MR88c: 41056)
• On a fixed point theorem for iterates in locally convex spaces, L.A. Khan, J. Natural Sciences and Mathematics 27(1)(1987), 1-5. (MR88g: 47111)
• Mackey space problem for double centralizer algebras, L.A. Khan, Punjab Univ. J. Math. 20(1987), 7-12. (MR 89f: 46109)
• Fixed point theorems for Mann iterates in metrizable linear topological spaces, L.A. Khan, Math. Japonica 33(2)(1988), 247-251. (MR 89g: 47079)
• On seminorm separability for vector-valued function spaces,L.A. Khan, Studia Sci. Math. Hungarica 24(1989), 43-45. (MR89m:6073)
• Fixed points by Ishikawaa iterates in metric linear spaces, L.A. Khan, Math. Reports Toyama Univ. 12(1989), 57-63. (MR90j:47075)
• Some fixed point theorems for involutory mappings in complete metrizable linear topological spaces, L.A. Khan,J. Natural Sciences and Mathematics, 30(1990), 45-50.