Liaqat Ali Khan (mathematician)
Encyclopedia
For other people with the same or similar name, see Liaqat Ali (disambiguation)
Dr. Prof. Liaqat Ali Khan or L.A. Khan is a Pakistan
i 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 Abdulaziz University, Jeddah. Currently, he is serving professor of mathematics
at the King Abdulaziz University, Jeddah.
, 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 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 Dr. K. Rowlands. Following his thesis, he was awarded his Ph.D. in mathematics
in 1977
in 1968 where he served as a lecturer
. In 1971, he moved to Islamabad
and joined Federal Government College as a lecturar. After his Ph.D. in 1977, he again joined Federal Government College Islamabad as a Lecture
, and 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 came back 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 Saudia Arabia where he joined King Abdulaziz University
Jeddah, as an associate professor. In 2003, he was upgraded to his position and serving as a full professor of mathematics at there.
on "Topological Vector Spaces of Continuous Vector-valued Functions". He joined International Center for Theoretical Physics (ICTP) as a visiting mathematician in 1990s. He 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.
Liaqat Ali (disambiguation)
Liaquat Ali Khan was the first Prime Minister of Pakistan.Liaqat Ali may also refer to:* Liaqat Ali Khan , Pakistan mathematician* Liaqat Ali , Pakistani Test cricketer...
Dr. Prof. Liaqat Ali Khan or L.A. Khan is a Pakistan
Pakistan
Pakistan , officially the Islamic Republic of Pakistan is a sovereign state in South Asia. It has a coastline along the Arabian Sea and the Gulf of Oman in the south and is bordered by Afghanistan and Iran in the west, India in the east and China in the far northeast. In the north, Tajikistan...
i mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and an academic who has been a noted researcher to the fields of Functional Analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, Linear topology
Linear topology
A linear bus topology is a network topology consisting of a main run of cable with a terminator at each end. All nodes are connected to the linear cable...
, and Topological algebra
Topological algebra
In mathematics, a topological algebra A over a topological field K is a topological vector space together with a continuous multiplication\cdot :A\times A \longrightarrow A\longmapsto a\cdot bthat makes it an algebra over K...
. He has supervised two doctoral students, fourteen M.Phil. students at the Quaid-i-Azam University
Quaid-i-Azam University
The Quaid-i-Azam University is a public, research university in Islamabad Capital Territory of Pakistan. It was initially founded as the "University of Islamabad" in July 1967...
and six M.Sc. students at the King Abdulaziz University, Jeddah. Currently, he is serving professor of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the King Abdulaziz University, Jeddah.
Education
Born in JhelumJhelum
Jhelum or Jehlum may refer to:* Jhelum, a city in Pakistan on the banks of the Jhelum River* Jhelum District, an administrative division in Punjab, Pakistan surrounding the city of Jhelum...
, Punjab
Punjab (Pakistan)
Punjab is the most populous province of Pakistan, with approximately 45% of the country's total population. Forming most of the Punjab region, the province is bordered by Kashmir to the north-east, the Indian states of Punjab and Rajasthan to the east, the Pakistani province of Sindh to the...
, Khan received his intermediate education from there and attended University of the Punjab
University of the Punjab
University of the Punjab , colloquially known as Punjab University, is located in Lahore, Punjab, Pakistan. The University of the Punjab is the oldest and biggest University of Pakistan. The University of the Punjab was formally established with the convening of the first meeting of its...
in 1964. He received his B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
in 1966. The same year, he was admitted to the graduate school
Graduate school
A graduate school is a school that awards advanced academic degrees with the general requirement that students must have earned a previous undergraduate degree...
of the Punjab University, and did his M.A.
Master of Arts (postgraduate)
A Master of Arts from the Latin Magister Artium, is a type of Master's degree awarded by universities in many countries. The M.A. is usually contrasted with the M.S. or M.Sc. degrees...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
in 1968. With an awarded scholarship in 1974, he traveled to Great Britain
Great Britain
Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...
to pursue doctoral studies in mathematics. He attended University of Wales
University of Wales
The University of Wales was a confederal university founded in 1893. It had accredited institutions throughout Wales, and formerly accredited courses in Britain and abroad, with over 100,000 students, but in October 2011, after a number of scandals, it withdrew all accreditation, and it was...
at the Aberystwyth
Aberystwyth
Aberystwyth is a historic market town, administrative centre and holiday resort within Ceredigion, Wales. Often colloquially known as Aber, it is located at the confluence of the rivers Ystwyth and Rheidol....
where, in 1977, he wrote his doctoral thesis on "The Strict Topology and its Generalizations" which was supervised by Dr. K. Rowlands. Following his thesis, he was awarded his Ph.D. in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
in 1977
Academic career
He joined Government College, PattokiGovernment College, Pattoki
The Government College Pattoki or Municipal College of Pattoki is located in Pattoki, Punjab, Pakistan, 78 km from Lahore. The college was founded in 1965 with classes held in the Zail Ghar; after two years the college moved to the present campus. The college was nationalized in 1972, by...
in 1968 where he served as a lecturer
Lecturer
Lecturer is an academic rank. In the United Kingdom, lecturer is a position at a university or similar institution, often held by academics in their early career stages, who lead research groups and supervise research students, as well as teach...
. In 1971, he moved to Islamabad
Islamabad
Islamabad is the capital of Pakistan and the tenth largest city in the country. Located within the Islamabad Capital Territory , the population of the city has grown from 100,000 in 1951 to 1.7 million in 2011...
and joined Federal Government College as a lecturar. After his Ph.D. in 1977, he again joined Federal Government College Islamabad as a Lecture
Lecture
thumb|A lecture on [[linear algebra]] at the [[Helsinki University of Technology]]A lecture is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical information, history,...
, and a visiting professor at the Quaid-i-Azam University
Quaid-i-Azam University
The Quaid-i-Azam University is a public, research university in Islamabad Capital Territory of Pakistan. It was initially founded as the "University of Islamabad" in July 1967...
Islamabad. In 1981, he went to Libya
Libya
Libya is an African country in the Maghreb region of North Africa bordered by the Mediterranean Sea to the north, Egypt to the east, Sudan to the southeast, Chad and Niger to the south, and Algeria and Tunisia to the west....
where he joined Garyounis University
Garyounis University
University of Benghazi , formerly known as the Garyounis University, is a public university in Benghazi, Libya.- History :It is the oldest and first Libyan university. It was founded on 15 December 1955 as The Libyan University...
Benghazi
Benghazi
Benghazi is the second largest city in Libya, the main city of the Cyrenaica region , and the former provisional capital of the National Transitional Council. The wider metropolitan area is also a district of Libya...
as an assistant professor. After spending five years there, he came back 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 Saudia Arabia where he joined King Abdulaziz University
King Abdulaziz University
King Abdulaziz University was founded in 1967 in Jeddah, Saudi Arabia. Designed by English architect John Elliott, it had 2,000 teachers and more than 37,000 students in 2000/2001....
Jeddah, 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 monographMonograph
A monograph is a work of writing upon a single subject, usually by a single author.It is often a scholarly essay or learned treatise, and may be released in the manner of a book or journal article. It is by definition a single document that forms a complete text in itself...
on "Topological Vector Spaces of Continuous Vector-valued Functions". He joined International Center for Theoretical Physics (ICTP) as a visiting mathematician in 1990s. He 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
- National Book Council (Pakistan) (1990)
- Silver MedalSilver medalA silver medal is a medal awarded to the second place finisher of contests such as the Olympic Games, Commonwealth Games, and contests with similar formats....
, University of the Punjab (1968)
Association and Fellowships
- Pakistan Mathematical Society (1977–present)
- American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
(1984–1986, 1996-todate). - London Mathematical SocietyLondon Mathematical Society-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
(1985–2010).
Research Papers
- 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 function 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.