Prof. Dr. Abdul Rahim Khan

Brief Bio

As an academic, I have a strong background in advanced analysis, nonlinear functional analysis, and their applications in numerical analysis, best approximations, iterative methods, and equilibrium problems. As a researcher, I have 40 years of experience. My main interest is in fixed point theory and its applications. I have published 176 papers in high-impact journals and 10 conference papers at prestigious conferences around the world. My research papers appeared in well-known journals such as Computer and Mathematics with Applications, Applied Math Letters, Symmetry, Mathematical Analysis and Applications, Numerical Functional Analysis and Optimization, Fixed Point Theory, Nonlinear Analysis, Glasgow Journal of Mathematics, Australian Journal of Mathematics, Applied Mathematics and Computation, Filomat, Optimization, Numerical Algorithms, Journal of Nonlinear Convex Analysis, and Carpathian Journal of Mathematics. In 1993, I wrote a book “Introduction to Lebesgue Integration” for graduate courses. The readers of this book, find it very useful and interesting to learn the fundamentals of Measure Theory.

Education
Ph.D. in Mathematics	University of Wales, United Kingdom	1983
M.Sc. in Mathematics	University of the Punjab, Lahore	1974
B.Sc. (Hons.)	University of the Punjab, Lahore	1973

Professional Experience
Professor	University of Southern Punjab, Multan	2022 – Till now
Professor	King Fahad University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia	2008 – 2022
Associate Professor	KFUPM, Dhahran, Saudi Arabia	1997 – 2008
Professor	Bahauddin Zakariya University (BZU), Multan	1996 – 1997
Associate Professor	Bahauddin Zakariya University, Multan	1988 – 1995
Assistant Professor	Bahauddin Zakariya University, Multan	1984 – 1988
Lecturer	University of Multan	1976 – 1984

Professional associations

Member, American Mathematical Society (1990-91, 1994-95, 2000-2011, and 2022-23).
Member, Japanese Association of Mathematical Sciences (2000-2001).
Life Member, Punjab Mathematical Society.
Life Member, Zakariyan Mathematical Society.
Member, Pakistan Mathematical Society.
Member, Pakistan Association for the Advancement of Science.

Research Interests

Research Impact:

Publications: 178
h-index: 24
Funded Projects: Completed (11 international projects as Principal Investigator).

Title	Year	Published Link
A decomposition theorem for submeasures	1985	Click to view
Random fixed point theorems for non expansive operators in Fréchet spaces	2001	Click to view
Properties of fixed point set of a multivalued map	2005	Click to view
Common fixed points of Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces	2008	Click to view
On modified Noor iterations for asymptotically nonexpansive mappings	2010	Click to view
Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications	2010	Click to view
Strong convergence of a general iteration scheme in CAT(0) spaces	2011	Click to view
A general convergence theorem for multiple-set feasibility problem in Hilbert spaces	2015	Click to view
On some mappings with a unique common fixed point	2020	Click to view
Fixed points of multivalued convex contractions with application	2025	Click to view

Khan, A. R., & Rowlands, K. (1985). A decomposition theorem for submeasures. Glasgow Mathematical Journal, 26, 69–74.

Khan, A. R., & Hussain, N. (2002). Random fixed point theorems for *-nonexpansive operators in Fréchet spaces. Journal of the Korean Mathematical Society, 39(1), 51–60.

Khan, A. R. (2005). Properties of fixed point set of a multivalued map. Journal of Applied Mathematics and Stochastic Analysis, 2005(3), 323–332.

Khan, A. R., Domlo, A. A., & Fukhar-ud-din, H. (2008). Common fixed points of Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. Journal of Mathematical Analysis and Applications, 341(1), 1–11.

Khan, A. R. (2010). On modified Noor iterations for asymptotically nonexpansive mappings. Bulletin of the Belgian Mathematical Society – Simon Stevin, 17(1), 127–140.

Khan, A. R., & Ahmed, M. A. (2010). Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications. Computers & Mathematics with Applications, 59(9), 2990–2995.

Khan, A. R., Khamsi, M. A., & Fukhar-ud-din, H. (2011). Strong convergence of a general iteration scheme in CAT(0) spaces. Nonlinear Analysis: Theory, Methods & Applications, 74(3), 783–791.

Khan, A. R., Abbas, M., & Shehu, Y. (2015). A general convergence theorem for multiple-set feasibility problem in Hilbert spaces. Carpathian Journal of Mathematics, 31(3), 349–357.

Khan, A. R., & Oyetunbi, D. M. (2020). On some mappings with a unique common fixed point. Journal of Fixed Point Theory and Applications, 22(2), Article 47.
Khan, A. R., Al-Sulami, H. H., Rashid, M., & Shabbir, F. (2025). Fixed points of multivalued convex contractions with application. PLOS ONE, 20(5), Article e0321860.

Teaching & Supervision

Courses:

Functional Analysis
Measure Theory
Real Analysis
Topology
Complex Analysis

Supervision:

Ph.D.: 6 (completed), 3 (ongoing)
M. Phil.: 20 (completed), 4(ongoing)

Teaching Philosophy

Professor Dr. Abdul Rahim Khan leverages a forty-year research career to bridge abstract mathematical theory with practical computational applications through rigorous, research-led instruction. By mentoring students in logical precision and high-impact documentation, he transforms foundational concepts into the expert skills necessary to solve complex, non-linear global challenges.

Collaborations and Honors

Merit Scholarship in B.Sc. Hons. (1970-73)
Merit Scholarship in M.Sc. (1974)
Central Overseas Training Scholarship, Govt. of Pakistan (1979-1983)
Post-Doctoral Fellowship, British Council (August 1994 –January 1995)
Certificate of Research Excellence, University of Southern Punjab (2025)

Awards & Recognition

Excellence in Research Award, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 2010.
Best Research Project Award, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 2012.
Best Research Project Award, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia, 2017.

Collaboration

Collaborated with many authors from around the globe, especially from the USA, Australia, the UK, Saudi Arabia, South Africa, and Romania. I am open to international collaborations in Fixed Point Theory, Iterative Methods, Equilibrium problems, and Optimization.