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Fixed Point Theory & Applications Research Group (FPTARG)

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Metric Fixed Point Theory

Metric Fixed Point Theory:

A. R. Khan, H. Fukhar-ud-din and A.A. Domlo, Approximating fixed points of some maps in uniformly convex metric spaces, Fixed point Theory and Appl. Volume 2010, Article ID 385986, 11 pages.
A. R. Khan and H. Fukhar-ud-din, Weak and strong convergence of Ishikawa iterates for nonself asymptotically quasi-nonexpansive mappings, PK ISSN 0022- 2941; CODEN JNSMAC, Vol. 50, No.1 & 2 (April & October 2010), 23-39.
A. R. Khan and H. Fukhar-ud-din, Weak Convergence of Ishikawa Iterates for Nonexpansive Maps, Proceedings of the World Congress on Engineering and Computer Science WCECS 2010, October 20-22, 2010, San Francisco, USA, 2010, 1026-1029.
Q. H. Ansari, L. C. Zeng, and S. Al-Homidan, Hybrid proximal-type algorithms for generalized equilibrium problems, maximal monotone operators and relatively nonexpansive mappings, Fixed Point Theory and Applications, Volume 2011, Article ID 973028, (2011), 23 pages.
A.R. Khan, M.A. Khamsi, H. Fukhar-Ud-din, "Strong Convergence of a General Iteration Scheme in CAT(0) Spaces", Nonlinear Analysis: Theory, Methods & Applications, 74 (2011),783-791.
Q. H. Ansari, and S. Al-Homidan, Fixed Point Theorems on Product Topological Semilattice Spaces, Generalized Abstract Economies and Systems of Generalized Vector Quasi-Equilibrium Problems, Taiwanese Journal of Mathematics, 15 (1) (2011), 307-330.
M. A. Khamsi, A. R. Khan, "Inequalities in Metric Spaces with Applications", Nonlinear Analysis TMA: 74 (2011) 4036-4045.
M, Abbas, M. A. Khamsi, A. R. Khan, "Common Fixed Point and Invariant Approximation in Hyperbolic Ordered Metric Spaces", Fixed Point Theory and Applications 2011, doi: 10.1186/1687-1812-2011-25.
Q. H. Ansari, S. Al-Homidan, and Jen-Chih Yao, Collectively Fixed Point and Maximal Element Theorems in Topological Semilattice Spaces, Applicable Analysis, 96 (6) June (2011), 865-888.
H. Fukhar-ud-din, A. A. Domlo and A. R. Khan, Strong convergence of an implicit algorithm in CAT(0) spaces, Fixed point Theory and Applications, 2011(2011), 1-11.
M.A. Khamsi, I. Louhichi, "A convergence result on random products of mappings in metric spaces", Fixed Point Theory and Applications 2012, 2012:43, doi:10.1186/1687-1812-2012-43.
A. R. Khan, H. Fukhar-ud-din, and M. A. A. Khan, An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spsces, Fixed Point Theory and Applications, 2012 (2012), pages 25.
H. Fukhar-ud-din, A. R. Khan and Z. Akhtar, Fixed point results for generalized nonexpansive maps in uniformly convex metric spaces, Nonlinear Analysis: Theory, Methods & Applications, (2012), 4747-4760.
H. Fukhar-ud-din, A. R. Khan, and M. A. A. Khan, A New Implicit Algorithm of Asymptotically Quasi-nonexpansive Maps in Uniformly Convex Banach Spaces, IAENG International Journal of Applied Mathematics, vol. 42, no. 3, pp. 171-175, 2012.
B Ibn Dehaish, M A Khamsi, A R Khan, "Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces", Journal of Mathematical Analysis and Applications, Vol. 397, Issue 2, (2013) 861-868.
H. Fukhar-ud-din, A. R. Khan, A. Kalsoom and M. A. A. Khan, One-step implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, J. Adv. Math. Stud., 6 (2013), No. 1, 73-81.
H. Fukhar-ud-din, A. R. Khan and M. Ubaid-ur-Rehman, Ishikawa type algorithm of two multivalued quasi-nonexpansive maps on nonlinear domains, Ann. Funct. Anal. 4 (2013), no. 2, 97-109.
M. Alshahrani, Q. H. Ansari, and S. Al-Homidan, System of Nonsmooth Variational Inequalities with Applications, To appear in Optimization (2014).
Saleh Almezel, Qamrul Hasan Ansari and Mohamed Amine Khamsi (Editors) Topics in Fixed Point Theory, Springer, Cham, Heidelberg, New York, Dordrecht, London, 2014.
H. Fukhar-Ud-din, M. A. Khamsi, "Approximating common fixed points in hyperbolic spaces", submitted.
A. N. Abdou, M. A. Khamsi, A. R. Khan, "Convergence of Ishikawa iterates of two mappings in Modular function spaces", submitted.

Discrete Fixed Point Theory:

B. Schroder, Ordered sets - an introduction, Birkhauser Verlag, Boston, Basel, Berlin. (2003).
B. Schroder, Examples of Powers of Ordered Sets with the Fixed Point Property, Order 23 (2006), 211-219.
T. Kulkarni and B. Schroder, An Enumeration Problem in Ordered Sets Leads to Possible Benchmarks for Run-Time Prediction Algorithms, invited lecture, in: Rokia Missaoui, Jurg Schmidt (ed.), Formal Concept Analysis: 4th International Conference, ICFCA 2006, Dresden, Germany, February 13-17, 2006, Proceedings, Lecture Notes in Computer Science 3874 (2006), Springer, 30-44.
M. R. Alfuraidan and J. I. Hall, Smith's Theorem and a characterization of the 6-cube as distance-transitive graph, J. Algebraic Comb. 24(2) (2006), 195-207.
M. R. Alfuraidan and J. I. Hall, Imprimitive Distance-Transitive Graphs with Primitive Core of Diameter at least 3, Michigan Math. J. 58 (2009), 31-77.
M. Z. Abu-Sbeih, M. A. Khamsi, "On Externally Complete subsets and Common fixed Points in Partially Ordered Sets", Fixed Point Theory and Applications 2011, 2011:97, doi:10.1186/1687-1812-2011-97.
M. Kukieła and B. Schroder, A 2-Antichain that is not Contained in any Finite Retract, Algebra Universalis 67 (2012), 59-62
B. Schroder, The Fixed Point Property for Ordered Sets (survey), Arabian Journal of Mathematics 1 (2012), 529-547.
M. R. Alfuraidan, Bipartite Distance-Transitive Doubles with Primitive Halved of Diameter Two, Graphs and Combinatorics 29 (5) (2013), 1151-1174.
M. R. Alfuraidan, Antipodal Distance-Transitive Graphs with Primitive Quotient of Diameter Two, Discrete Mathematics 313 (21) 2013, 2409-2422.
B. Schroder, The Fixed Vertex Property for Graphs, submitted to Order
M. R. Alfuraidan, M. A. Khamsi, "Caristi Fixed Point Theorem in Metric Spaces with a Graph", to appear in Abstract and Applied Analysis, 2014.

Applications of Fixed Point Theory:

Q. H. Ansari, L.C. Ceng, A.R. Khan and J.-C. Yao , Viscosity Approximation Methods for Strongly Positive and Monotone Operators, Fixed Point Theory, 10 (2009), 35-71.
Q. H. Ansari, L.C. Ceng, S. Al-Homidan and J.-C. Yao, An Iterative Scheme for Equilibrium Problems and Fixed Points Problems of Strict Pseudo-Contraction Mappings, Journal of Computational and Applied Mathematics, 223(2)(2009), 967-974.
Q. H. Ansari, L.C. Ceng, A.R. Khan and J.-C. Yao, Strong Convergence of Composite Iterative Schemes for Zeros of m-Accretive Operators in Banach Spaces, Nonlinear Analysis, Theory, Methods and Applications, 70 (2009), 1830-1840.
Q. H. Ansari, and S. Al-Homidan, Quasi-equilibrium problems with lower and upper bounds in ordered topological spaces, Journal of Nonlinear and Convex Analysis, 11(2), (2010), 345-355.
Q. H. Ansari, and S. Al-Homidan, Generalized Minty Vector Variational-like Inequalities and Vector Optimization Problems, Journal of Optimization Theory and Applications, 144 (1) (2010), 1-11.
S. Al-Homidan, Q.H. Ansari and J.-C. Yao, Nonsmooth Invexities, Invariant Monotonicities and Nonsmooth Vector Variational-like Inequalities with Applications to Vector Optimization, in Recent Developments in Vector Optimization, Edited by Q.H. Ansari and J.-C. Yao, Springer-Verlag, Berlin, 2012.
Q. H. Ansari, and S. Al-Homidan, , Relations between generalized vector variational-like inequalities and vector optimization problems, Taiwanese Journal of Mathematics 16(3) (2012), 987-998.
M. Alshahrani, Q. H. Ansari, and S. Al-Homidan, Existence Results for Nonsmooth Vector Quasi-Variational-like Inequalities, Abstract and Applied Analysis Volume 2013 (2013), Article ID 376829, 7 pages http://dx.doi.org/10.1155/2013/376829.
Q. H. Ansari, L. C. Zeng , and S. Al-Homidan, Relaxed extragradient-like method for general system of generalized nonlinear mixed equilibrium problems and fixed point problems, To appear in Fixed Point Theory and Applications (2013).
M. Alshahrani, Q. H. Ansari, and S. Al-Homidan, Nonsmooth variational-like inequalities and nonsmooth vector optimizatization, To appear in Optimization Letters (2013).
Q. H. Ansari, and S. Al-Homidan, Nonsmooth Weighted Variational Inequalities and Nonsmooth Vector Optimization, To appear in Journal of Nonlinear and Convex Analysis (2014).
L. C. Ceng, S. Al-Homidan, and Q. H. Ansari, Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems, To appear in Fixed Point Theory and Applications.

Citations

The members have collected so far over 3130 citations according to the Web of Knowledge.