Safeer Hussain Khan
Qatar University
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Featured researches published by Safeer Hussain Khan.
Computers & Mathematics With Applications | 2011
Safeer Hussain Khan; Mujahid Abbas
In this paper, we get some results on strong and @?-convergence in CAT(0) spaces for an iterative scheme which is both faster than and independent of the Ishikawa scheme. We also obtain some results for two mappings using the Ishikawa-type iteration scheme. The motivation of the present work comes from that of Dhompongsa and Panyanak (2008) [3].
Fixed Point Theory and Applications | 2011
Mujahid Abbas; Safeer Hussain Khan; Talat Nazir
In this paper, using the setting of a generalized metric space, a unique common fixed point of four R-weakly commuting maps satisfying a generalized contractive condition is obtained. We also present example in support of our result.2000 MSC: 54H25; 47H10; 54E50.
Applied Mathematics Letters | 2011
Mujahid Abbas; Safeer Hussain Khan; Abdul Rahim Khan; Ravi P. Agarwal
In this paper, we introduce a new one-step iterative process to approximate common fixed points of two multivalued nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems for the proposed process under some basic boundary conditions.
Fixed Point Theory and Applications | 2013
Safeer Hussain Khan
We introduce a new iterative process which can be seen as a hybrid of Picard and Mann iterative processes. We show that the new process converges faster than all of Picard, Mann and Ishikawa iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points, 2002) for contractions. We support our analytical proof by a numerical example. We prove a strong convergence theorem with the help of our process for the class of nonexpansive mappings in general Banach spaces and apply it to get a result in uniformly convex Banach spaces. Our weak convergence results are proved when the underlying space satisfies Opial’s condition or has Fréchet differentiable norm or its dual satisfies the Kadec-Klee property.MSC:47H10, 54H25.
Computers & Mathematics With Applications | 2008
Safeer Hussain Khan; N. Hussain
In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that our theorems can be generalized to the case of finitely many mappings.
International Journal of Mathematics and Mathematical Sciences | 2004
Hafiz Fukhar-ud-din; Safeer Hussain Khan
A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.
Computers & Mathematics With Applications | 2011
Safeer Hussain Khan; Isa Yildirim; B. E. Rhoades
′) Weak and strong convergence a b s t r a c t In this paper, we introduce a new one-step iterative process to compute the common fixed points of two multivalued nonexpansive mappings. Furthermore, we also prove some strong and weak convergence theorems in uniformly convex Banach spaces.
Computers & Mathematics With Applications | 2010
Safeer Hussain Khan; Isa Yildirim; Murat Ozdemir
In this paper, we study an implicit iterative algorithm for two nonexpansive mappings and two finite families of nonexpansive mappings in Banach spaces. We prove some weak and strong convergence theorems for these iterative algorithms. Our results extend some existing results.
Journal of Inequalities and Applications | 2014
Mujahid Abbas; Safeer Hussain Khan; Mihai Postolache
Recently, Karapınar and Tas (Comput. Math. Appl. 61:3370-3380, 2011) extended the class of Suzuki-generalized nonexpansive mappings to the class of SKC mappings. In this paper, we investigate SKC mappings to get a criterion to guarantee a fixed point, via extending the results proved by Karapınar and Tas into the class of CAT(0) spaces. Further, by using Ishikawa-type iteration scheme for two mappings, we derive approximation fixed point sequence. Our results extend, improve and unify some existing results in this direction, such as (Nonlinear Anal. Hybrid Syst. 4:25-31, 2010) by Nanjaras et al. or (Comput. Math. Appl. 61:109-116, 2011) by Khan and Abbas.MSC:47H09, 47H10, 49M05.
Fixed Point Theory and Applications | 2012
Safeer Hussain Khan; Arif Rafiq; Nawab Hussain
In this paper, we study a three-step iterative scheme with error terms for solving nonlinear ϕ-strongly accretive operator equations in arbitrary real Banach spaces.