Safeer Hussain Khan

Strong and Δ-convergence of some iterative schemes in CAT(0) spaces

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].

Common fixed points of R-weakly commuting maps in generalized metric spaces

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.

Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme

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.

A Picard-Mann hybrid iterative process

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.

Convergence theorems for nonself asymptotically nonexpansive mappings

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.

CONVERGENCE OF TWO-STEP ITERATIVE SCHEME WITH ERRORS FOR TWO ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

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.

RETRACTED: A one-step iterative process for two multivalued nonexpansive mappings in Banach spaces

′) 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.

Convergence of an implicit algorithm for two families of nonexpansive mappings

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.

Existence and approximation results for SKC mappings in CAT(0)CAT(0)(

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.

A three-step iterative scheme for solving nonlinear ϕ-strongly accretive operator equations in Banach spaces

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.