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Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl...

In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through △-convergence and strong convergence under some weaker...

February 2014; Accepted 8 March 2014; Published 30 March 2014
Academic Editor: Abdul Latif
Copyright © 2014 **Safeer** **Hussain** **Khan**. This is an open access article distributed under the Creative Commons

February 2014; Accepted 8 March 2014; Published 30 March 2014
Academic Editor: Abdul Latif
Copyright © 2014 **Safeer** **Hussain** **Khan**. This is an open access article distributed under the Creative Commons

The existence of fixed points of single-valued mappings in modular function spaces has been studied by many authors. The approximation of fixed points in such spaces via convergence of an iterative process for single-valued mappings has also been attempted very recently by Dehaish and Kozlowski (Fixed Point Theory Appl. 2012:118, 2012). In this paper, we initiate the study of...

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...

Information Technology, Abbotabad, Pakistan
Received 21 August 2013; Accepted 5 December 2013; Published 11 February 2014
Academic Editors: A. Bellouquid and C. Zhai
Copyright © 2014 **Safeer** **Hussain** **Khan** et

**Safeer** **Hussain** **Khan**
1
Isa Yildirim
0
0
Department of Mathematics, Ataturk University
, Erzurum 25240,
Turkey
1
Department of Mathematics, Statistics and Physics,Qatar University
, Doha 2713,
Qatar

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.

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.

Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F:=F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠∅. Let T1,T2:K→E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences {kn(i)}⊂[1,∞) satisfying ∑n=1∞(kn(i)-1)<∞(i=1,2), respectively. For any given x1∈K...