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Iterative approximation of common attractive points of further generalized hybrid mappings

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...

Common fixed points of two multivalued nonexpansive maps in Kohlenbach hyperbolic spaces

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...

Approximating fixed points of multivalued ρ-nonexpansive mappings in modular function spaces

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...

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...

Fixed points of multivalued nonexpansive mappings in Banach spaces

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

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.

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.