In this paper, weak and strong convergence of two-step iteration sequences to a common fixed point for a pair of a finite family of asymptotically nonexpansive mappings and a finite family of generalized nonexpansive multivalued mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented. The results obtained in this paper extend and improve some recent known res...

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K → K be an I-asymptotically quasi-nonexpansive type mapping and I : K → K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type ma...

and Applied Analysis 3 4 if E is a reflexive, strictly convex, and smooth Banach space, then for all x, y ∈ E, φ ( x, y ) 0 iff x y. 1.7 For more details see 2, 3 . Let C be a closed convex subset of E, and let T be a mapping from C into itself. We denote by F T the set of fixed point of T . A point p in C is said to be an asymptotic fixed point of T 8 if C contains a sequence {xn}which converg...

where / is a mapping of X into its adjoint space X* such that for all u in X, (J(u)} ^)=|M| 2 d ||/(^)|| HMI* In some recent papers ([7], [8], [9]), we have presented an existence theory for solutions of nonlinear functional equations in uniformly convex Banach spaces X involving nonexpansive and accretive mappings. These results were obtained by interweaving the fixed point theory of nonexpans...

and Applied Analysis 3 for all x, y ∈ C, where cn max{0, supx,y∈C ‖Tnx − Tny‖ − ‖x − y‖ } so that limn→∞cn 0. Hence, T is a generalized asymptotically nonexpansive mapping. The mapping T : C → C is said to be demiclosed at 0 if for each sequence {xn} in C converging weakly to x and {Txn} converging strongly to 0, we have Tx 0. A Banach space E is said to satisfy Opial’s property, see 4 , if for...

The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the generalized f-projection operator for a countable family of relatively quasi-nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong convergence theorem for a countable family of relatively quasi-nonexpa...

In this paper, two examples of quasi-firmly type nonexpansive mappings are given to prove that the concept is different from nonexpansive mapping. Furthermore, it is studied to the convergence of the sequence of successive approximations for this class of mappings only when the super limit of iteration coefficients is less than 1. In particular, the Picard iteration {T x0} of such a mapping con...

This paper?s objective is to put forward anewkind of E?type contraction, which includes rational expression, by considering Proinov type functions and CG?simulation functions. contraction termed as a Suzuki-Proinov generalized (?,Z* E)?contraction mapping. Further, some common fixed point theorems using these new mappings, are triangular ??admissible pairs, demonstrated in the setting modular b...

The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem for a maximal monotone operator and the fixed point problem for a relatively nonexpansive mapping.