in this paper, we prove the existence of fixed point for j-type multi-valuedmap t in cat(0) spaces and also we prove the strong convergence theoremsfor ishikawa iteration scheme without using the xed point of involving map.

In this paper, we prove the existence of fixed point for J-type multi-valuedmap T in CAT(0) spaces and also we prove the strong convergence theoremsfor Ishikawa iteration scheme without using the xed point of involving map.

In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...

Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spa...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

The Mann iterative scheme was invented in 1953, see [7], and was used to obtain convergence to a fixed point for many functions for which the Banach principle fails. For example, the first author in [8] showed that, for any continuous selfmap of a closed and bounded interval, the Mann iteration converges to a fixed point of the function. In 1974, Ishikawa [5] devised a new iteration scheme to e...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand Abstract We prove a convergence theorem of the Mann iteration scheme for a uniformly L-Lipschitzian asymptotically demicontractive mapping in a CAT(κ ) space with κ > 0. We also obtain a convergence theorem of the Ishikawa iteration scheme for a uniformly L-Lipsc...