We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in  the unit ball of  the Hilbert space. ...

A new general composite implicit random iteration scheme with perturbed mapping is proposed and obtain necessary and sufficient conditions for strong convergence of proposed iteration scheme to random fixed point of a finite family of random nonexpansive mappings are obtained.

We introduce a new modified Halpern-type iteration for a family of Bregman relatively nonexpansive mappings and establish strong convergence theorems in reflexive Banach spaces. The results extend the corresponding results obtained by many authors. Mathematics Subject Classification: 47H09; 47H10

We prove that any Banach space X whose Banach-Mazur distance to a Hilbert space is less than √ 5+ √ 13 2 has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of a Banach space X . A mapping T : C → C is said to be nonexpansive if ‖T x− T y‖ ≤ ‖x− y‖ for any x, y ∈ C. A nonempty weakly compact convex set C is said to have the fixed point property if ev...

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...