Some new results on cyclic relatively nonexpansive mappings in convex metric spaces

Some Results for Cyclic Nonlinear Contractive Mappings in Metric Spaces

In this paper, the concept of cyclic (φ− ψ)-Kannan and cyclic (φ− ψ)-Chatterjea contractions, and fixed point theorems for these types of mappings in the context of complete metric spaces have been introduced. The results proved here extend some fixed point theorems in the literature.

New hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces

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...

Coincidence Quasi-Best Proximity Points for Quasi-Cyclic-Noncyclic Mappings in Convex Metric Spaces

We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al cite{Gabeleh}. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings ...

On the Weak Relatively Nonexpansive Mappings in Banach Spaces

A Projection Method for Relatively Nonexpansive Mappings in Banach Spaces

We introduce a new projection algorithm for solving the fixed point problem of relatively nonexpansive mappings in the framework of Banach spaces. We also prove the strong convergence theorem for such mappings. Mathematics Subject Classification: 47H09, 47H10