Indeed, we propose different approaches, based on shrinking projection algorithms, to solve the equilibrium problem in a Banach space.
Inspired and motivated by the work of Nakajo and Takahashi [5], Takahashi et al. [6], Dong et al. [7], Ceng et al. [17] and Cholamjiak and Suantai [20], we propose a hybrid method based on the shrinking effect of the two half-spaces, namely C n and Q n, of the underlying Hilbert space H.
The analytical solution for diffusion control, which is based on the shrinking core model, gives the fractional exchange as a function of the diffusivities and valencies of the counter-ions.
A simple combustion model, based on the shrinking core conversion model, has been developed to analyse the combustion behaviour of sludge char particles.
The strong convergence theorem of the iterative scheme to a common element of the three aforementioned sets is obtained based on the shrinking projection method which extends and improves that of Ezeora and Shehu [9] and many others.
The strong convergence theorem of the iterative scheme to a common element of the three aforementioned sets is obtained based on the shrinking projection method which extends and improves that of Ezeora and Shehu (Thai J. Math. 9(201199-409, 2011) and many others.
Motivated and inspired by the results mentioned and related literature, we propose an iterative algorithm based on the shrinking projection method for finding a common element of the set of solutions of split generalized equilibrium problems and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces.
In 2008, Takahashi and Zembayashi [21] introduced an explicit algorithm based on the shrinking projection method for finding a common solution of the set of fixed points of a relatively nonexpansive mapping T and the set of solutions of an equilibrium problem.
Motivated by these results, we investigated the common element problems of the generalized equilibrium problem (2.1) and quasi-nonexpansive mappings based on the shrinking projection algorithm.
