In this paper, we first introduce the class of generalized nonexpansive mappings in Banach spaces. This class contains both the classes of nonexpansive and ̨-nonexpansive mappings. In addition, we obtain some fixed point and coincidence point theorems for generalized nonexpansive mappings in uniformly convex Banach spaces. Our results extend some wellknown results in literature. 2010 Mathematic...

Recently‎, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $alpha-psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractiv...

We introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

In this paper, an iterative scheme for finding common solutions of the set fixed points a pair asymptotically quasi-nonexpansive mapping and minimizers minimization problem is constructed. Using idea jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on space or operator. Our improve, extend generalize many important in literature.

The authors have obtained the following results: 1 the definition of uniformly closed countable family of nonlinear mappings, 2 strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, 3 two examples of uniformly closed countable families of nonlinear mappings and applications, 4 an...