We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

In this paper, we consider the weak and strong convergence of implicit iteration process to a common fixed point of a finite family of nonself Ii-asymptotically quasi-nonexpansive mappings. Our results of this paper improve and extend the corresponding results of Shazad [8], Temir [5] and Gul [J. Math. Anal. Appl. 329(2007), 759-765]. Mathematics Subject Classification: 47H09, 47J25

Throughout this paper, we always assume thatH is a real Hilbert space, whose inner product and norm are denoted by 〈·, ·〉 and ‖ · ‖. → and ⇀ are denoted by strong convergence and weak convergence, respectively. Let C be a nonempty closed convex subset ofH and T : C → C a mapping. In this paper, we denote the fixed point set of T by F T . T is said to be a contraction if there exists a constant ...

In this paper, we establish a weak convergence theorem and some strong convergence theorems of an explicit iteration process for a finite family of strictly asymptotically pseudo-contractive mappings in the intermediate sense and also establish a strong convergence theorem by a new hybrid method for above said iteration scheme and mappings in the setting of Hilbert spaces. AMS Mathematics Subje...

We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi-φ-asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Fréchet differentiable norm under weaker conditions. The method of the proo...