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...

In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergence theorem for the ergodic theorem of Baillon’s type. Our result of the ergodic theorem of Baillon’s type improves and generalizes many existence theorems of this type of problem. Two nume...

We denote by F(T) the set of fixed points of T. Numerous problems in physics, optimization, and economics reduce to find a solution of the equilibrium problem. Some methods have been proposed to solve the equilibrium problem in a Hilbert spaces; see, for instance, Blum and Oettli [1], Combettes and Hirstoaga [2], and Moudafi [3]. Recently, Tada and Takahashi [4, 5] and S. Takahashi and W. Takah...

We study the convergence of Ishikawa iteration process for the class of asymptotically κ-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Weak convergence theorem is established. We also obtain a strong convergence theorem by using hybrid projection for this iteration process. Our results improve and extend the corresponding results announced by...

‎A new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of systems of‎ ‎variational inequalities is introduced and studied‎. ‎Moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎a ‎system of variational inequalities of an inverse strongly mono...

In this paper, we first obtain a weak mean convergence theorem of Baillon’s type for generalized hybrid mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem of Halpern’s type for generalized hybrid mappings in a Hilbert space.

In this paper, based on viscosity technique with perturbation, we introduce a new non-linear viscosity algorithm for finding a element of the set of fixed points of nonexpansivemulti-valued mappings in a Hilbert space. We derive a strong convergence theorem for thisnew algorithm under appropriate assumptions. Moreover, in support of our results, somenumerical examples (u...

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

In this paper, we introduce a new iterative scheme by viscosity approximation methods for strict pseudo-contractive nonself-mappings in Hilbert spaces and obtain a strong convergence theorem. The theorem improves and extends the result of Shimizu and Takahashi [T. Shimizu, W. Takahashi, Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211 (199...