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We approximate the fixed point of the Suzuki's generalized nonexpansive mappings via the Picard-Ishikawa hyprid iterative process, recently introduced by Okeke [18]. We prove some weak and strong convergence theorems of this type of mappings in the setting of uniformly convex Banach spaces. We apply our results in finding the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation in Banach spaces. Finally, we give several numerical examples to validate our analytical results. Our results extend and improve several known results in literature, including the results of Okeke [18], Ullah and Arshad [30] and Craciun and Serban [7] among others. [ABSTRACT FROM AUTHOR]

This paper deals with a split equality hierarchical fixed point problem in real Hilbert spaces which is an important and natural extension of hierarchical fixed point problem and split equality fixed point problem. An iterative algorithm where the stepsizes do not depend on the operator norms, so called simultaneous Krasnoselski-Mann algorithm is suggested for solving the split equality hierarchical fixed point problem. Further we prove a weak convergence theorem for the sequence generated by this algorithm. This special aspect of the algorithm together with the convergence result makes it an interesting scheme. Furthermore, we give some examples to justify the main result. Finally, we show that our purposed iterative algorithm is more efficient than some other known iterative algorithms. On the other hand, the framework is general and allows us to treat in a unified way several iterative algorithms, recovering, developing and improving some recently known related convergence results in the literature. [ABSTRACT FROM AUTHOR]

Let C be a nonempty subset of a Banach space X. A mapping T: C → C is said to satisfy(Bγ,μ) condition if there exists γ ∈ [0,1] and μ ∈ [0, ½] satisfying 2μ ≤ γ such that for each x,y ∈ C, γ||x-Tx||≤||x-y||+μ||y-Ty|| implies ||Tx-Ty||≤(1-γ)||x-y||+μ(||x-Ty||+||y-Tx||). In this paper, we obtain some convergence theorems for such mappings using M iterative process in uniformly convex Banach space setting. Our results extend and improve many results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to investigate a split feasibility problem based on a fixed point algorithm. A weak convergence theorem of solutions is established in the framework of infinite dimensional Hilbert spaces. As an application, a split equality problem is also investigated. [ABSTRACT FROM AUTHOR]