Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption

Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption

for all x ∈ E, where 〈·,·〉 denotes the generalized duality pairing. It is well known that if E is a uniformly smooth Banach space, then J is single valued and such that J(−x) =−J(x), J(tx) = tJ(x) for all x ∈ E and t ≥ 0; and J is uniformly continuous on any bounded subset of E. In the sequel, we shall denote single-valued normalized duality mapping by j by means of the normalized duality mappi...

A New Iterative Method for the Split Common Fixed Point Problem in Hilbert Spaces

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we propose a new algorithm that is completely different from the existing algorithms. Under standard assumptions, we establish a weak convergence theorem of the proposed algorith...

Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators

Common fixed points of quasi-contractive operators

We establish a general theorem to approximate common fixed points of quasi-contractive operators on a normed space through the modified Ishikawa iteration process with errors in the sense of Liu [8]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1]. 2000 Mathematical Subject Clasification: Primary 47H10, 47H17: Secondary 54H25

Iterative Approximation of Fixed Points for Strongly Pseudo-contractive Mappings

The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multivalued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.