Abstract
We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others.
Highlights
Throughout this paper we denoted by Æ and Ê the set of all positive integers and all positive real numbers, respectively
We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping
Using the viscosity approximation method, Moudafi 6 introduced the iterative process for nonexpansive mappings see 3, 7 for further developments in both Hilbert and Banach spaces and proved that if H is a real Hilbert space, the sequence {xn} generated by the following algorithm: x0 ∈ C chosen arbitrarily, 1.4 xn 1 αnf xn 1 − αn Txn, ∀n ≥ 0, where f : C → C is a contraction mapping with constant α ∈ 0, 1 and {αn} ⊂ 0, 1 satisfies certain conditions, converges strongly to a fixed point of T in C which is unique solution x∗
Summary
Throughout this paper we denoted by Æ and Ê the set of all positive integers and all positive real numbers, respectively. Using the viscosity approximation method, Moudafi 6 introduced the iterative process for nonexpansive mappings see 3, 7 for further developments in both Hilbert and Banach spaces and proved that if H is a real Hilbert space, the sequence {xn} generated by the following algorithm: x0 ∈ C chosen arbitrarily, 1.4 xn 1 αnf xn 1 − αn Txn, ∀n ≥ 0, where f : C → C is a contraction mapping with constant α ∈ 0, 1 and {αn} ⊂ 0, 1 satisfies certain conditions, converges strongly to a fixed point of T in C which is unique solution x∗
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
