Abstract
Let E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping j, path convergence is proved for a nonexpansive mapping T : K → K. As an application, we prove strong convergence theorem for common zeroes of a finite family of m‐accretive mappings of K to E. As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from K to E under certain mild conditions.
Highlights
Let E be a real Banach space with dual E∗ and K a nonempty, closed and convex subset of E
Let T : K → K be a nonexpansive mapping with F T / ∅
Motivated by the results of Yao et al 15, we proved path convergence for a nonexpansive mapping in a uniformly smooth real Banach space which is uniformly convex and E admits weakly sequentially continuous duality mapping j
Summary
Let E be a real Banach space with dual E∗ and K a nonempty, closed and convex subset of E. Yao et al 15 proved path convergence for a nonexpansive mapping in a real Hilbert space For t ∈ 0, 1 , let the net {xt} be generated by xt T PK 1 − t xt , as t → 0, the net {xt} converges strongly to a fixed point of T They applied Theorem 1.1 to prove the following theorem. Motivated by the results of Yao et al 15 , we proved path convergence for a nonexpansive mapping in a uniformly smooth real Banach space which is uniformly convex and E admits weakly sequentially continuous duality mapping j. An iterative scheme is constructed to converge to a common fixed point assuming existence of a finite family of pseudocontractive mappings from K to E under certain mild conditions
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 callDisclaimer: 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.
