A Note on Convergence of a Sequence and Its Applications to Geometry of Banach Spaces

Hemant Kumar Pathak
2011 Advances in Pure Mathematics  
The purpose of this note is to point out several obscure places in the results of Ahmed and Zeyada [J. Math. Anal. Appl. 274 (2002) 458-465]. In order to rectify and improve the results of Ahmed and Zeyada, we introduce the concepts of locally quasi-nonexpansive, biased quasi-nonexpansive and conditionally biased quasi-nonexpansive of a mapping w.r.t. a sequence in metric spaces. In the sequel, we establish some theorems on convergence of a sequence in complete metric spaces. As consequences of
more » ... our main result, we obtain some results of Ghosh and Debnath [
doi:10.4236/apm.2011.13009 fatcat:zukvnewiefakxkrfqdzrvzh4ou