Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings

Let[inline-graphic not available: see fulltext] be a real Banach space,[inline-graphic not available: see fulltext] a closed convex nonempty subset of[inline-graphic not available: see fulltext], and[inline-graphic not available: see fulltext] asymptotically quasi-nonexpansive mappings with sequences (resp.)[inline-graphic not available: see fulltext] satisfying[inline-graphic not available: see fulltext] as[inline-graphic not available: see fulltext], and[inline-graphic not available: see fulltext]. Let[inline-graphic not available: see fulltext] be a sequence in[inline-graphic not available: see fulltext]. Define a sequence[inline-graphic not available: see fulltext] by[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext]. Let[inline-graphic not available: see fulltext]. Necessary and sufficient conditions for a strong convergence of the sequence[inline-graphic not available: see fulltext] to a common fixed point of the family[inline-graphic not available: see fulltext] are proved. Under some appropriate conditions, strong and weak convergence theorems are also proved.