full2010.pdf - page 444

406
O48
ªœ„µ¦šÎµŽÊεš¸É¤¸‡nµ‡¨µ—Á‡¨ºÉ°œ„ε„´ Á¡ºÉ °®µ‹»—˜¦¹Š¦nª¤
宦´„µ¦Âž¨Šœ·—‡ª°ÅŽœ°œÁ°„Žr ¡œŽ¸¢Äœž¦·£¼¤·µœµ‡
A Common Fixed Point Iterative Process with Errors
for a Quasi-nonexpansive Mappings in Banach spaces
¡´ ˜¦µ£¦–r Á„oµÁ°¸Ê¥œ 1 ¨³‹´œšœµ Å°¥¦µ„µ–‹œ„»¨ 2
Pattraporn Kaonein 1* and Jantana Ayaragarnchanakul 2
š‡´—¥n °
Ä®o X Áž}œž¦·£¼¤·µœµ‡Á·Š‹¦·Š ¨³Ä®o C Áž}œ´ÁŽ˜‡°œÁª„Žržd —¨³Å¤nªnµŠ °Š X 宦´ 1, 2 i
Įo :
i T C Co Áž}œ¢{Š„r´œœ·—‡ª°ÅŽœ°œÁ°„Žr¡œŽ¸ ¢ Ž¹ÉŠ 1 2 F T F Tˆ z ‡ Ĝ C Á¦µ¤¸‡ªµ¤œÄ‹¨Îµ—´
Ĝ„¦³ªœ„µ¦˜n°Åžœ¸Ê 宦´  1 x C ¨³ 1 n t œ·¥µ¤¨Îµ—´ ^ `n x ¨³ ^ `n y
2 1
n n n n n n n n y T x a x a v E E
1 1 1
n n n n n n n n x T y b y b u D D
×¥š¸É ^ `n a , ^ `n b ¨³ ^ `n E Áž}œ¨Î µ—´Äœ > @0,1 ¨³ ^ `n u ¨³ ^ `n v Áž}œ¨Îµ—´Äœ C Á¦µ¡· ¼ ‹œr„µ¦¨¼n Á oµ °Š
¨Îµ—´ ^ `n x ޼n‹»—˜¦¹Š¦n ª¤ °Š 1 T ¨³ 2 T £µ¥Ä˜o ÁŠºÉ°œÅ š¸ÉÁ®¤µ³¤
‡ÎµÎµ‡´ : ¢{Š„r ´œœ·—‡ª°ÅŽœ°œÁ°„Žr¡œŽ¸¢ ž¦· £¼¤·µœµ‡ ‡°œÁª„Žr ´ÁŽ˜žd— ‹»—˜¦¹Š¦nª¤
Abstract
Let X be a real Banach space and let C be a nonempty closed convex subset of X . For 1, 2, i let
:
i T C Co be a quasi-nonexpansive mapping such that 1 2 F T F Tˆ z ‡ in C . We are interested in
sequences in the following process. For 1 x C and 1 n t define the sequences ^ `n x and ^ `n y by
2 1
n n n n n n n n y T x a x a v E E
1 1 1
n n n n n n n n x T y b y b u D D
where ^ `n a , ^ `n b , ^ `n D and ^ `n E are sequences in > @0,1 and ^ `n u and ^ `n v are sequences in C .
We prove some convergence theorems for common fixed point of 1 T and 2 T under appropriate conditions.
Keywords: Quasi-nonexpansive mapping, Banach space, Closed convex subset, Common fixed point
1 œ´„«¹ „¬µž¦·µÃš £µ‡ª·µ‡–·˜«µ˜¦r ‡–³ª·š¥µ«µ˜¦r ¤®µª·š¥µ¨´¥Š ¨µœ‡¦· œš¦r Š ¨µ 90112
Master’ s Degree Student, Department of Mathematics, Faculty of Science, Prince of Songkla University, Songkhla, 90112.
Corresponding author : Ú¦«´¡šr 08 4069 9019 E-mail:nannannna@hotmail.com
2 ¦«. —¦. £µ‡ª·µ‡–·˜«µ˜¦r ‡–³ª·š¥µ«µ˜¦r ¤®µª· š¥µ¨´¥Š ¨µœ‡¦· œš¦r Š ¨µ 90112
Assoc. Prof. Dr., Department of Mathematics, Faculty of Science, Prince of Songkla University, Songkhla, 90112 .