full2010.pdf - page 437

399
O47
Á„–”r„µ¦¨¼n Á oµ °Š¦³Á¸¥ª·›¸šÎµŽÊε‹»—˜¦¹Š¦nª¤¡¦o°¤‡ªµ¤‡¨µ—Á‡¨ºÉ°œ
宦´„µ¦nŠ„¹ÉŠÅ¤n¥µ¥Äœž¦·£¼¤·µœµ‡
Convergence Criteria of a Common Fixed Point Iterative Process with Errors
for Quasi-Nonexpansive Mappings in Banach Spaces
‹»”µ¦´˜œr »œ·š1 ¨³‹´œšœµ Å°¥¦µ„µ‹œ„»¨2
Jutharat Boonsanit1* and Jantana Ayaragarnchanakul2
š‡´—¥n °
Ä®o X Áž}œž¦·£¼¤·µœµ‡Á·Š‹¦· Š Ä®o C Áž}œÁŽ˜¥n°¥Å¤n ªnµŠ °Š X Ž¹ÉŠ¤¸ ‡»–¤´˜·žd— ¨³Áž}œÁŽ˜‡°œ -
Áª„Žr Á¤ºÉ° 1, 2 i Ä®o :
i T C Co Áž}œ„µ¦n Š„¹ÉŠÅ¤n¥µ¥Ž¹É Š 1 2 ( ) ( ) F T F T I ˆ z Ĝ C ¨³Ä®o ^ `n D , ^ `n E
Áž}œ¨Îµ—´Äœ [0,1) ¨³ ^ `n u , ^ `n v Áž} œ¨Îµ—´Äœ C Î µ®¦´ 1 x C ¨³ 1 n t œ·¥µ¤¨Îµ—´ ^ `n x ¨³ ^ `n y
—´Šœ¸Ê
2 1
n n n n n n y T x x v E E
1 1 1
n n n n n n x T y y u D D
Á¦µÄ®oÁŠºÉ°œÅ š¸É‹ÎµÁž}œÂ¨³Á¡¸¥Š¡°š¸É‹³šÎµÄ®oŗo ªnµ ¨Îµ—´ ^ `n x š¸Éœ· ¥µ¤ oµŠ˜oœ ¨¼nÁ oµ¼n‹»—˜¦¹Š¦n ª¤µŠ‹»— °Š 1 T
¨³ 2 T
‡ÎµÎµ‡´ : „µ¦nŠ„¹ÉŠÅ¤n¥µ¥ ž¦·£¼¤·µœµ‡ ‹»—˜¦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 T I ˆ z in . C Let ^ `n D and ^ `n E be
sequences in [0,1) and ^ `n u and ^ `n v be sequences in . C 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 y T x x v E E
1 1 1 .
n n n n n n x T y y u D D
1œ´„«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 6597 9563 E-mail :npaew@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