Fixed point property for affine nonexpansive mappings on a very large class of nonweakly compact subsets in c0 respect to an equivalent norm

Abstract

O¨ ZETYU¨ KSEKALI˙SANSATEZac0'DA ZAYIF-KOMPAKT OLMAYAN KU¨MELERI˙N C¸ OK GENI˙S¸ BI˙RSINIFINDA BI˙R ES¸DEG˘ ER NORMA GO¨ RE AFI˙N GENI˙S¸LEMEYENFONKS˙IYONLAR ˙IC¸ ˙IN SAB˙IT NOKTA TEOR˙IS˙ISerap ORANKafkasa U¨ niversitesiaFenaBilimleriaEnstitu¨su¨Matematik AnabilimaDalıDanıs¸man:aYrd.aDoc¸.aDr.aVeyselaNEZ˙IR2011'de, LennardaveaNezir ispatlamıs¸tır ki!b = (bn)n2N herhangi bir reel terimlive 0 < m := infn2N bn, M := supn2Nbn < 1 olacak s¸ekilde sınırlı dizi olmak ¨uzerebu dizi yardımıyla her n 2 N ic¸in fn := abn en ve n := aPnk=1fn alınarak kurulan(n)n2N dizisinin kapalı konveks kabu˘gu E = co(fn : n 2 Ng)ak¨umesiaafinak k1-genis¸lemeyenafonksiyonlaraic¸inasabitanoktaateorisinia(S.N.T'yi)abozar. Aynı s¸ekilde, Nezir'indoktora tezinde g¨ozlemlemis¸lerdir ki (c0; kk1) da c0-toplam baz dizilerinden olan, her n 2N ic¸in n := n(b1e1+b2e2+b3e3+

ABSTRACTMasteraofaScienceaThesisFIXED POINT PROPERTY FOR AFFINE NONEXPANSIVE MAPPINGSON A VERY LARGE CLASS OF NONWEAKLY COMPACT SUBSETS INc0 RESPECT TO AN EQUIVALENT NORMSerap ORANKAFKASaUNIVERSITYTHEaGRADUATEaSCHOOLaOFaNATURALaANDaAPPLIEDaSCIENCEDEPARTMENTaOFaMATHEMATICSSupervisor:aVeyselaNEZ˙IRIna2011, LennardaandaNezir provedathat foraallasequences!b = (bn)n2N inaR with0 < m := infn2N bnaandaM := supn2Nbn < 1, byadefiningafn := bn en andan :=Pnk=1fnfor each n 2 N, theaclosedaconvexahull of (n)n2N,aE = co(fn : n 2 Ng) fails thefixedapointaproperty (FPP)aforaaffineak k1-nonexpansiveamappings. Similarly, inatheaPh.D.thesisaofaNezir, they observed some c0-summing basic sequences in (c0; k k1), and forn := n(b1e1+b2e2+b3e3+