On the existence and uniqueness of solutions of a certain class of non-linear singular integral equations
Küçük Resim Yok
Tarih
2011
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this study, the existence of a solution of the non-linear singular integral equation system$w(z) = f1 \\biggl ( z,w(z),h(z), T_G g_1(· ,w(·), h(·))(z)$, $. \\hspace{40mm} \\Pi_Gg_1(· ,w(·), h(·))(z) \\biggr )$, $h(z) = f_2 \\biggl ( z,w(z), h(z), T_Gg_2(·,w(·), h(·))(z)$,$. \\hspace{40mm} \\Pi_Gg_2(· ,w(·), h(·))(z) \\biggr )$ , has been investigated. This system is more general than the one$w(z) = f_1 (z,w(z), h(z), T_Gg_1(· ,w(·), h(·))(z))$, $h(z) = f_2 (z,w(z), h(z),\\Pi_Gg_2(·,w(·), h(·)) (z))$,studied by Musayev and Duz (Existence and uniqueness theorems for a certain class of non linear singular integral equations SJAM 10 (1), 3– 18, 2009). Here, $T_Gf(z)$ and $\\Pi_Gf(z) are the Vekua integral operators defined by $T_Gf(z)=- \\frac{1}{\\pi} \\int_G \\int \\frac{f(\\varsigma)}{\\varsigma - z} d\\xi d\\eta$, $\\Pi_Gf(z)=- \\frac{1}{\\pi} \\int_G \\int \\frac{f(\\varsigma)}{(\\varsigma - z)^2} d\\xi d\\eta$.
Açıklama
Anahtar Kelimeler
Matematik, İstatistik ve Olasılık
Kaynak
Hacettepe Journal of Mathematics and Statistics
WoS Q Değeri
Scopus Q Değeri
Cilt
40
Sayı
1
