ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF A CERTAIN CLASS OF NON-LINEAR SINGULAR INTEGRAL EQUATIONS

Murat DÜZ

ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF A CERTAIN CLASS OF NON-LINEAR SINGULAR INTEGRAL EQUATIONS

Authors : Murat DÜZ

Pages : 41-52

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Publication Date : 2011-01-01

Article Type : Research Paper

Abstract :In this study, the existence of a solution of the non-linear singular integral equation system winsert ignore into journalissuearticles values(z); = f1 z, winsert ignore into journalissuearticles values(z);, hinsert ignore into journalissuearticles values(z);, TGg1insert ignore into journalissuearticles values( · , winsert ignore into journalissuearticles values( · );, hinsert ignore into journalissuearticles values( · ););insert ignore into journalissuearticles values(z);, ΠGg1insert ignore into journalissuearticles values( · , winsert ignore into journalissuearticles values( · );, hinsert ignore into journalissuearticles values( · ););insert ignore into journalissuearticles values(z); , hinsert ignore into journalissuearticles values(z); = f2 z, winsert ignore into journalissuearticles values(z);, hinsert ignore into journalissuearticles values(z);, TGg2insert ignore into journalissuearticles values( · , winsert ignore into journalissuearticles values( · );, hinsert ignore into journalissuearticles values( · ););insert ignore into journalissuearticles values(z);, ΠGg2insert ignore into journalissuearticles values( · , winsert ignore into journalissuearticles values( · );, hinsert ignore into journalissuearticles values( · ););insert ignore into journalissuearticles values(z); , has been investigated. This system is more general than the onewinsert ignore into journalissuearticles values(z); = f1z, winsert ignore into journalissuearticles values(z);, hinsert ignore into journalissuearticles values(z);, TGg1insert ignore into journalissuearticles values( · , winsert ignore into journalissuearticles values( · );, hinsert ignore into journalissuearticles values( · ););insert ignore into journalissuearticles values(z); , hinsert ignore into journalissuearticles values(z); = f2 z, winsert ignore into journalissuearticles values(z);, hinsert ignore into journalissuearticles values(z);, ΠGg2insert ignore into journalissuearticles values( · , winsert ignore into journalissuearticles values( · );, hinsert ignore into journalissuearticles values( · ); insert ignore into journalissuearticles values(z););, studied by Musayev and Duz insert ignore into journalissuearticles values(Existence and uniqueness theorems for a certain class of non linear singular integral equations SJAM 10 insert ignore into journalissuearticles values(1);, 3– 18, 2009);. Here, TGfinsert ignore into journalissuearticles values(z); and ΠGfinsert ignore into journalissuearticles values(z); are the Vekua integral operators defined by TGfinsert ignore into journalissuearticles values(z); = − 1 π ZZ G finsert ignore into journalissuearticles values(ς); ς − z dξ dη, ΠGfinsert ignore into journalissuearticles values(z); = − 1 π ZZ G finsert ignore into journalissuearticles values(ς); insert ignore into journalissuearticles values(ς − z); 2 dξ d
Keywords : Holder continui, Fixed point theor, Contraction mappi, 2000 AMS Classification 45 E 05

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