Yazar "Temizer, O. Faruk" seçeneğine göre listele

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    On the solutions of the linear integral equations of Volterra type
    (Wiley, 2007) Odemir, Ismet; Temizer, O. Faruk
    Some boundaries about the solution of the linear Volterra integral equations of the form f (t) = 1-K * f were obtained as vertical bar f (t)vertical bar <= 1, vertical bar f (t)vertical bar <= 2 and vertical bar f (t)vertical bar <= 4 in (J. Math. Anal. Appl. 1978; 64:381-397; Int. J. Math. Math. Sci. 1982; 5(1):123-131). The boundary of the solution function of an equation in this type was found as vertical bar f (t)vertical bar <= 2(n) in (Integr Equ. Oper Theory 2002; 43:466-479), where t is an element of [0, infinity) and n is a natural number such that n >= 2. In (Math. Comp. 2006; 75:1175-1199), it is shown that the boundary of the solution function of an equation in the same form can also be derived as that of (Integr Equ. Oper Theory 2002; 43:466-479) under different conditions than those of (Integr Equ. Oper Theory 2002; 43:466-479). In the present paper, the sufficient conditions for the boundedness of functions f, f', f '',..., f((n+3)), (n is an element of N) defined on the infinite interval [0, infinity) are given by our method, where f is the solution of the equation f (t) = 1 - K * f. Copyright (C) 2007 John Wiley & Sons, Ltd.
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    Some Bounded Linear Integral Operators and Linear Fredholm Integral Equations in the Spaces H?,?,? ((a,b) x (a,b), X) and H?,?(a,b), X)
    (Hindawi Publishing Corp, 2013) Ozdemir, Ismet; Akhmedov, Ali M.; Temizer, O. Faruk
    The spaces H-alpha,H-delta,H-gamma ((a,b) x (a,b), R) and H-alpha,H-delta ((a,b), R) were defined in ((Huseynov (1981)), pages 271-277). Some singular integral operators on Banach spaces were examined, (Dostanic (2012)), (Dunford (1988), pages 2419-2426 and (Plamenevskiy (1965)). The solutions of some singular Fredholm integral equations were given in (Babolian (2011), Okayama (2010), and Thomas (1981)) by numerical methods. In this paper, we define the sets H-alpha,H-delta,H-gamma ((a,b) x(a,b), X) and H-alpha,H-delta ((a,b), X) by taking an arbitrary Banach space X instead of R, and we showthat these sets which are different from the spaces given in (Dunford (1988)) and (Plamenevskiy (1965)) are Banach spaces with the norms parallel to center dot parallel to(alpha,delta,gamma) and parallel to . parallel to(alpha,delta) Besides, the bounded linear integral operators on the spaces H-alpha,H-delta,H-gamma ((a,b) x (a,b), X) and H-alpha,H-delta ((a,b), X), some of which are singular, are derived, and the solutions of the linear Fredholmintegral equations of the form f(s) = phi(s) + lambda integral(b)(a)A(s,t) f(t)dt, f(s) = phi(s) + lambda integral(b)(a)A(t,s)f(t)dt and f(s, t) = phi(s, t) + lambda integral(b)(a) (s, t)f(t, s)dt are investigated in these spaces by analytical methods.