Mathematics & Physics 2016, 9(3), 374–383 УДК 517.55 On a Class of A-Analytic Functions Azimbai Sadullaev∗ Nasridin M.Jabborov† National University of Uzbekistan Vuzgorodok, Tashkent, 100174 Uzbekistan Received 10.05.2016, received in revised form 06.06.2016, accepted 01.07.2009 We consider A-analytic functions in case when A is anti-holomorphic function. <...> In paper for A-analytic functions the integral theorem of Cauchy, integral formula of Cauchy, expansion to Taylor series, expansion to Loran series, Picard’s big theorem and Montel’s theorem are proved. <...> Keywords: A-analytic function, integral theorem of Cauchy, integral formula of Cauchy, Taylor series, Loran series, Picard’s big theorem, Montel’s theorem. <...> Introduction and preliminaries Quoting from a well-known American mathematician Lipman Bers [1]: "It would be tempting to rewrite history and to claim that quasiconformal transformations have been discovered in connection with gas-dynamical problems. <...> The present work is devoted to the theory of analytic solutions of the Beltrami equation f¯ z(z) = A(z)fz(z), (1) which directly related to the quasi-conformal mappings. <...> The function A(z) is, in general, assumed to be measurable with |A(z)| C < 1 almost everywhere in the domain D ⊂ C under consideration. <...> Note that if the function |A(z)| C < 1 is defined only in the domain D ⊂ C, then it can be extended to the whole C by setting A ≡ 0 outside D, so the Theorem 1.1 holds for any domain D ⊂ C. ∗sadullaev@mail.ru †jabborov61@mail.ru ⃝ Siberian Federal University. <...> All rights reserved c – 374 – otzsch [2] and Ahlfors [3] from the point of view of function Azimbai Sadullaev, Nasridin M.Jabborov On a Class of A-Analytic Functions Theorem 1.2 (see [5,6]). <...> The set of all generalized solutions of equation (1) is exhausted by the formula f(z) = Φ[χ(z)], where χ(z) is a homeomorphic solution from Theorem 1.1, and Φ(ξ) is a holomorphic function in the domain χ(D). <...> Moreover, if the generalized solution f(z) has isolated singular points, the holomorphic function Φ = f ◦ χ−1 also has isolated singular points <...>