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    Application of the Leray-Schauder alternative to nonlinear singular operator equations
    (Pergamon-Elsevier Science Ltd, 2009) Altun, İshak; Koca, Kerim
    In this paper, we study the problem of existence of solution of nonlinear singular integral equations of the form {w(z) = Phi(z) + T(G)F (., w (.), h (.)) (z) h(z) = Phi'(z) + Pi(G)F (., w (.), h (.)) (z), z is an element of G subset of C. (C) 2009 Elsevier Ltd. All rights reserved.
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    A boundary value problem for nonhomogeneous Vekua equation in Wiener-type domains
    (2007) Koca, Kerim; Çelebi, Okay
    In this article we take the nonhomogeneous Vekua equation w_{\overline{z}} Aw B\overline{w} F; z \in D subject to the conditions Rew \partial D\varphi , \varphi \in C{\alpha}(\partial D) Imw (z_0) c_0 , z_0 \in overline{D}. where A,B,F \in L_p(D) , p > 2. We want to derive the conditions under which the solution exists in Wiener-type domains.
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    A Dirichlet problem for generalized analytic functions
    (2006) Düz, Murat; Koca, Kerim
    For the existence of the solution for the Dirichlet Problem frac{partial w}{partial overline{z}}-(AwBoverline{w}), z in D Rew_{partial D}g, g in C{alpha}partial D Imw(z_0)c_0, z_0 in overline{D} in a domain having a smooth boundary Dsubset C, necessary conditions are studied. Here we assumed that z in D,g in C{alpha}(partial D),z_0 in overline{D} and A,B in C{alpha}(overline{D}).
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    Neumann boundary value problem for Bitsadze equation in a ring domain
    (Springernature, 2020) Gencturk, Ilker; Koca, Kerim
    In this article, we investigate Neumann boundary value problem for Bitsadze equation in a ring domain by using same problem for the first order partial differential equations.
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    A note on maximal commutators and commutators of maximal functions
    (Math Soc Japan, 2015) Agcayazi, Mujdat; Gogatishvili, Amiran; Koca, Kerim; Mustafayev, Rza
    In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for these operators are proved.
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    THE COMPLEX LINE (p, q)-INTEGRAL AND (p, q)-GREEN'S FORMULA
    (Ivane Javakhishvili Tbilisi State Univ, 2023) Gencturk, Ilker; Koca, Kerim
    In this study, we present the complex line (p, q)-integral and multiple (p, q)-integral by using the concept of (p, q)-calculus. The (p, q)-Green's formula and the (p, q)-Gauss formulas are obtained with appropriate conditions in a complex plane.
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    THE COMPLEX LINE (p, q)-INTEGRAL AND (p, q)-GREEN’S FORMULA
    (A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University, 2023) Gençtürk, Ilker; Koca, Kerim
    In this study, we present the complex line (p, q)-integral and multiple (p, q)-integral by using the concept of (p, q)-calculus. The (p, q)-Green’s formula and the (p, q)-Gauss formulas are obtained with appropriate conditions in a complex plane. © 2023 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.