Aksoy, Ümit
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U., Aksoy
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Ümit Aksoy
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Aksoy, Ümit
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Aksoy, Ue.
Aksoy, Ue
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Ümit Aksoy
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Aksoy,Ü.
Ümit, Aksoy
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Aksoy, Ue.
Aksoy, Ue
Job Title
Profesör Doktor
Email Address
umit.aksoy@atilim.edu.tr
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
41
Articles
33
Citation Count
445
Supervised Theses
2
41 results
Scholarly Output Search Results
Now showing 1 - 10 of 41
Book Part Citation Count: 0Dirichlet Problem for Inhomogeneous Biharmonic Equation in Clifford Analysis(Springer Science and Business Media Deutschland GmbH, 2022) Aksoy,Ü.; Çelebi,A.O.; MathematicsAn integral representation formula in terms of the bi-Laplacian operator is obtained and Dirichlet problem for the bi-Poisson equation is solved in Clifford analysis. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.Article Citation Count: 7Norm estimates of a class of Calderon-Zygmund type strongly singular integral operators(Taylor & Francis Ltd, 2007) Aksoy, Ue; Celebi, A. O.; MathematicsIn this article, we prove the L-p boundedness of a class of Calderon - Zygmund type strongly singular operators. In particular, we give an estimate for the L-2 norm of these operators in the unit disc of the complex plane.Article Citation Count: 23Meir-Keeler Type Contractions on Modular Metric Spaces(Univ Nis, Fac Sci Math, 2018) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Rakocevic, Vladimir; MathematicsIn this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.Article Citation Count: 8AV Bitsadze's observation on bianalytic functions and the Schwarz problem(Taylor & Francis Ltd, 2019) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay; MathematicsAccording to an observation of A.V. Bitsadze from 1948 the Dirichlet problem for bianalytic functions is ill-posed. A natural boundary condition for the polyanalytic operator, however, is the Schwarz condition. An integral representation for the solutions in the unit disc to the inhomogeneous polyanalytic equation satisfying Schwarz boundary conditions is known. This representation is extended here to any simply connected plane domain having a harmonic Green function. Some other boundary value problems are investigated with some Dirichlet and Neumann conditions illuminating that just the Schwarz problem is a natural boundary condition for the Bitsadze operator.Article Neumann problem for generalized n-Poisson equation(Journal of Mathematical Analysis and Applications, 2009) Aksoy, Ümit; Çelebi, Okay; MathematicsUsing a hierarchy of integral operators having higher-order Neumann functions and their derivatives as kernels, the Neumann problem for a 2nth order linear partial complex differential equation is discussed. The solvability of the problem is obtained.Article A HIERARCHY OF SINGULAR INTEGRAL OPERATORS FOR MIXED BOUNDARY VALUE PROBLEMS(2011) Aksoy, Ümit; Çelebi, Okay; MathematicsA class of integral operators having a hierarchy of polyharmonic kernels is introduced and some properties are derived. Iterated mixed boundary value problems for complex model equations and linear elliptic complex partial differential equations are discussed in the unit disc of the complex plane.Article Citation Count: 67FIXED POINTS OF GENERALIZED α-ADMISSIBLE CONTRACTIONS ON b-METRIC SPACES WITH AN APPLICATION TO BOUNDARY VALUE PROBLEMS(Yokohama Publ, 2016) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MathematicsA general class of alpha-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations.Conference Object Citation Count: 1On the methods of pricing American options: case study(Springer, 2018) Aydogan, Burcu; Aksoy, Umit; Ugur, Omur; MathematicsIn this study, a comparative analysis of numerical and approximation methods for pricing American options is performed. Binomial and finite difference approximations are discussed; furthermore, Roll-Geske-Whaley, Barone-Adesi and Whaley and Bjerksund-Stensland analytical approximations as well as the least-squares Monte Carlo method of Longstaff and Schwartz are presented. Applicability and efficiency in almost all circumstances, numerical solutions of the corresponding free boundary problem is emphasized. Methods used in pricing American options are also compared on dividend and non-dividend paying assets; and their pros and cons are discussed along with numerical experiments.Article Citation Count: 123ON THE SOLUTIONS OF FRACTIONAL DIFFERENTIAL EQUATIONS VIA GERAGHTY TYPE HYBRID CONTRACTIONS(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MathematicsThe aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.Article Norm estimates of a class of Calderon–Zygmund type strongly singular integral operators(Integral Transforms and Special Functions, 2007) Aksoy, Ümit; Çelebi, Okay; MathematicsIn this article, we prove the Lp boundedness of a class of Calderon–Zygmund type strongly singular operators. In particular, we give an estimate for the L2 norm of these operators in the unit disc of the complex plane.
