Profile URL: https://hdl.handle.net/20.500.14411/6803
Job Title:Profesör Doktor
Email Address:umit.aksoy@atilim.edu.tr
Main Affiliation: Mathematics
Scopus ID: 24402879000
Name Variants:
U., Aksoy A., Umit Ü., Aksoy Aksoy,U. Aksoy,Umit Aksoy, Umit Umit, Aksoy U.,Aksoy Ü.,Aksoy Ümit Aksoy A.,Umit Aksoy U. Aksoy, Ümit Aksoy,Ü. Ümit, Aksoy A., Ümit A.,Ümit Aksoy, U. Aksoy, Ue. Aksoy, Ue
43 results
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Article A Survey on Boundary Value Problems for Complex Partial Differential Equations(Advances in Dynamical Systems and Applications, 2010) Aksoy, Ümit; Çelebi, A. OkayIn this article, the recent results on basic boundary value problems of complex analysis are surveyed for complex model equations and linear elliptic complex par tial differential equations of arbitrary order on simply connected bounded domains, particularly in the unit disc, on unbounded domains such as upper half plane and upper right quarter plane and on multiply connected domains containing circular rings.Article Complex Partial Differential Equations(Springer, 2025-02) Aksoy, Ü.; Begehr, H.; Çelebi, A.; Shupeyeva, B.The Schwarz and iterated Dirichlet boundary-value problems are reported on for the polyanalytic operator in certain plane domains having a harmonic Green function. Hybrid polyharmonic Green functions are reviewed upon which open a variety of boundary-value problems for the polyharmonic operator. This topic is far from being complete. The higher the order of the polyharmonic operator the richer is the theory of related hybrid Green functions: they are constructed by continued convoluting harmonic Green, Neumann, Robin functions also incorporating polyharmonic Green–Almansi functions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.Article Citation - WoS: 11Citation - Scopus: 13A New Approach To the Existence and Uniqueness of Solutions for A Class of Nonlinear Q-Fractional Boundary Value Problems(Institute of Applied Mathematics of Baku State University, 2025) Karapinar, E.; Sevinik-Adiguzel, R.; Aksoy, U.; Erhan, I. M.; Sevinik Adıgüzel, RezanThe object of this study is a boundary value problem associated with a q-difference equation of fractional order. The existence and uniqueness of a solution in the case of multi-point boundary conditions is studied from the viewpoint of fixed point theory. An integral equation equivalent to the boundary value problem is derived and the fixed points of the related integral operator are investigated by using a contractive condition involving a comparison function. The Ulam-Hyers stability of the problem is also discussed. Theoretical results are followed by a particular example.Article Citation - WoS: 2Citation - Scopus: 3Optimal Limit Order Book Trading Strategies With Stochastic Volatility in the Underlying Asset(Springer, 2022-06-17) Aydogan, Burcu; Ugur, Omur; Aksoy, UmitIn quantitative finance, there have been numerous new aspects and developments related with the stochastic control and optimization problems which handle the controlled variables of performing the behavior of a dynamical system to achieve certain objectives. In this paper, we address the optimal trading strategies via price impact models using Heston stochastic volatility framework including jump processes either in price or in volatility of the price dynamics with the aim of maximizing expected return of the trader by controlling the inventories. Two types of utility functions are considered: quadratic and exponential. In both cases, the remaining inventories of the market maker are charged with a liquidation cost. In order to achieve the optimal quotes, we control the inventory risk and follow the influence of each parameter in the model to the best bid and ask prices. We show that the risk metrics including profit and loss distribution (PnL), standard deviation and Sharpe ratio play important roles for the trader to make decisions on the strategies. We apply finite differences and linear interpolation as well as extrapolation techniques to obtain a solution of the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. Moreover, we consider different cases on the modeling to carry out the numerical simulations.Article Citation - WoS: 2Citation - Scopus: 4Fixed Point Theorems for Mappings With a Contractive Iterate at a Point in Modular Metric Spaces(House Book Science-casa Cartii Stiinta, 2022-06-15) Karapinar, Erdal; Aksoy, Umit; Fulga, Andreea; Erhan, Inci M.In this manuscript, we introduce two new types of contraction, namely, w-contraction and strong Sehgal w-contraction, in the framework of modular metric spaces. We indicate that under certain assumptions, such mappings possess a unique fixed point. For the sake of completeness, we consider examples and an application to matrix equations.Article Citation - WoS: 3Citation - Scopus: 3Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions(Springer-verlag Italia Srl, 2021-06-28) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan SevinikThis study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.Article On a Boundary Value Problem for a Class of Second-Order Complex Partial Differential Equations(Univ Simon Bolivar, 2023) Aksoy, Umit; Celebi, Ahmet OkayIn this article, a boundary value problem for a second-order complex partial differential equation whose main part is the Laplacian, is introduced and its solvability is discussed by reduction of the problem into the Schwarz problem for a first-order equation. The condition for solvability is presented and an estimate for the unique solution is provided.Article Citation - WoS: 8Citation - Scopus: 9Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem Revisited(Taylor & Francis Ltd, 2020-02-24) Aksoy, Umit; Begehr, Heinrich; Celebi, A. OkayThe extension of the Schwarz representation formula to simply connected domains with harmonic Green function and its polyanalytic generalization is not valid in general. They do hold only for certain domains.Article Citation - WoS: 17Citation - Scopus: 18Weak Ψ-Contractions on Partially Ordered Metric Spaces and Applications To Boundary Value Problems(Springeropen, 2014-09-23) Karapinar, Erdal; Erhan, Inci M.; Aksoy, UmitA class of weak psi-contractions satisfying the C-condition is defined on metric spaces. The existence and uniqueness of fixed points of such maps are discussed both on metric spaces and on partially ordered metric spaces. The results are applied to a first order periodic boundary value problem.Conference Object Analysis of the Parameters That Effects the Operating Frequencies and Bandwidth of a Cpw-Fed Patch Antenna(Ieee, 2013) Dagdeviren, Birkan; Kapusuz, K. Yavuz; Can, Sultan; Aydin, ElifIn this study, the analysis of the effect of antenna parameters to the operating frequency is performed in a coplanar waveguide fed patch antenna. The effect of the size and the substrate of the design dual frequency antenna to the operating frequency and bandwidth are also evaluated. Bandwidth of the upper and lower frequency is also investigated and results are demonstrated. The method to increase the bandwidth is also presented by using the chosen parameters.