Aksoy, Ümit
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Aksoy, Ue
Job Title
Profesör Doktor
Email Address
umit.aksoy@atilim.edu.tr
Main Affiliation
Mathematics
Status
Website
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
40
Articles
31
Citation Count
445
Supervised Theses
2
12 results
Scholarly Output Search Results
Now showing 1 - 10 of 12
Article Citation - WoS: 0Citation - Scopus: 0Dirichlet-Type Problems for n-poisson Equation in Clifford Analysis(Taylor & Francis Ltd, 2022) Aksoy, Umit; Celebi, A. Okay; MathematicsIterated Dirichlet problem, also called as Riquier or Navier problem, and polyharmonic Dirichlet problem are studied for n-Poisson equation in Clifford analysis using iterated polyharmonic Green function and polyharmonic Green-Almansi type function appropriate for the boundary conditions of the problems.Article Citation - WoS: 1Citation - Scopus: 2Optimal Limit Order Book Trading Strategies With Stochastic Volatility in the Underlying Asset(Springer, 2023) Aydogan, Burcu; Ugur, Omur; Aksoy, Umit; MathematicsIn 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: 45Citation - Scopus: 47F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales(Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MathematicsIn this paper we investigate the existence and uniqueness of fixed points of certain (phi,F)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results.Article Citation - WoS: 1Citation - Scopus: 2Fixed Point Theorems for Mappings With a Contractive Iterate at a Point in Modular Metric Spaces(House Book Science-casa Cartii Stiinta, 2022) Karapinar, Erdal; Aksoy, Umit; Fulga, Andreea; Erhan, Inci M.; MathematicsIn 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: 118Citation - Scopus: 126Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions(Springer-verlag Italia Srl, 2021) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MathematicsThis 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 Citation - Scopus: 0On a boundary value problem for a class of second-order complex partial differential equations(Universidad Simon Bolivar, 2023) Aksoy,Ü.; Çelebi,A.O.; MathematicsIn 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. © 2023, Universidad Simon Bolivar. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1A Normal Distribution on Time Scales With Application(Univ Nis, Fac Sci Math, 2022) Aksoy, Umit; Cuchta, Tom; Georgiev, Svetlin; Okur, Yeliz Yolcu; MathematicsWe introduce a new normal distribution on time scales. Based on this generalized normal distribution, a Brownian motion is introduced and its quadratic variation is derived.Article Citation - WoS: 3Citation - Scopus: 2On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation(Taylor & Francis Ltd, 2021) Aksoy, Umit; Erhan, Inci M.; Fulga, Andreea; Karapinar, Erdal; MathematicsIn this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.Article Citation - WoS: 7Citation - Scopus: 7Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem Revisited(Taylor & Francis Ltd, 2021) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay; MathematicsThe 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: 129Citation - Scopus: 142On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; Mathematics; 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.
