Ümit Aksoy

Aksoy, Ümit

Profile URL

https://hdl.handle.net/20.500.14411/6803

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

Job Title

Profesör Doktor

Email Address

umit.aksoy@atilim.edu.tr

Main Affiliation

Mathematics

Scopus Author ID

24402879000

Full item page

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Scholarly Output

43

Articles

34

Views / Downloads

74/59

Supervised MSc Theses

2

Supervised PhD Theses

0

WoS Citation Count

732

Scopus Citation Count

716

Patents

0

Projects

0

WoS Citations per Publication

17.02

Scopus Citations per Publication

16.65

Open Access Source

6

Supervised Theses

2

Journal	Count
Complex Variables and Elliptic Equations	6
Filomat	3
Applied and Computational Mathematics	2
Integral Transforms and Special Functions	2
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas	2

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Scopus Quartile Distribution

Competency Cloud

Scholarly Output Search Results

Now showing 1 - 10 of 15

Complex Partial Differential Equations
(Springer, 2025) 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.
Citation - WoS: 8
Citation - Scopus: 10
A 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, Rezan
The 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.
Citation - WoS: 2
Citation - Scopus: 2
Optimal Limit Order Book Trading Strategies With Stochastic Volatility in the Underlying Asset
(Springer, 2023) Aydogan, Burcu; Ugur, Omur; Aksoy, Umit
In 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.
Citation - WoS: 1
Citation - Scopus: 4
Fixed 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.
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.
Citation - WoS: 3
Citation - Scopus: 3
Uniqueness 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.; Adiguzel, Rezan Sevinik
This 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.
On a Boundary Value Problem for a Class of Second-Order Complex Partial Differential Equations
(Univ Simon Bolivar, 2023) Aksoy, Umit; Celebi, Ahmet Okay
In 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.
Citation - WoS: 8
Citation - Scopus: 9
Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem Revisited
(Taylor & Francis Ltd, 2021) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay
The 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.
Citation - WoS: 2
Citation - Scopus: 2
A Normal Distribution on Time Scales With Application
(Univ Nis, Fac Sci Math, 2022) Aksoy, Umit; Cuchta, Tom; Georgiev, Svetlin; Okur, Yeliz Yolcu
We 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.
Citation - WoS: 3
Citation - Scopus: 4
On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation
(Taylor & Francis Ltd, 2021) Aksoy, Umit; Erhan, Inci M.; Fulga, Andreea; Karapinar, Erdal
In 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.
Citation - WoS: 201
Citation - Scopus: 181
On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation
(Wiley, 2020) Sevinik Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan Sevinik
The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2