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

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Sustainable Development Goals

SDG data is not available

This researcher does not have a Scopus ID.

This researcher does not have a WoS ID.

Scholarly Output

42

Articles

33

Views / Downloads

236/317

Supervised MSc Theses

2

Supervised PhD Theses

0

WoS Citation Count

790

Scopus Citation Count

866

Patents

0

Projects

0

WoS Citations per Publication

18.81

Scopus Citations per Publication

20.62

Open Access Source

6

Supervised Theses

2

Journal	Count
Complex Variables and Elliptic Equations	6
Filomat	3
Integral Transforms and Special Functions	2
Applied and Computational Mathematics	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 42

Weak Ψ -Contractions on Partially Ordered Metric Spaces and Applications To Boundary Value Problems
(2015) Aksoy, Ümit
Recent developments in fixed point theory have been encouraged by the applicability of the results in the area of boundary value problems for differential and integral equations. Especially in the last few years, a lot of publications in fixed point theory have presented results directly related to specific initial or boundary value problems. These problems include not only ordinary and partial differential equations, but also fractional differential equations.
Norm Estimates of a Class of Calderon–zygmund Type Strongly Singular Integral Operators
(Integral Transforms and Special Functions, 2007) Aksoy, Ümit; Çelebi, Okay
In 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.
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: 52
Citation - Scopus: 62
F-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.
In 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.
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: 144
Citation - Scopus: 156
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 - Scopus: 6
Mixed Boundary Value Problems for Higher-Order Complex Partial Differential Equations
(Univ Simon Bolivar, 2010) Aksoy,U.; Okay Ĉedil,; elebi,A.; Celebi, Ahmet Okay; Ĉedil, Okay
In this paper, we introduce the operators related to mixed boundary value problems for general linear elliptic partial complex differential equations in the unit disc of the complex plane. The solvability of the relevant boundary value problems will be studied by transforming them into singular integral equations. © 2010, by Oldenbourg Wissenschaftsverlag, München, Germany. All rights reserved.
Citation - WoS: 12
Citation - Scopus: 15
Schwarz Problem for Higher-Order Complex Partial Differential Equations in the Upper Half Plane
(Wiley-v C H verlag Gmbh, 2019) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay
Linear and nonlinear elliptic complex partial differential equations of higher-order are considered under Schwarz conditions in the upper-half plane, Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schvvarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro-differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively.
Citation - Scopus: 18
Dirichlet Problems for the Generalized N-Poisson Equation
(Springer International Publishing, 2010) Aksoy,Ü.; Çelebi,A.O.
Polyharmonic hybrid Green functions, obtained by convoluting polyharmonic Green and Almansi Green functions, are taken as kernels to define a hierarchy of integral operators. They are used to investigate the solvability of some types of Dirichlet problems for linear complex partial differential equations with leading term as the polyharmonic operator. © 2009 Birkhäuser Verlag Basel/Switzerland.