Browsing by Author "Aksoy, Umit"

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Citation - WoS: 10
Citation - Scopus: 10
Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem
(Taylor & Francis Ltd, 2019) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
According 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.
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; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
Dirichlet-Type Problems for n-poisson Equation in Clifford Analysis
(Taylor & Francis Ltd, 2022) Aksoy, Umit; Celebi, A. Okay; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Iterated 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.
Citation - WoS: 49
Citation - Scopus: 56
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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 3
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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 25
Citation - Scopus: 32
Fixed Point Theorems in Complete Modular Metric Spaces and an Application To Anti-Periodic Boundary Value Problems
(Univ Nis, Fac Sci Math, 2017) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Caratheodory's type is considered in the framework of modular metric spaces.
Citation - WoS: 68
FIXED 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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
A 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.
Citation - WoS: 27
Citation - Scopus: 29
Meir-Keeler Type Contractions on Modular Metric Spaces
(Univ Nis, Fac Sci Math, 2018) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Rakocevic, Vladimir; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
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; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
On a Boundary Value Problem for a Class of Second-Order Complex Partial Differential Equations
(Univ Simon Bolivar, 2023) Aksoy, Umit; Celebi, Ahmet Okay; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 3
Citation - Scopus: 3
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; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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: 1
Citation - Scopus: 1
On the Methods of Pricing American Options: Case Study
(Springer, 2018) Aydogan, Burcu; Aksoy, Umit; Ugur, Omur; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In 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.
Citation - WoS: 191
Citation - Scopus: 148
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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2
Citation - WoS: 143
Citation - Scopus: 155
On 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; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
The 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.
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; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
Polynomial Logistic Distribution Associated With a Cubic Polynomial
(Taylor & Francis inc, 2017) Aksoy, Umit; Ostrovska, Sofiya; Ozban, Ahmet Yasar; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Let P(x) be a polynomial monotone increasing on ( - , +). The probability distribution possessing the distribution function is called the polynomial logistic distribution with associated polynomial P. This has recently been introduced by Koutras etal., who have also demonstrated its importance for modeling financial data. In this article, the properties of the polynomial logistic distribution with an associated polynomial of degree 3 have been investigated in detail. An example of polynomial logistic distribution describing daily exchange rate fluctuations for the US dollar versus the Turkish lira is provided.
Citation - WoS: 10
Citation - Scopus: 13
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; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.
Several Outcomes of Fixed-Point Theory in Interpolative Metric Spaces
(Univ Politecnica Valencia, Editorial UPV, 2025) Karapinar, Erdal; Kadioglu, Kaan; Turkmenel, Merve Gulcin; Aksoy, Umit; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
This paper aims to generalize and improve the recent fixed-point theorems in the setting of interpolative metric spaces. More precisely, we investigate the existence and uniqueness of the fixed-point for certain operators of the Ciric-Reich-Rus-type, via admissible mapping in the context of interpolative metric spaces.
Special Issue: in Honour of Professor A. Okay Celebi on the Occasion of His 70th Birthday Preface
(Taylor & Francis Ltd, 2013) Aksoy, Umit; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
[No Abstract Available]
Citation - WoS: 134
Citation - Scopus: 140
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.; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
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.