Hikmet Koyunbakan - Academia.edu (original) (raw)

Papers by Hikmet Koyunbakan

Journal of Advances in Applied & Computational Mathematics

This paper aims to express the solution of an inverse Sturm-Liouville problem with constant delay... more This paper aims to express the solution of an inverse Sturm-Liouville problem with constant delay using a conformable derivative operator under mixed boundary conditions. For the problem, we stated and proved the specification of the spectrum. The asymptotics of the eigenvalues of the problem was obtained and the solutions were extended to the Regge-type boundary value problem. As such, a new result, as an extension of the classical Sturm-Liouville problem to the fractional phenomenon, has been achieved. The uniqueness theorem for the solution of the inverse problem is proved in different cases within the interval (0,π). The results in the classical case of this problem can be obtained at α=1. 2000 Mathematics Subject Classification. 34L20,34B24,34L30.

Qualitative Theory of Dynamical Systems

Numerical Functional Analysis and Optimization

Abstract In this work, we study an inverse nodal problem for a differential pencil with boundary ... more Abstract In this work, we study an inverse nodal problem for a differential pencil with boundary condition depends on eigenparameter. We show that there exists a solution of the problem that satisfied the conditions. Also, we give eigenvalues, nodal points and some formulas for Although there were given some results for this type problem, we think that inverse nodal problems have not solved yet.

Communications in Statistics - Theory and Methods, 2021

In this short note we analyze the asymptotics of eigenvalues, and Ambarzumyan type theorem for en... more In this short note we analyze the asymptotics of eigenvalues, and Ambarzumyan type theorem for energy dependent potential problem with boundary condition including spectral parameter. We should mention that results are more general then the results given in [18].

International Journal of Analysis and Applications, 2017

We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical con... more We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical convergence on an arbitrary time scale. Moreover, (θ,m)-uniform strongly p-lacunary summability and some inclusion relations about these new concepts are also presented.

Inverse nodal problem on the string operator is the finding the density function using nodal sequ... more Inverse nodal problem on the string operator is the finding the density function using nodal sequence {z (n) k }. In this paper, we solve a stability problem using nodal set of eigenfunctions and show that the space of high order density functions is homeomorphic to the partition set of the space of quasinodal sequences. Basically, this method is similar to (2) and (6) which is given for Sturm-Liouville and Hill operators, respectively. Keywords. String equation, Inverse nodal problem, Lipschitz stability. AMS (MOS) subject classication: 34A55, 34L05, 34L20, 34D20

Applied Mathematics and Computation, 2005

In this study, a kind of explicit exact and numerical solutions to the Lienard equation is obtain... more In this study, a kind of explicit exact and numerical solutions to the Lienard equation is obtained, and the applications of the results to this equation has been compared with their known theoretical solution. This paper is particularly concerned with the Adomian decomposition method and the numerical results demonstrate that the new method is relatively accurate and easily implemented.

Applicable Analysis, 2005

In this article, we solve a problem obtained by the transformation operator using the decompositi... more In this article, we solve a problem obtained by the transformation operator using the decomposition method. We give the components of K(x, t) nucleus function and their numerical results, partially, when q(x) potential function is a special function (hydrogen atom and solution of the KdV equation …).

Proceedings of the Bulgarian Academy of Sciences

We consider an inverse nodal problem for p-Laplacian string equation under some boundary conditio... more We consider an inverse nodal problem for p-Laplacian string equation under some boundary conditions. Asymptotic formulas for eigenvalues and nodal parameters are constructed by modified Pr¨ufer substitution. The most important process is to apply modified Pr¨ufer substitution to get an exhaustive asymptotic estimate for eigenvalues. Moreover, a reconstruction formula for density function of p-aplacian string equation is obtained by nodal parameters. Generated outcomes are the generalization of the known string problem.

Inverse problem for Schrodinger operator consists of reconstruction potential function of this op... more Inverse problem for Schrodinger operator consists of reconstruction potential function of this operator by its spectrum and norming constants. In this study, we solve an inverse problem for Schrodinger operator using the nodal set of eigenfunctions. We prove the uniqueness theorem and give a reconstruction formula for the potential function. The technique that we use to obtain the results is an adaptation of the method discussed in the references [1], [2].

birkaç terimin tamçözümlertam¸tamçözümler elde etmek için yeterli oldu˘ gunu göstermi¸göstermi¸st... more birkaç terimin tamçözümlertam¸tamçözümler elde etmek için yeterli oldu˘ gunu göstermi¸göstermi¸stir. Anahtar Kelimeler. Difüzyon operatorü, Adomian ayrı¸sımayrı¸sım metodu, He'nin varyasyonel iterasyon metodu. Abstract. In this study, we obtain approximate solutions for diffusion equation on a finite interval by the Adomian decomposition method (ADM) and variational iteration method (VIM) for three cases and then the numerical results are compared. These results show that the ADM leads to more accurate results, and they indicate that only a few terms are sufficient to obtain accurate solutions.

In this study, we will define λ−density of a set and λ−statistical convergence on an arbitrary ti... more In this study, we will define λ−density of a set and λ−statistical convergence on an arbitrary time scale. Moreover, some relations about these new notions are also obtained. AMS (MOS) subject classification: 40A05, 40C05, 46A45, 34A40, 39A13

We consider a quadratic Sturm-Liouville problem. In this paper, some uniqueness theorems are exte... more We consider a quadratic Sturm-Liouville problem. In this paper, some uniqueness theorems are extended to the case in which the governing second-order ordinary differential equation contains both ) (x q and ) (x p instead of only ) (x q . It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the functions ) (x q and ) (x p are zero.

Qualitative Theory of Dynamical Systems

In this study, we obtain approximate solutions for diusion equation on a nite interval by the Ado... more In this study, we obtain approximate solutions for diusion equation on a nite interval by the Adomian decomposition method (ADM) and variational iteration method (VIM) for three cases and then the numerical results are compared. These results show that the ADM leads to more accurate results, and they indicate that only a few terms are sucient to obtain accurate solutions.

Ambarzumyan's theorem for quadratic pencil of Schrodinger problem is extended to second order... more Ambarzumyan's theorem for quadratic pencil of Schrodinger problem is extended to second order differential systems of dimension . It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the matrix valued functions both and are zero by imposing a condition on . In scaler case, this problem was solved in [1].

In this article, we extend solution of inverse nodal problem for one-dimensional p-Laplacian equa... more In this article, we extend solution of inverse nodal problem for one-dimensional p-Laplacian equation to the case when the boundary condition is polynomially eigenparameter. To find the spectral data as eigenvalues and nodal parameters, a Prüfer substitution is used. Then, we give a reconstruction formula of the potential function by using nodal lengths. This method is similar to used in [24], and our results are more general.

The inverse nodal problem for Sturm-Liouville operator with a constant delay has been investigate... more The inverse nodal problem for Sturm-Liouville operator with a constant delay has been investigated in the present paper. To do so, we have computed the nodal points and nodal lengths. Therefore, we have tried Chebyshev interpolation method to obtain the numerical solution of inverse nodal problem. Following that, a number of numerical examples have been given. The numerical calculations in the present paper have been conducted via pc applying some programs encoded in Matlab software.

Journal of Advances in Applied & Computational Mathematics

This paper aims to express the solution of an inverse Sturm-Liouville problem with constant delay... more This paper aims to express the solution of an inverse Sturm-Liouville problem with constant delay using a conformable derivative operator under mixed boundary conditions. For the problem, we stated and proved the specification of the spectrum. The asymptotics of the eigenvalues of the problem was obtained and the solutions were extended to the Regge-type boundary value problem. As such, a new result, as an extension of the classical Sturm-Liouville problem to the fractional phenomenon, has been achieved. The uniqueness theorem for the solution of the inverse problem is proved in different cases within the interval (0,π). The results in the classical case of this problem can be obtained at α=1. 2000 Mathematics Subject Classification. 34L20,34B24,34L30.

Qualitative Theory of Dynamical Systems

Numerical Functional Analysis and Optimization

Abstract In this work, we study an inverse nodal problem for a differential pencil with boundary ... more Abstract In this work, we study an inverse nodal problem for a differential pencil with boundary condition depends on eigenparameter. We show that there exists a solution of the problem that satisfied the conditions. Also, we give eigenvalues, nodal points and some formulas for Although there were given some results for this type problem, we think that inverse nodal problems have not solved yet.

Communications in Statistics - Theory and Methods, 2021

In this short note we analyze the asymptotics of eigenvalues, and Ambarzumyan type theorem for en... more In this short note we analyze the asymptotics of eigenvalues, and Ambarzumyan type theorem for energy dependent potential problem with boundary condition including spectral parameter. We should mention that results are more general then the results given in [18].

International Journal of Analysis and Applications, 2017

We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical con... more We introduce (θ,m)-uniform lacunary density of any set and (θ,m)-uniform lacunary statistical convergence on an arbitrary time scale. Moreover, (θ,m)-uniform strongly p-lacunary summability and some inclusion relations about these new concepts are also presented.

Inverse nodal problem on the string operator is the finding the density function using nodal sequ... more Inverse nodal problem on the string operator is the finding the density function using nodal sequence {z (n) k }. In this paper, we solve a stability problem using nodal set of eigenfunctions and show that the space of high order density functions is homeomorphic to the partition set of the space of quasinodal sequences. Basically, this method is similar to (2) and (6) which is given for Sturm-Liouville and Hill operators, respectively. Keywords. String equation, Inverse nodal problem, Lipschitz stability. AMS (MOS) subject classication: 34A55, 34L05, 34L20, 34D20

Applied Mathematics and Computation, 2005

In this study, a kind of explicit exact and numerical solutions to the Lienard equation is obtain... more In this study, a kind of explicit exact and numerical solutions to the Lienard equation is obtained, and the applications of the results to this equation has been compared with their known theoretical solution. This paper is particularly concerned with the Adomian decomposition method and the numerical results demonstrate that the new method is relatively accurate and easily implemented.

Applicable Analysis, 2005

In this article, we solve a problem obtained by the transformation operator using the decompositi... more In this article, we solve a problem obtained by the transformation operator using the decomposition method. We give the components of K(x, t) nucleus function and their numerical results, partially, when q(x) potential function is a special function (hydrogen atom and solution of the KdV equation …).

Proceedings of the Bulgarian Academy of Sciences

We consider an inverse nodal problem for p-Laplacian string equation under some boundary conditio... more We consider an inverse nodal problem for p-Laplacian string equation under some boundary conditions. Asymptotic formulas for eigenvalues and nodal parameters are constructed by modified Pr¨ufer substitution. The most important process is to apply modified Pr¨ufer substitution to get an exhaustive asymptotic estimate for eigenvalues. Moreover, a reconstruction formula for density function of p-aplacian string equation is obtained by nodal parameters. Generated outcomes are the generalization of the known string problem.

Inverse problem for Schrodinger operator consists of reconstruction potential function of this op... more Inverse problem for Schrodinger operator consists of reconstruction potential function of this operator by its spectrum and norming constants. In this study, we solve an inverse problem for Schrodinger operator using the nodal set of eigenfunctions. We prove the uniqueness theorem and give a reconstruction formula for the potential function. The technique that we use to obtain the results is an adaptation of the method discussed in the references [1], [2].

birkaç terimin tamçözümlertam¸tamçözümler elde etmek için yeterli oldu˘ gunu göstermi¸göstermi¸st... more birkaç terimin tamçözümlertam¸tamçözümler elde etmek için yeterli oldu˘ gunu göstermi¸göstermi¸stir. Anahtar Kelimeler. Difüzyon operatorü, Adomian ayrı¸sımayrı¸sım metodu, He'nin varyasyonel iterasyon metodu. Abstract. In this study, we obtain approximate solutions for diffusion equation on a finite interval by the Adomian decomposition method (ADM) and variational iteration method (VIM) for three cases and then the numerical results are compared. These results show that the ADM leads to more accurate results, and they indicate that only a few terms are sufficient to obtain accurate solutions.

In this study, we will define λ−density of a set and λ−statistical convergence on an arbitrary ti... more In this study, we will define λ−density of a set and λ−statistical convergence on an arbitrary time scale. Moreover, some relations about these new notions are also obtained. AMS (MOS) subject classification: 40A05, 40C05, 46A45, 34A40, 39A13

We consider a quadratic Sturm-Liouville problem. In this paper, some uniqueness theorems are exte... more We consider a quadratic Sturm-Liouville problem. In this paper, some uniqueness theorems are extended to the case in which the governing second-order ordinary differential equation contains both ) (x q and ) (x p instead of only ) (x q . It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the functions ) (x q and ) (x p are zero.

Qualitative Theory of Dynamical Systems

In this study, we obtain approximate solutions for diusion equation on a nite interval by the Ado... more In this study, we obtain approximate solutions for diusion equation on a nite interval by the Adomian decomposition method (ADM) and variational iteration method (VIM) for three cases and then the numerical results are compared. These results show that the ADM leads to more accurate results, and they indicate that only a few terms are sucient to obtain accurate solutions.

Ambarzumyan's theorem for quadratic pencil of Schrodinger problem is extended to second order... more Ambarzumyan's theorem for quadratic pencil of Schrodinger problem is extended to second order differential systems of dimension . It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the matrix valued functions both and are zero by imposing a condition on . In scaler case, this problem was solved in [1].

In this article, we extend solution of inverse nodal problem for one-dimensional p-Laplacian equa... more In this article, we extend solution of inverse nodal problem for one-dimensional p-Laplacian equation to the case when the boundary condition is polynomially eigenparameter. To find the spectral data as eigenvalues and nodal parameters, a Prüfer substitution is used. Then, we give a reconstruction formula of the potential function by using nodal lengths. This method is similar to used in [24], and our results are more general.

The inverse nodal problem for Sturm-Liouville operator with a constant delay has been investigate... more The inverse nodal problem for Sturm-Liouville operator with a constant delay has been investigated in the present paper. To do so, we have computed the nodal points and nodal lengths. Therefore, we have tried Chebyshev interpolation method to obtain the numerical solution of inverse nodal problem. Following that, a number of numerical examples have been given. The numerical calculations in the present paper have been conducted via pc applying some programs encoded in Matlab software.