Browsing by Author "Akin, Lutfi"

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A Characterization of Approximation of Hardy Operators in VLS
(2018) Akin, Lutfi; 04.02. Department of Management / İşletme Bölümü; 04. Faculty of Economics and Administrative Sciences / İktisadi ve İdari Bilimler Fakültesi; 01. Mardin Artuklu University / Mardin Artuklu Üniversitesi
Variable exponent spaces and Hardy operator space have played an important role in recent harmonic analysis because they have an interesting norm including both local and global properties. The variable exponent Lebesgue spaces are of interest for their applications to modeling problems in physics, and to the study of variational integrals and partial diﬀerentialequations with non-standard growth conditions. This studies also has been stimulated by problems of elasticity, fluid dynamics, calculus of variations, and differential equations with non-standard growth conditions. In this study, we will discuss a characterization of approximation of Hardy operators in variable Lebesgue spaces.
Citation - WoS: 1
A Characterization of Boundedness of Fractional Maximal Operator with Variable Kernel on Herz-Morrey Spaces
(Global Science Press, 2020) Akin, Lutfi
A significant number of studies have been carried out on the generalized Lebesgue spaces L-p(x), Sobolev spaces W-1,W- p(x) and Herz spaces. In this paper, we demonstrated a characterization of boundedness of the fractional maximal operator with variable kernel on Herz-Morrey spaces.
Citation - WoS: 1
Citation - Scopus: 1
A Characterization of Some Class Nonlinear Eigenvalue Problem in VELS
(Hindawi Ltd, 2019) Akin, Lutfi
A normal mode analysis of a vibrating mechanical or electrical system gives rise to an eigenvalue problem. Faber made a fairly complete study of the existence and asymptotic behavior of eigenvalues and eigenfunctions, Green's function, and expansion properties. We will investigate a new characterization of some class nonlinear eigenvalue problem.
A Characterization of Some Class Nonlinear Eigenvalue Problem in Vels
(2019) Akin, Lutfi; 04.02. Department of Management / İşletme Bölümü; 04. Faculty of Economics and Administrative Sciences / İktisadi ve İdari Bilimler Fakültesi; 01. Mardin Artuklu University / Mardin Artuklu Üniversitesi
In last the quarter century, many researchers have been interested by the theory of the variable exponent functionspace and its applications. We well-know that a normal mode analysis of a vibrating mechanical or electrical systemgives rise to an eigenvalue problem. We will investigate a characterization of some class nonlinear eigenvalueproblem in variable exponent Lebesgue spaces.
Citation - WoS: 8
Citation - Scopus: 8
A New Approach for the Fractional Integral Operator in Time Scales With Variable Exponent Lebesgue Spaces
(MDPI, 2021) Akin, Lutfi
Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond-alpha integral operator M-a,delta(c) to the norm of the centered fractional maximal diamond-alpha integral operator M-a(c) on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales.
Citation - WoS: 8
A New Approach for Weighted Hardy's Operator in VLS
(Walter de Gruyter GmbH, 2019) Akin, Lutfi; Dusunceli, Faruk
A considerable number of research has been carried out on the generalized Lebesgue spaces L-p(x) and boundedness of different integral operators therein. In this study, a new approach for weighted increasing near the origin and decreasing near infinity exponent function that provides a boundedness of the Hardy's operator in variable exponent space is given.
On Innovative Conditions for Weighted Hardy-Type Inequalities on Time Scales
(Wiley, 2025) Akin, Lutfi; Dinc, Yavuz
This article presents necessary and sufficient conditions for novel characterizations of weighted Hardy-type inequalities applying the chain rule, Minkowski's inequality, and H & ouml;lder's inequality with nabla calculus on time scales. Properties of time scales and Okpoti inequality are exploited to derive our results. These results differ from classical weighted Hardy-type inequalities because they are examined on time scales that combine discrete and continuous cases.
Citation - WoS: 10
Citation - Scopus: 11
On the Fractional Maximal Delta Integral Type Inequalities on Time Scales
(MDPI, 2020) Akin, Lutfi
Time scales have been the target of work of many mathematicians for more than a quarter century. Some of these studies are of inequalities and dynamic integrals. Inequalities and fractional maximal integrals have an important place in these studies. For example, inequalities and integrals contributed to the solution of many problems in various branches of science. In this paper, we will use fractional maximal integrals to establish integral inequalities on time scales. Moreover, our findings show that inequality is valid for discrete and continuous conditions.
Citation - WoS: 3
Citation - Scopus: 3
Some Properties for Higher Order Commutators of Hardy-Type Integral Operator on Herz-Morrey Spaces With Variable Exponent
(Yildiz Technical Univ, 2019) Akin, Lutfi; Akın, Lütfi; Zeren, Yusuf; 04.02. Department of Management / İşletme Bölümü; 04. Faculty of Economics and Administrative Sciences / İktisadi ve İdari Bilimler Fakültesi; 01. Mardin Artuklu University / Mardin Artuklu Üniversitesi
In this work, the boundedness for higher order commutators of Hardy-Type integrals is obtained on HerzMorrey spaces with variable exponent M(K)over dot(p,q(.))(beta(.)lambda) (R-n) applying some properties of variable exponent.