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Öğe AĞIRLIKLI VE DEĞİŞKEN ÜSLÜ LEBESGUE UZAYINDA HARDY OPERATÖRÜNÜN KOMPAKTLIĞI(2014-06-24) AKIN, Lutfi…Öğe Approximation To Generalized Taylor Derivatives By Integral Operator Families(MSU J. of Sci, 2017-12-15) AKIN, Lutfi; Zeren, YusufThis theory has important applications of polynomial approximation in various areas of functional analysis, Fourier analysis, application mathematic, operator theory, in the field generalized derivatives and numerical solutions of differential and integral equations, etc. The study of approximation theory is a well-established area of research which deals with the problem of approximating a function f by means of a sequence n L of positive linear operators. This theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.Öğe A Characterization of Approximation of Hardy Operators in VLS(Celal Bayar University Journal of Science, 2018) AKIN, LutfiVariable 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 differential equations 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.Öğe A Characterization of Some Class Nonlinear Eigenvalue Problem in VELS(Sakarya University Journal of Science, 2019-08-01) AKIN, LutfiIn last the quarter century, many researchers have been interested by the theory of the variable exponent function space and its applications. We well-know that a normal mode analysis of a vibrating mechanical or electrical system gives rise to an eigenvalue problem. We will investigate a characterization of some class nonlinear eigenvalue problem in variable exponent Lebesgue spaces.Öğe COMPACTIFICATION OF WEIGHTED HARDY OPERATOR IN VARIABLE EXPONENT LEBESGUES SPACES(Asian Journal of Mathematics and Computer Research, 2017-03-24) Mamedov, Ferman; Zeren, Yusuf; AKIN, LutfiWe study necessity and sufficiency conditions for the weighted Hardy operator x v w H f x v x f t w t dt 0 , ( ) ( ) ( ) ( ) to be compact from Lp(.) (0, l) to Lq(.) (0,l) .Öğe Compactness of Fractional Maximal Operator in Weighted and Variable Exponent Spaces(Erzincan University Journal of Science and Technology, 2019-05-24) AKIN, LutfiWe have studied necessary and sufficienty conditions for the weighted fractional maximal operator to be compactness from ) , 0( (.) l Lp to ) , 0( (.) l Lq .Öğe Öğe Matematik Diyarında Bir Mola(ALTIN NOKTA BASIM YAYIN DAĞITIM BİLİŞİM, 2017-09-27) AKIN, LutfiÇocuklarına matematiği sevdirmek çoğu aile için son derece zorlu bir süreçtir. Bu aslında oldukça doğaldır ki matematik, çok fazla beyin gücü gerektiren bir yetenektir. Bu durum çocuklar tarafından zor bir iş olarak algılanabilir. Ama her şeyde olduğu gibi matematik öğreniminde de ilk ilke “sevmek”tir. Chicago ve Western Üniversiteleri tarafından 2012’de yapılan bir araştırma matematikle çok fazla uğraşan kişilerin fiziksel acı-ya benzer bir acı yaşadıklarını gösteriyor. Aileler de çocukken formüller-le, sembollerle ve denklemlerle yaşadıkları zorlukları iyi bildikleri için genellikle çocuklarına matematiğin zor olduğunu söylemeye meyilli oluyorlar. Aslında en büyük hata bu noktada yapılmış oluyor. Sonuç olarak matematiğin zor olduğu düşüncesi, çocukların aklına yerleşir ve onlar da matematiği akademik hayatlarında karşılaşmak zorunda kala-cakları korkunç bir canavar olarak görürlerÖğe On a New Approximation for Weighted Integral-Type Inequalities in V ELS(Gece Publishing ABD Adres/ USA Address: 387 Park Avenue South, 5th Floor, New York, 10016, USA Telefon/Phone: +1 347 355 10 70, 2019-03-15) AKIN, LutfiThe variable exponent Lebesgue spaces are of interest for their applications to modeling problems in physics and to the study of variational integrals and partial differential equations with non-standard growth conditions. We refer to [1-7]. This studies also has been stimulated by problems of elasticity, fluid dynamics, calculus of variations and differential equations with non-standard growth conditions. More results for Hardy-type inequalities in variable exponent Lebesgue spaces can be found in F. I. Mamedov et al., [9]; L. Akın [10, 11]; A. Kufner and L. E. Persson [14]; V. Kokilashvili and S. Samko [15] and references thereinÖğe On a New Characterization of Some Class Nonlinear Eigenvalue Problem(Advances in Mathematical Physics, 2019-02-07) AKIN, LutfiA 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.Öğe On Some Properties of Hardy- Littlewood Maximal Operators on Hardy Spaces Built upon BFS(Gece Publishing ABD Adres/ USA Address: 387 Park Avenue South, 5th Floor, New York, 10016, USA Telefon/Phone: +1 347 355 10 70, 2019-03-15) AKIN, LutfiOperator theory studied by very mathematicians, we refer to [1,2,3,4,5]. Compactification of weighted Hardy operator in variable exponent Lebesgue spaces has been proof by [6]. Generalized duality of some Banach function spaces has been proof by [7]. On two weight criterions for the Hardy-Littlewood maximal operator in BFS has been proven, we refer to [8]. A Characterization of Approximation of Hardy Operators in VLS has been proven by [9]. We know that it is established an integraltype necessary and sufficient condition on weights which provides the boundedness of the Hardy-Littlewood maximal operator from weighted Lebesgue spaces into p-convex weighted BFS, we refer to [11].Öğe ON TWO WEIGHT CRITERIONS FOR THE HARDY LITTLEWOOD MAXIMAL OPERATOR IN BFS(Asian Journal of Science and Technology, 2018-05-30) AKIN, LutfiOur aim of this paper is to prove two-weight criterions for the Hardy-Littlewood maximal operator from weighted Lebesgue spaces into Banach function spaces (BFS). We used boundedness of geometric mean operator and sufficient condition on the weights for boundedness of certain sublinear operator from weighted Lebesgue spaces into weighted Musielak-Orlicz spacesÖğe A Research Approximation to Generalized Riemann Derivatives by Integral Operator Families(Mathematics and Computer Science, 2018-01-19) AKIN, LutfiApproximation theory has very important applications of polynomial approximation in various areas of functional analysis, Harmonic analysis, Fourier analysis, application mathematic, operator theory in the field generalized derivatives and numerical solutions of differential and integral equations, etc. Integral operators is very important in Harmonic and Fourier analysis. The study of approximation theory is a well-established area of research which deals with the problem of approximating a function f by means of a sequence n L of positive linear operators. Generalized derivatives (Riemann, Peano and Taylor derivative) are more general than ordinary derivative. Approximation theory is very important for mathematical world. Nowadays, many mathematicians are working in this field.Öğe Some Weighted Martingale Inequalities on Rearrangement Invariant Quasi-Banach Function Spaces(MSU J. of Sci.,, 2017-12-15) AKIN, LutfiThe Burkholder-Davis-Gundy’s inequalities and the sharp maximal function inequalities for martingale inequalities are established for rearrangement invariant quasi-Banach function spaces. Martingale inequalities very important in mathematic Martingale inequalities are worked by very mathematicians. We will establish some weighted Martingale inequalities for rearrangement invariant quasi-Banach function spaces
