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Papers by Hüseyin Yildirim
International Journal of Pure and Applied Mathematics
Page 1. International Journal of Pure and Applied Mathematics Volume 31 No. 3 2006, 337-343... more Page 1. International Journal of Pure and Applied Mathematics Volume 31 No. 3 2006, 337-343 NORM INEQUALITIES WITH NON-ISOTROPIC KERNELS Mehmet Zeki ...
... MEHMET ZEKI SARIKAYA AND HÜSEYIN YILDIRIM Abstract. ... Riesz potential, shift operator and M... more ... MEHMET ZEKI SARIKAYA AND HÜSEYIN YILDIRIM Abstract. ... Riesz potential, shift operator and Morrey space. Page 2. 208 MEHMET ZEKI SARIKAYA AND HÜSEYIN YILDIRIM Denote by Ty the generalized shift operator acting according to the law Ty x F(x) = Cv ∫ π 0 ... ∫ π ...
Journal of Inequalities in Pure and Applied Mathematics
ÖZET Wegener granülomatözü (WG), üst ve alt solunum yolları ile böbreği tutabilen, çok sistem tut... more ÖZET Wegener granülomatözü (WG), üst ve alt solunum yolları ile böbreği tutabilen, çok sistem tutulumlu granülomatöz vaskülitis ile karakterize bir hastalıktır. Tanı konulması geciktiğinde mortal seyreden bir hastalık olan WG'nin, kliniğimize değişik ön tanılarla ...
TAIWANESE JOURNAL OF MATHEMATICS
In this paper, the inequality of Hardy-Littlewood-Sobolev type is established for the generalized... more In this paper, the inequality of Hardy-Littlewood-Sobolev type is established for the generalized Riesz potentials generated by the generalized shift operator with the functions in Sobolev spaces W m p,v (R + n).
International Journal of Applied Mathematics and Statistics
In this study, we obtain a new proofs of some Hardy-type in-equalities associated with generalize... more In this study, we obtain a new proofs of some Hardy-type in-equalities associated with generalized translation.
We study the solution of the equation □ B,c 1 k □ B,c 2 k u(x)=δ, where u(x) is an unknown functi... more We study the solution of the equation □ B,c 1 k □ B,c 2 k u(x)=δ, where u(x) is an unknown function and δ is a Dirac-delta function, □ B,c 1 k and □ B,c 2 k are the ultra-hyperbolic Bessel operator iterated k-times and are defined by □ B,c 1 k =1 c 1 2 (B x 1 +B x 2 +⋯+B x p )-(B x p+1 +⋯+B x p+q ) k □ B,c 2 k =1 c 2 2 (B x 1 +B x 2 +⋯+B x p )-(B x p+1 +⋯+B x p+q ) k where p+q=n, B x i =∂ 2 ∂x i 2 +2v i x i ∂ ∂x i , where 2v i =2α i +1, α i >-1 2[6], x i >0, i=1,2,⋯,n, c 1 and c 2 is positive constant, k is a nonnegative integer and n is the dimension of the ℝ n + . Firstly, it is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the ultra-hyperbolic Bessel operator iterated k-times.
Tuberkuloz ve toraks
Wegener granulomatosis (WG) is characterized by granulomatous vasculitis that involves multisyste... more Wegener granulomatosis (WG) is characterized by granulomatous vasculitis that involves multisystem, including upper and lower airways and kidney. WG may be a mortal disease if the diagnosis is delayed. The aim of this study is to present three patients admitted with different prediagnosis but after the investigations were diagnosed as WG and followed in our clinic. The cases were discussed with the literature knowledge. All three patients were diagnosed as WG with clinical, radiological and pathological findings. c-ANCA was positive in two patients, and negative one. Complete remission was established with treatment in one case. The treatment of other patients going on, however, the third patient was lost to follow up.
Chest
... Correspondence to: Youri Ganshchak, EKP, PhD, Department of Extra-Corporeal Circulation, Univ... more ... Correspondence to: Youri Ganshchak, EKP, PhD, Department of Extra-Corporeal Circulation, University Hospital Maastricht, Maastricht, the Netherlands ... MD Ozkan Alatas, MD Muzaffer Metintas, MD Aysen Ozarslan, MD Sinan Erginel, MD Hüseyin Yildirim, MD Osmangazi ...
Kyungpook Mathematical Journal
This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities wi... more This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.
We prove a sharp Hardy type integral inequality by using the generalized Riesz potential generate... more We prove a sharp Hardy type integral inequality by using the generalized Riesz potential generated by a generalized shift operator. Our results improve and extend the well-known results of G. H. Hardy, J. E. Littlewood and G. Pólya [Inequalities. Cambridge, England: At the University Press (1952; Zbl 0047.05302)].
In this paper, we establish several new inequalities for some twice differantiable mappings that ... more In this paper, we establish several new inequalities for some twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
International Journal of Pure and Applied Mathematics
Page 1. International Journal of Pure and Applied Mathematics Volume 31 No. 3 2006, 337-343... more Page 1. International Journal of Pure and Applied Mathematics Volume 31 No. 3 2006, 337-343 NORM INEQUALITIES WITH NON-ISOTROPIC KERNELS Mehmet Zeki ...
... MEHMET ZEKI SARIKAYA AND HÜSEYIN YILDIRIM Abstract. ... Riesz potential, shift operator and M... more ... MEHMET ZEKI SARIKAYA AND HÜSEYIN YILDIRIM Abstract. ... Riesz potential, shift operator and Morrey space. Page 2. 208 MEHMET ZEKI SARIKAYA AND HÜSEYIN YILDIRIM Denote by Ty the generalized shift operator acting according to the law Ty x F(x) = Cv ∫ π 0 ... ∫ π ...
Journal of Inequalities in Pure and Applied Mathematics
ÖZET Wegener granülomatözü (WG), üst ve alt solunum yolları ile böbreği tutabilen, çok sistem tut... more ÖZET Wegener granülomatözü (WG), üst ve alt solunum yolları ile böbreği tutabilen, çok sistem tutulumlu granülomatöz vaskülitis ile karakterize bir hastalıktır. Tanı konulması geciktiğinde mortal seyreden bir hastalık olan WG'nin, kliniğimize değişik ön tanılarla ...
TAIWANESE JOURNAL OF MATHEMATICS
In this paper, the inequality of Hardy-Littlewood-Sobolev type is established for the generalized... more In this paper, the inequality of Hardy-Littlewood-Sobolev type is established for the generalized Riesz potentials generated by the generalized shift operator with the functions in Sobolev spaces W m p,v (R + n).
International Journal of Applied Mathematics and Statistics
In this study, we obtain a new proofs of some Hardy-type in-equalities associated with generalize... more In this study, we obtain a new proofs of some Hardy-type in-equalities associated with generalized translation.
We study the solution of the equation □ B,c 1 k □ B,c 2 k u(x)=δ, where u(x) is an unknown functi... more We study the solution of the equation □ B,c 1 k □ B,c 2 k u(x)=δ, where u(x) is an unknown function and δ is a Dirac-delta function, □ B,c 1 k and □ B,c 2 k are the ultra-hyperbolic Bessel operator iterated k-times and are defined by □ B,c 1 k =1 c 1 2 (B x 1 +B x 2 +⋯+B x p )-(B x p+1 +⋯+B x p+q ) k □ B,c 2 k =1 c 2 2 (B x 1 +B x 2 +⋯+B x p )-(B x p+1 +⋯+B x p+q ) k where p+q=n, B x i =∂ 2 ∂x i 2 +2v i x i ∂ ∂x i , where 2v i =2α i +1, α i >-1 2[6], x i >0, i=1,2,⋯,n, c 1 and c 2 is positive constant, k is a nonnegative integer and n is the dimension of the ℝ n + . Firstly, it is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the ultra-hyperbolic Bessel operator iterated k-times.
Tuberkuloz ve toraks
Wegener granulomatosis (WG) is characterized by granulomatous vasculitis that involves multisyste... more Wegener granulomatosis (WG) is characterized by granulomatous vasculitis that involves multisystem, including upper and lower airways and kidney. WG may be a mortal disease if the diagnosis is delayed. The aim of this study is to present three patients admitted with different prediagnosis but after the investigations were diagnosed as WG and followed in our clinic. The cases were discussed with the literature knowledge. All three patients were diagnosed as WG with clinical, radiological and pathological findings. c-ANCA was positive in two patients, and negative one. Complete remission was established with treatment in one case. The treatment of other patients going on, however, the third patient was lost to follow up.
Chest
... Correspondence to: Youri Ganshchak, EKP, PhD, Department of Extra-Corporeal Circulation, Univ... more ... Correspondence to: Youri Ganshchak, EKP, PhD, Department of Extra-Corporeal Circulation, University Hospital Maastricht, Maastricht, the Netherlands ... MD Ozkan Alatas, MD Muzaffer Metintas, MD Aysen Ozarslan, MD Sinan Erginel, MD Hüseyin Yildirim, MD Osmangazi ...
Kyungpook Mathematical Journal
This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities wi... more This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.
We prove a sharp Hardy type integral inequality by using the generalized Riesz potential generate... more We prove a sharp Hardy type integral inequality by using the generalized Riesz potential generated by a generalized shift operator. Our results improve and extend the well-known results of G. H. Hardy, J. E. Littlewood and G. Pólya [Inequalities. Cambridge, England: At the University Press (1952; Zbl 0047.05302)].
In this paper, we establish several new inequalities for some twice differantiable mappings that ... more In this paper, we establish several new inequalities for some twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.