TR-Dizin İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8652
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Article Citation - WoS: 15Citation - Scopus: 14A Spectral Technique for Solving Two-Dimensional Fractional Integral Equations With Weakly Singular Kernel(Hacettepe Univ, Fac Sci, 2018) Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Baleanu, Dumitru; Amin, Ahmed Z. M.; 56389; MatematikThis paper adapts a new numerical technique for solving twodimensional fractional integral equations with weakly singular. Using the spectral collocation method, the fractional operators of Legendre and Chebyshev polynomials, and Gauss-quadrature formula, we achieve a reduction of given problems into those of a system of algebraic equations. We apply the reported numerical method to solve several numerical examples in order to test the accuracy and validity. Thus, the novel algorithm is more responsible for solving two-dimensional fractional integral equations with weakly singular.Article Citation - WoS: 16Citation - Scopus: 20Common fixed point theorems in cone banach spaces(Hacettepe Univ, Fac Sci, 2011) Abdeljawad, Thabet; Tas, Kenan; Karapınar, Erdal; 19184; 4971; MatematikRecently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.Article Citation - WoS: 27Citation - Scopus: 26Completion of cone metric spaces(Hacettepe Univ, Fac Sci, 2010) Abdeljawad, Thabet; MatematikIn this paper a completion theorem for cone metric spaces and a com- pletion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space E.Article Citation - WoS: 9Citation - Scopus: 10Diagnosis of osteoarthritic changes, loss of cervical lordosis, and disc space narrowing on cervical radiographs with deep learning methods(Turkish Joint Diseases Foundation, 2022) Maras, Yuksel; Tokdemir, Gul; Ureten, Kemal; Atalar, Ebru; Duran, Semra; Maras, Hakan; 17411; 34410; Bilgisayar MühendisliğiObjectives: In this study, we aimed to differentiate normal cervical graphs and graphs of diseases that cause mechanical neck pain by using deep convolutional neural networks (DCNN) technology. Materials and methods: In this retrospective study, the convolutional neural networks were used and transfer learning method was applied with the pre-trained VGG-16, VGG-19, Resnet-101, and DenseNet-201 networks. Our data set consisted of 161 normal lateral cervical radiographs and 170 lateral cervical radiographs with osteoarthritis and cervical degenerative disc disease. Results: We compared the performances of the classification models in terms of performance metrics such as accuracy,Article Citation - WoS: 2Citation - Scopus: 6Diamond alpha Hardy-Copson type dynamic inequalities(Hacettepe Univ, Fac Sci, 2022) Kayar, Zeynep; Kaymakcalan, Billur; 109448; MatematikIn this paper two kinds of dynamic Hardy-Copson type inequalities are derived via diamond alpha integrals. The first kind consists of twelve new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together. The second kind involves another twelve new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Hardy-Copson type inequalities. Our approach is quite new due to the fact that it uses time scale calculus rather than algebra. Therefore both kinds of our results unify some of the known delta and nabla Hardy-Copson type inequalities into one diamond alpha Hardy-Copson type inequalities and offer new Hardy-Copson type inequalities even for the special cases.Article Citation - Scopus: 0Edelstein-type fixed point theorems in compact TVS-cone metric spaces(Hacettepe University, 2014) Abdeljawad, Thabet; MatematikIn this paper we prove two fixed point theorems in compact cone metricspaces over normal cones. The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11]. Thesecond theorem generalizes the main result in [10] and the first theorem.However, the two theorems fail in different categories. Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.Article Citation - WoS: 0Citation - Scopus: 1Linear contrasts in one-way classification AR(1) model with gamma innovations(Hacettepe Univ, Fac Sci, 2016) Senoglu, Birdal; Bayrak, Ozlem Turker; 56416In this study, the explicit estimators of the model parameters in oneway classification AR(1) model with gamma innovations are derived by using modified maximum likelihood (MML) methodology. We also propose a new test statistic for testing linear contrasts. Monte Carlo simulation results show that the MML estimators have higher efficiencies than the traditional least squares (LS) estimators and the proposed test has much better power and robustness properties than the normal theory test.Article Citation - WoS: 2Citation - Scopus: 2New common fixed point theorems of gregus type for r-weakly commuting mappings in 2-metric spaces(2009) Murthy, P.p.; Tas, Kenan; 4971; MatematikIn this paper we extend and generalize a theorem of M.R. Singh, L. S. Singh and P.P. Murthy (Common fixed points of set valued mappings, Int. J. Math. Sci., 25 (6), 411–415, 2001) in a 2-metric space with a Gregu˘s type condition, and give some common fixed point theorems of set-valued maps in 2-metric spaces.Article Citation - WoS: 9Citation - Scopus: 8On the existence interval for the initial value problem of a fractional differential equation(Hacettepe Univ, Fac Sci, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; MatematikWe compute via a comparison function technique, a new bound for the existence interval of the initial value problem for a fractional differential equation given by means of Caputo derivatives. We improve in this way the estimate of the existence interval obtained very recently in the literature.Article Citation - WoS: 7Citation - Scopus: 8Representation for the reproducing kernel Hilbert space method for a nonlinear system(Hacettepe Univ, Fac Sci, 2019) Akgul, Esra Karatas; Akgul, Ali; Khan, Yasir; Baleanu, Dumitru; 56389; MatematikWe apply the reproducing kernel Hilbert space method to a nonlinear system in this work. We utilize this technique to overcome the nonlinearity of the problem. We obtain accurate results. We demonstrate our results by tables and figures. We prove the efficiency of the method.Article Citation - WoS: 5Citation - Scopus: 7The diagnosis of femoroacetabular impingement can be made on pelvis radiographs using deep learning methods(Turkish Joint Diseases Foundation, 2023) Atalar, Ebru; Ureten, Kemal; Kanatli, Ulunay; Ciceklidag, Murat; Kaya, Ibrahim; Vural, Abdurrahman; Maras, YukselObjectives: The aim of this study was to evaluate diagnostic ability of deep learning models, particularly convolutional neural network models used for image classification, for femoroacetabular impingement (FAI) using hip radiographs. Materials and methods: Between January 2010 and December 2020, pelvic radiographs of a total of 516 patients (270 males, 246 females; mean age: 39.1 +/- 3.8 years; range, 20 to 78 years) with hip pain were retrospectively analyzed. Based on inclusion and exclusion criteria, a total of 888 hip radiographs (308 diagnosed with FAI and 508 considered normal) were evaluated using deep learning methods. Pre-trained VGG-16, ResNet-101, MobileNetV2, and Inceptionv3 models were used for transfer learning. Results: As assessed by performance measures such as accuracy, sensitivity, specificity, precision, F-1 score, and area under the curve (AUC), the VGG-16 model outperformed other pre-trained networks in diagnosing FAI. With the pre-trained VGG-16 model, the results showed 86.6% accuracy, 82.5% sensitivity, 89.6% specificity, 85.5% precision, 83.9% F1 score, and 0.92 AUC. Conclusion: In patients with suspected FAI, pelvic radiography is the first imaging method to be applied, and deep learning methods can help in the diagnosis of this syndrome.
