Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Correction Citation - WoS: 5Citation - Scopus: 1Meir-Keeler Α-Contractive Fixed and Common Fixed Point Theorems (Vol 2013, Pg 19, 2013)(Springer international Publishing Ag, 2013) Gopal, Dhananjay; Abdeljawad, ThabetIn this note we correct some errors that appeared in the article (Abdeljawad in Fixed Point Theory Appl. 2013:19, 2013) by modifying some conditions in the main theorems and by giving an example to support. MSC: 47H10, 54H25.Article Citation - WoS: 7Citation - Scopus: 10Common Fixed Point Theorems for Generalized (φ,ψ)-Weak Contraction Condition in Complete Metric Spaces(Springer international Publishing Ag, 2015) Tas, Kenan; Patel, Uma Devi; Murthy, Penumarthy ParvateesamThe intent of this manuscript is to establish some common fixed point theorems in a complete metric space under weak contraction condition for two pairs of discontinuous weak compatible maps. The results proved herein are the generalization of some recent results in literature. We give an example to support our results.Article Citation - WoS: 52Citation - Scopus: 57Damped Wave Equation and Dissipative Wave Equation in Fractal Strings Within the Local Fractional Variational Iteration Method(Springer international Publishing Ag, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein; Su, Wei-HuaIn this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions. MSC: 74H10, 35L05, 28A80.Article Citation - WoS: 9Citation - Scopus: 11Study on Application of Hybrid Functions To Fractional Differential Equations(Springer international Publishing Ag, 2018) Baleanu, D.; Torkzadeh, L.; Nouri, K.In this study we propose an efficient technique for approximate solution of linear and nonlinear differential equations with fractional order. The operational matrices based upon block-pulse functions and Chebyshev polynomials of the second kind are used for this purpose. Also, we focus on the upper bound of error for performance of the our estimates. The numerical results confirm the convergence of the suggested method. Correspondingly, the obtained results of our method are compared with other approaches in terms of efficiency and accuracy.Article Citation - Scopus: 1Inference of Autoregressive Model With Stochastic Exogenous Variable Under Short-Tailed Symmetric Distributions(Springer international Publishing Ag, 2018) Bayrak, Ozlem Tuker; Akkaya, Aysen DenerIn classical autoregressive models, it is assumed that the disturbances are normally distributed and the exogenous variable is non-stochastic. However, in practice, short-tailed symmetric disturbances occur frequently and exogenous variable is actually stochastic. In this paper, estimation of the parameters in autoregressive models with stochastic exogenous variable and non-normal disturbances both having short-tailed symmetric distribution is considered. This is the first study in this area as known to the authors. In this situation, maximum likelihood estimation technique is problematic and requires numerical solution which may have convergence problems and can cause bias. Besides, statistical properties of the estimators can not be obtained due to non-explicit functions. It is also known that least squares estimation technique yields neither efficient nor robust estimators. Therefore, modified maximum likelihood estimation technique is utilized in this study. It is shown that the estimators are highly efficient, robust to plausible alternatives having different forms of symmetric short-tailedness in the sample and explicit functions of data overcoming the necessity of numerical solution. A real life application is also given.Article Citation - WoS: 77Citation - Scopus: 75On Vibrations in Thermoelasticity Without Energy Dissipation for Micropolar Bodies(Springer international Publishing Ag, 2016) Baleanu, Dumitru; Marin, MarinWe consider a micropolar thermoelastic body occupying a prismatic cylinder that is free of loads on lateral surface (no body force, no body couple, and no heat supply). On the base of the cylinder are prescribed a time-dependent displacement, a microrotation, and a thermal displacement, which are harmonic in time, and collaborate to induce the motion of the considered body. With the help of a measure associated with the corresponding steady-state vibration and by assuming that the exciting frequency is lower than a certain critical frequency, we will obtain a spatial decay estimate.Article Citation - WoS: 22Citation - Scopus: 26Constantin's Inequality for Nabla and Diamond-Alpha Derivative(Springer international Publishing Ag, 2015) Kaymakcalan, Billur; Pelen, Neslihan Nesliye; Guvenilir, Ayse FezaCalculus for dynamic equations on time scales, which offers a unification of discrete and continuous systems, is a recently developed theory. Our aim is to investigate Constantin's inequality on time scales that is an important tool used in determining some properties of various dynamic equations such as global existence, uniqueness and stability. In this paper, Constantin's inequality is investigated in particular for nabla and diamond-alpha derivatives.Article Citation - WoS: 62Citation - Scopus: 82Meir-Keeler Α-Contractive Fixed and Common Fixed Point Theorems(Springer international Publishing Ag, 2013) Abdeljawad, ThabetGeneralized Meir-Keeler alpha-contractive functions and pairs are introduced and their fixed and common fixed point theorems are obtained. Also, the so-called generalized Meir-Keeler alpha-f-contractive maps commuting with f are introduced and their coincidence and common fixed point theorems are investigated. New sufficient conditions different from those in (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012) are used. An application to the coupled fixed point is established as well. An example is given to show that the alpha-Meir-Keeler generalization is real. AMS Subject Classification: 47H10, 54H25.Article Citation - WoS: 13Citation - Scopus: 20Coupled Fixed Point Theorems for Partially Contractive Mappings(Springer international Publishing Ag, 2012) Abdeljawad, ThabetRecently, some authors have started to generalize fixed point theorems for contractive mappings in a class of generalized metric spaces in which the self-distance need not be zero. These spaces, partial metric spaces, were first introduced by Matthews in 1994. The proved fixed point theorems have been obtained for mappings satisfying contraction type conditions empty of the self-distance. In this article, we prove some coupled fixed point theorems for mappings satisfying contractive conditions allowing the appearance of self-distance terms. These partially contractive mappings do reflect the structure of the partial metric space, and hence their coupled fixed theorems generalize the previously obtained by (Aydi in Int. J. Math. Sci. 2011:Article ID 647091, 2011). Some examples are given to support our claims. MSC: 47H10, 54H25.Article Citation - WoS: 21Citation - Scopus: 18Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces(Springer international Publishing Ag, 2012) Mukheimer, A.; Zaidan, Y.; Abdeljawad, T.; Alzabut, J. O.We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.