Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 10Citation - Scopus: 12Diamond Alpha Bennett-Leindler Type Dynamic Inequalities and Their Applications(Wiley, 2022) Kaymakcalan, Billur; Pelen, Neslihan Nesliye; Kayar, ZeynepIn this paper, two kinds of dynamic Bennett-Leindler type inequalities via the diamond alpha integrals are derived. The first kind consists of eight new integral inequalities which can be considered as mixed type in the sense that these inequalities contain delta, nabla and diamond alpha integrals together due to the fact that convex linear combinations of delta and nabla Bennett-Leindler type inequalities give diamond alpha Bennett-Leindler type inequalities. The second kind involves four new inequalities, which are composed of only diamond alpha integrals, unifying delta and nabla Bennett-Leindler type inequalities. For the second type, choosing alpha=1 or alpha=0 not only yields the same results as the ones obtained for delta and nabla cases but also provides novel results for them. Therefore, both kinds of our results expand some of the known delta and nabla Bennett-Leindler type inequalities, offer new types of these inequalities, and bind and unify them into one diamond alpha Bennett-Leindler type inequalities. Moreover, an application of dynamic Bennett-Leindler type inequalities to the oscillation theory of the second-order half linear dynamic equation is developed and presented for the first time ever.Article Citation - WoS: 14Citation - Scopus: 16Bennett-Leindler Type Inequalities for Nabla Time Scale Calculus(Springer Basel Ag, 2021) Kayar, Zeynep; Kaymakcalan, Billur; Pelen, Neslihan NesliyeIn this study, we generalize the converse of Hardy and Copson inequalities, which are known as Bennett and Leindler type inequalities, for nabla time scale calculus. This generalization allows us not only to unify all the related results existing in the literature for an arbitrary time scale but also to obtain new results which are analogous to the results of the delta time scale calculus.Article Citation - WoS: 4Citation - Scopus: 5Necessary and Sufficient Condition for Existence of Periodic Solutions of Predator-Prey Dynamic Systems With Beddington-Deangelis Functional Response(Springeropen, 2016) Guvenilir, A. Feza; Kaymakcalan, Billur; Pelen, Neslihan NesliyeWe consider two-dimensional predator-prey systems with Beddington-DeAngelis-type functional response on periodic time scales. For this special case, we try to find the necessary and sufficient conditions for the considered system when it has at least one w-periodic solution. This study is mainly based on continuation theorem in coincidence degree theory and will also give beneficial results for continuous and discrete cases. Especially, for the continuous case, by using the study of Cui and Takeuchi (J. Math. Anal. Appl. 317: 464-474, 2006), to obtain the globally attractive w-periodic solution of the given system, an inequality is given as a necessary and sufficient condition. Additionally, for the continuous case in this study, the open problem given in the discussion part of the study of Fan and Kuang (J. Math. Anal. Appl. 295: 15-39, 2004) is solved.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.