WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 3Completion of Tvs-Cone Metric Spaces and Some Fixed Point Theorems(Gazi Univ, 2011) Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikIn this paper a completion theorem for cone metric spaces and a completion theorem for cone normed space over a complete locally convex topological vector space E are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the topology of the locally convex space E. Very recently some fixed point theorems obtained in cone Banach spaces are generalized to locally convex cone Banach spaces. These theorems can not be generalized or proved trivially by using the nonlinear scalarization function used very recently by Wei-Shih Du in " A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis Theory Methods and Applications 72 (5):2259-2261 (2010)".Article Citation - WoS: 142Citation - Scopus: 170On Delta and Nabla Caputo Fractional Differences and Dual Identities(Hindawi Ltd, 2013) Abdeljawad, ThabetWe investigate two types of dual identities for Caputo fractional differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. Two types of Caputo fractional differences are introduced; one of them (dual one) is defined so that it obeys the investigated dual identities. The relation between Riemann and Caputo fractional differences is investigated, and the delta and nabla discrete Mittag-Leffler functions are confirmed by solving Caputo type linear fractional difference equations. A nabla integration by parts formula is obtained for Caputo fractional differences as well.