Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Citation - WoS: 27
Citation - Scopus: 26
Completion of Cone Metric Spaces
(Hacettepe Univ, Fac Sci, 2010) Abdeljawad, Thabet
In 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.
Citation - WoS: 13
Citation - Scopus: 20
Coupled Fixed Point Theorems for Partially Contractive Mappings
(Springer international Publishing Ag, 2012) Abdeljawad, Thabet
Recently, 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.
Citation - WoS: 84
Citation - Scopus: 100
Dual Identities in Fractional Difference Calculus Within Riemann
(Springeropen, 2013) Abdeljawad, Thabet
We investigate two types of dual identities for Riemann fractional sums and 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. These dual identities insist that in the definition of right fractional differences, we have to use both nabla and delta operators. The solution representation for a higher-order Riemann fractional difference equation is obtained as well.
Edelstein-Type Fixed Point Theorems in Compact Tvs-Cone Metric Spaces
(Hacettepe University, 2014) Abdeljawad, Thabet
In 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.
Citation - WoS: 80
Citation - Scopus: 94
Fixed Points for Generalized Weakly Contractive Mappings in Partial Metric Spaces
(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, Thabet
Partial metric spaces were introduced by S. G. Matthews in 1994 as a part of the study of denotational semantics of dataflow networks. In this article, we prove fixed point theorems for generalized weakly contractive mappings on partial metric spaces. These theorems generalize many previously obtained results. An example is given to show that our generalization from metric spaces to partial metric spaces is real. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 62
Citation - Scopus: 82
Meir-Keeler Α-Contractive Fixed and Common Fixed Point Theorems
(Springer international Publishing Ag, 2013) Abdeljawad, Thabet
Generalized 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.
Citation - WoS: 1631
Citation - Scopus: 1853
On Conformable Fractional Calculus
(Elsevier Science Bv, 2015) Abdeljawad, Thabet
Recently, the authors Khalil et al. (2014) introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed. (C) 2014 Elsevier By. All rights reserved.
Citation - WoS: 141
Citation - Scopus: 169
On Delta and Nabla Caputo Fractional Differences and Dual Identities
(Hindawi Ltd, 2013) Abdeljawad, Thabet
We 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.
Citation - WoS: 590
Citation - Scopus: 675
On Riemann and Caputo Fractional Differences
(Pergamon-elsevier Science Ltd, 2011) Abdeljawad, Thabet
In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B., Atici F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 6
Order Norm Completions of Cone Metric Spaces
(Taylor & Francis inc, 2011) Abdeljawad, Thabet
In this article, a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are constructed by means of an equivalence relation defined via an ordered cone norm on the Banach space E whose cone is strongly minihedral and ordered closed. This order norm has to satisfy the generalized absolute value property. In particular, if E is a Dedekind complete Banach lattice, then, together with its absolute value norm, satisfy the desired properties.

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