Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
6 results
Search Results
Article Citation - WoS: 6Citation - Scopus: 5Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces(Univ Osijek, dept Mathematics, 2011) Turkoglu, Duran; Abdeljawad, Thabet; Abuloha, Muhib; Abdeljawad, Thabet; MatematikIn this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ciric in [8, 27] are recovered.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 Ample Spectrum Contractions in Branciari Distance Spaces(Yokohama Publ, 2021) Karapinar, Erdal; Karapınar, Erdal; Lopez de Hierro, Antonio Francisco Roldan; Shahzad, Naseer; De Hierro, A.F.R.L.; MatematikVery recently, the notion of ample spectrum contraction has been introduced in order to unify, under the same axioms, a large number of contractive mappings that have had great success in the field of Fixed Point Theory in recent years and that have been used in a wide variety of applications in Nonlinear Analysis (Meir-Keeler contractions, Geragthy contractions, contractions under simulation functions, contractions under R-functions, etc.) However, the subtle conditions that define ample spectrum contractions cannot be extended as they are to new kinds of abstract metric spaces because they involve key properties that are only fulfilled in metric spaces. In this paper, based on a very recent work in which the authors unravel the essential properties of the topology in Branciari spaces, we investigate the reasons why the proposed axiomatic fails in Branciari spaces and we illustrate how to overcome such drawbacks. As a consequence, we characterize the notion of ample spectrum contraction in the setting of Branciari distance spaces and we also investigate the existence and uniqueness of fixed points for such family of contractions in the context of complete Branciari distance spaces.Article Citation - WoS: 22Citation - Scopus: 28Non-Instantaneous Impulsive Fractional Integro-Differential Equations With State-Dependent Delay Br(Univ Maragheh, 2022) Salim, Abdelkrim; Aissani, Khalida; Benchohra, Mouffak; Karapinar, Erdal; Benkhettou, NadiaThis paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point theory. Finally, an example to confirm of the results is provided.Article Citation - WoS: 6Citation - Scopus: 9Neutral Functional Sequential Differential Equations With Caputo Fractional Derivative on Time Scales(Springernature, 2022) Lazreg, Jamal Eddine; Benkhettou, Nadia; Benchohra, Mouffak; Karapinar, ErdalIn this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray-Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.Article Citation - WoS: 5Citation - Scopus: 4Approximate Controllability of Second-Order Nonlocal Impulsive Functional Integro-Differential Systems in Banach Spaces(Korean Mathematical Soc, 2018) Arjunan, Mani Mallika; Nagaraj, Mahalingam; Suganya, Selvaraj; Baleanu, DumitruThis manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.