WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - Scopus: 13Existence of Fixed Point and Best Proximity Point of P-Cyclic Orbital φ-Contraction Map(Vilnius University Press, 2022) Magadevan, Prabavathy; Karapınar, Erdal; Karpagam, SaravananIn this manuscript, p-cyclic orbital phi-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function phi is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.Article Citation - WoS: 146Citation - Scopus: 166On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Karapınar, Erdal; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MatematikThe aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.Article Citation - WoS: 1Citation - Scopus: 1Solving Existence Problems Via F-Contraction in Modified B-Metric Spaces(Turkic World Mathematical Soc, 2022) Karapinar, E.; Karapınar, Erdal; Sedghi, S.; Shobe, N.; MatematikIn this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also define basic topological notions in expanded b -metric to able to investigate the existence of fixed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein.Article Citation - WoS: 4Existence and Uniqueness of Solutions for a Nabla Fractional Boundary Value Problem With Discrete Mittag{leffler Kernel(inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2021) Jonnalagadda, Jagan Mohan; Baleanu, Dumitru; Baleanu, Dumitru; MatematikWe consider a two-point boundary-value problem of order 1 < alpha < 3/2 involving nabla fractional differences with discrete Mittag-Leffler kernels. In [2], the authors obtained an expression for the Green's function of this boundary value problem. We determine an upper bound for the Green's function and derive a Lyapunov-type inequality. Further, we also establish sufficient conditions on existence and uniqueness of solutions for the corresponding nonlinear problem using fixed point theorems.Article Citation - Scopus: 1Existence Results for an Impulsive Pantograph Differential Equations Within Exponential Kernel(Univ Politehnica Bucharest, Sci Bull, 2022) Kavitha, Velusamy; Baleanu, Dumitru; Kanimozhi, Palanisamy; Arjunan, Mani Mallika; Baleanu, Dumitru; MatematikThis manuscript deals with the existence results for an impulsive pantograph integro-differential equations (IPIDE) through Caputo-Fabrizio (CF) operator. Certain novel existence findings are shown using fixed point approaches. Finally, two numerical examples are provided in the work to demonstrate the application of our theoretical findings.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 - Scopus: 1Remarks on Some Generalizations of ?-Contraction(Univ Politehnica Bucharest, Sci Bull, 2023) Karapinar, Erdal; Cvetkovic, MarijaThe concept of 0-contraction was modified and generalized in several ways during the last decade. Some assumptions concerning the class T are shown to be superfluous in order to obtain a unique fixed point for a ?-type contraction, ?-Suzuki type and, consequently, ?-contraction. Improvement of several previously published results are derived with a modified contractive condition and we have presented an example of possible application. The same approach was used for the F-Suzuki contraction and numerous generalizations are made.Article Citation - WoS: 4Citation - Scopus: 4Fixed Point Theorems for Basic Θ-Contraction and Applications(North Univ Baia Mare, 2024) Cvetkovic, Marija; Karapinar, Erdal; Petrusul, Drian; Petruşel, AdrianThe main aim of this paper is omitting some superfluous assumptions in the definition of the class of functions Theta, by means of which were defined and studied various classes of theta-contractions, and still obtaining the uniqueness of the fixed point for this new type of contractive mappings. Several generalizations of continuous theta-contractions are presented along with their applications to the study of integral equations.Article Citation - WoS: 6Citation - Scopus: 7Fixed Point Results of a New Family of Hybrid Contractions in Generalised Metric Space With Applications(Amer inst Mathematical Sciences-aims, 2022) Jiddah, Jamilu Abubakar; Noorwali, Maha; Shagari, Mohammed Shehu; Rashid, Saima; Jarad, FahdIn this manuscript, a novel general family of contraction, called hybrid-interpolative ReichIstrat,escu-type (G-alpha-mu)-contraction is introduced and some fixed point results in generalised metric space that are not deducible from their akin in metric spaces are obtained. The preeminence of this class of contraction is that its contractive inequality can be extended in a variety of manners, depending on the given parameters. Consequently, a number of corollaries that reduce our result to other wellknown results in the literature are highlighted and analysed. Substantial examples are constructed to validate the assumptions of our obtained theorems and to show their distinction from corresponding results. Additionally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution of a family of integral equations.Article Citation - WoS: 6Citation - Scopus: 7Fixed Point Results in C*-Algebra Bipolar Metric Spaces With an Application(Amer inst Mathematical Sciences-aims, 2023) Gnanaprakasam, Arul Joseph; Isik, Huseyin; Jarad, Fahd; Mani, GunaseelanIn this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on C*-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.