Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 17Citation - Scopus: 13Best Proximity Points for Cyclical Contraction Mappings With 0-Boundedly Compact Decompositions(Eudoxus Press, Llc, 2013) Abdeljawad, Thabet; Abdeljawad, T.; Alzabut, J. O.; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.; MatematikThe existence of best proximity points for cyclical type contraction mappings is proved in the category of partial metric spaces. The concept of 0-boundedly compact is introduced and used in the cyclical decomposition. Some possible generalizations to the main results are discussed. Further, illustrative examples are given to demonstrate the effectiveness of our results.Article Citation - WoS: 12Citation - Scopus: 13Mann and Ishikawa Iterative Processes for Cyclic Relatively Nonexpansive Mappings in Uniformly Convex Banach Spaces(Yokohama Publications, 2021) Aliyari, M.; Gabeleh, M.; Karapinar, E.In this manuscript, we study the convergence of best proximity points for cyclic relatively nonexpansive mappings in the setting of uniformly convex Banach spaces by using a projection operator defined on proximal pairs. To this end, we consider the Mann and Ishikawa iteration schemes and obtain strong convergence results for cyclic relatively nonexpansive mappings. A nu¬merical example is presented to support the main result. We then discuss on noncyclic version of relatively nonexpansive mappings in order to study some convergence conclusions in both uniformly convex Banach spaces and Hilbert spaces. © 2021 Yokohama Publications. All rights reserved.Article Global Optimization and Applications To a Variational Inequality Problem(de Gruyter Poland Sp Z O O, 2021) Adeel, Muhammad; Aydi, Hassen; Baleanu, Dumitru; Hussain, AzharIn the present paper, we study the existence and convergence of the best proximity point for cyclic Theta-contractions. As consequences, we extract several fixed point results for such cyclic mappings. As an application, we present some solvability theorems in the topic of variational inequalities.Article Citation - WoS: 12Citation - Scopus: 13Existence of Fixed Point and Best Proximity Point of P-Cyclic Orbital Φ-Contraction Map(Vilnius Univ, inst Mathematics & informatics, 2022) Karpagam, Saravanan; Karapinar, Erdal; Magadevan, PrabavathyIn 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: 2Citation - Scopus: 2A Discussion on the Coincidence Quasi-Best Proximity Points(Univ Nis, Fac Sci Math, 2021) Abkar, Ali; Karapinar, Erdal; Fouladi, FarhadIn this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validity of the main result.Article Citation - WoS: 12Citation - Scopus: 9Best Proximity Point Results for Contractive and Cyclic Contractive Type Mappings(Taylor & Francis inc, 2021) Karapinar, Erdal; Kanta Dey, Lakshmi; Hiranmoy, GaraiThe essential importance of the best proximity point theory is that "best proximity point theory" appears in the coincidence of "metric fixed point theory" and "optimization theory." So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce a new type of proximal property of a pair of subsets of a metric space, which we designate as proximal weakly compact pair. After this, we come up with some new type of proximal contractive and proximal cyclic contractive mappings. Then we investigate the existence of best proximity point(s) in these newly originated mappings in the setting of proximal weakly compact pair of subsets in a metric space.