Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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: 10Citation - Scopus: 11Chaotic Attractors and Fixed Point Methods in Piecewise Fractional Derivatives and Multi-Term Fractional Delay Differential Equations(Elsevier, 2023) Jarad, Fahd; Panda, Sumati Kumari; Abdeljawad, ThabetUsing generalized cyclic contractions, we establish some fixed point results in controlled rectangular metric spaces. Some subsequent outcomes are obtained. Moreover, some necessary conditions to demonstrate the existence of solutions for the multi-term fractional delay differential equations with wth order and the piecewise equations under the setting of non-singular type derivative are established in this paper. In order to demonstrate the effectiveness of our results, we provided some numerical examples.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.Article Citation - WoS: 21Citation - Scopus: 18Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces(Springer international Publishing Ag, 2012) Mukheimer, A.; Zaidan, Y.; Abdeljawad, T.; Alzabut, J. O.We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.