2 results
Search Results
Now showing 1 - 2 of 2
Article Citation - WoS: 5Citation - Scopus: 7On Jaggi Type Contraction Mappings(Univ Politehnica Bucharest, Sci Bull, 2018) Karapinar, Erdal; MathematicsBy a work of Jaggi, it is known that the existence of certain inequalities for continuous maps over metric spaces implies the existence and uniqueness of fixed points. In this paper, we show that if p denotes a partial metric, the existence of a rational form of type p(Tt,Ts) <= a(1) p(t,Tt).p(s,Ts)/d(t,s)+a(2)p(t,s) for some a 1 and a 2 with a(1) + a(2) < 1 for a continuous map T over a partial metric space leads to the same conclusions, that is, the existence and uniqueness of fixed points.Article Citation - WoS: 146Citation - Scopus: 157On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; MathematicsThe 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.
