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Article Weak Ψ -Contractions on Partially Ordered Metric Spaces and Applications To Boundary Value Problems(2015) Aksoy, ÜmitRecent developments in fixed point theory have been encouraged by the applicability of the results in the area of boundary value problems for differential and integral equations. Especially in the last few years, a lot of publications in fixed point theory have presented results directly related to specific initial or boundary value problems. These problems include not only ordinary and partial differential equations, but also fractional differential equations.Article Norm Estimates of a Class of Calderon–zygmund Type Strongly Singular Integral Operators(Integral Transforms and Special Functions, 2007) Aksoy, Ümit; Çelebi, OkayIn this article, we prove the Lp boundedness of a class of Calderon–Zygmund type strongly singular operators. In particular, we give an estimate for the L2 norm of these operators in the unit disc of the complex plane.Article Anılması Gereken Bir Kitap: Geometri(Bilim ve Teknoloji, 2013) Başkaya, O. TuncayAtatürk’ün devrimlerini, görüşlerini, ülkemize kazandırdığı sayısız yenilik ve zenginlikleri hepimiz biliriz. Ama onun başlı başına bir kitap, hem de bir geometri kitabı, yazdığından kaçımızın haberi vardır? Geometri’nin 1937 yılında yapılan ilk basımında, kitabın üstünde yazar adı belirtilmemiştir. Ancak, Atatürk’ün kitabı 1936-1937 yıllarında Dolmabahçe sarayında, hiç bir yardım almaksızın ve kendisinin türettiği Türkçe kelimelerle yazdığı bilinmektedir. 2007 yılında ise, kitap Yetmişbeşinci Dil Bayramı kapsamında tekrar düzenlenerek yeni şekliyle basılmıştır.Article Remarks on Some Coupled Fixed Point Theorems in G-Metric Spaces(2014) Agarwal, Ravi P.; Karapınar, ErdalIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems in the context of (ordered) G-metric spaces are in fact immediate consequences of usual fixed point theorems that are either well known in the literature or can be obtained easily.Article Temel Bilimler-matematik(Bilim ve Teknoloji, 2015) Başkaya, TuncayBenim Ankara Emek Mahallesi’nde bir berberim var: Ünsal Usta. Ankara’nın en eski ustalarından, kendisini yetiştirmiş, hazırcevap, nüktedan, zarif bir beyefendi. Uzunca bir süre önce bana sordu, “Hocam, niye insanlar matematikten korkuyor ve sevmiyor? Hepimiz her gün kullanıyoruz ama korkuyoruz. Siz matematikçisiniz, sevdirmek için bir şeyler yapmak mümkün değil mi?” O gün kendisine bazı açıklamalar yaptım. Çok mutlu oldu ve “Ben de sizin söylediklerinizden bazılarını düşünmüştüm ama eksikmiş,” dedi. Ünsal Usta’nın, mesleğini doğrudan ilgilendirmediği halde, böylesi önemli bir konu üzerinde düşünüyor olması beni etkiledi. Bir süre sonra da bu yazıyı yazmayı düşündüm. Matematiği sever misin? Bu soru toplumun geniş kesimlerine sorulduğunda alınacak cevap yüksek oranda, maalesef, “Hayır,” olacaktır, çünkü Matematik, sevilmemenin ötesinde, insanlara korkutucu gelmektedir. Günlük yaşamda bu denli çok kullandığı halde herkesin Matematikten korkma nedeni ne olabilir?Article Some Remarks About the Existence of Coupled G-Coincidence Points(Journal of Inequalities and Applications, 2015) Erhan, İnci M.; Shahzad, NaseerVery recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps.Article Operator Splitting of the Kdv-Burgers Type Equation With Fast and Slow Dynamics(2015) Aydın, Ayhan; Karasözen, BülentThe Korteweg de Vries-Burgers (KdV-Burgers) type equation arising from the discretiza tion of the viscous Burgers equation with fast dispersion and slow diffusion is solved using operator splitting. The dispersive and diffusive parts are discretized in space by second order conservative finite differences. The resulting system of ordinary differential equations are composed using the time reversible Strang splitting. The numerical results reveal that the periodicity of the solutions and the invariants of the KdV-Burgers equation are well preserved.Article A Survey on Boundary Value Problems for Complex Partial Differential Equations(Advances in Dynamical Systems and Applications, 2010) Aksoy, Ümit; Çelebi, A. OkayIn this article, the recent results on basic boundary value problems of complex analysis are surveyed for complex model equations and linear elliptic complex par tial differential equations of arbitrary order on simply connected bounded domains, particularly in the unit disc, on unbounded domains such as upper half plane and upper right quarter plane and on multiply connected domains containing circular rings.Article Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions(Computer Physics Communications, 2007) Aydın, Ayhan; Karasözen, BülentWe consider for the integration of coupled nonlinear Schrödinger equations with periodic plane wave solutions a splitting method from the class of symplectic integrators and the multi-symplectic six-point scheme which is equivalent to the Preissman scheme. The numerical experiments show that both methods preserve very well the mass, energy and momentum in long-time evolution. The local errors in the energy are computed according to the discretizations in time and space for both methods. Due to its local nature, the multi-symplectic six-point scheme preserves the local invariants more accurately than the symplectic splitting method, but the global errors for conservation laws are almost the same.Article A Fixed Point Theorem for Set-Valued Quasi-Contractions in B-Metric Space(2014) Karapınar, Erdal; Aydı, Hassen; Bota, Monica-felicia; Mıtrovıć, SlobodankaIn this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.
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