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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 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 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 An Unconventional Splitting for Korteweg de Vries–Burgers Equation(EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2015) Aydın, AyhanNumerical solutions of the Korteweg de Vries–Burgers (KdVB) equation based on splitting is studied. We put a real parameter into a KdVB equation and split the equation into two parts. The real parameter that is inserted into the KdVB equation enables us to play with the splitted parts. The real parameter enables to write the each splitted equation as close to the Korteweg de Vries (KdV) equation as we wish and as far from the Burgers equation as we wish or vice a versa. Then we solve the splitted parts numerically and compose the solutions to obtained the integrator for the KdVB equation. Finally we present some numerical experiments for the solution of the KdV, Burger’s and KdVB equations. The numerical experiments shows that the new splitting gives feasible and valid results.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 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 Neumann problem for generalized n-Poisson equation(Journal of Mathematical Analysis and Applications, 2009) Aksoy, Ümit; Çelebi, OkayUsing a hierarchy of integral operators having higher-order Neumann functions and their derivatives as kernels, the Neumann problem for a 2nth order linear partial complex differential equation is discussed. The solvability of the problem is obtained.Article A Hierarchy of Singular Integral Operators for Mixed Boundary Value Problems(2011) Aksoy, Ümit; Çelebi, OkayA class of integral operators having a hierarchy of polyharmonic kernels is introduced and some properties are derived. Iterated mixed boundary value problems for complex model equations and linear elliptic complex partial differential equations are discussed in the unit disc of the complex plane.
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