Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science
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Publication Analytic Functions With Conic Domains Associated With Certain Generalized q-integral Operator(Korean Mathematical Society, 2023) Ahuja, Om P.; ÇETİNKAYA, ASENA; Jain, Naveen KumarIn this paper, we define a new subclass of k-uniformly starlike functions of order-gamma (0 <= gamma < 1) by using certain generalized q integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q sufficient coefficient condition, q-Fekete-Szego inequalities, q-Bieberbach De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order-gamma by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.Publication A New Topology Via a Topology(American Institute of Physics Inc., 2022) DAĞCI, FİKRİYE İNCE; Çakallı, HüseyinIn this extended abstract, we modify the definition of h-open set introduced in [1] by F. Abbas who neglects that the set of all h-open sets is a topology, and we show that the union of any family of h-open subsets of X is h-open that ensures that the set of all h-open subsets of a topological space (X, τ) forms a topology which is finer than τ, where a subset A of a topological space (X, τ) is said to be h-open if A ⊆ Int(A ∪ U) for every non-empty subset U of X such that U ∈ τ. We also give continuity type theorems. © 2022 American Institute of Physics Inc.. All rights reserved.Publication On Group Analysis of Optimal Control Problems in Economic Growth Models(American Institute of Mathematical Sciences, 2020) POLAT, GÜLDEN GÜN; Özer, TeomanThe optimal control problems in economic growth theory are analyzed by considering the Pontryagin's maximum principle for both current and present value Hamiltonian functions based on the theory of Lie groups. As a result of these necessary conditions, two coupled first-order differential equations are obtained for two different economic growth models. The first integrals and the analytical solutions (closed-form solutions) of two different economic growth models are analyzed via the group theory including Lie point symmetries, Jacobi last multiplier, Prelle-Singer method,_-symmetry and the mathematical relations among them.Publication A Survey on the Theory of Integral and Related Operators in Geometric Function Theory(Springer, 2021) Ahuja, Om P.; ÇETİNKAYA, ASENAA brief tour of more than one hundred years of the historical development of some of the popular integral and related operators in Geometric Function Theory (GFT) is given in this article. The strengths and discovery of the methods used in these operators lie in their ability to unify a large number of diverse operators and results. We also address some of the q- analogues of the integral operators in GFT. Since there are several surveys and books in GFT, we present here only a selection of the results related to our precise objectives. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.Publication Unique Recovery of Unknown Spatial Load in Damped Euler-Bernoulli Beam Equation From Final Time Measured Output(IOP Publishing Ltd., 2021) Hasanov, Alemdar; Romanov, Vladimir; BAYSAL, ONURIn this paper we discuss the unique determination of unknown spatial load F(x) in the damped Euler-Bernoulli beam equation rho(x)u(tt)+mu u(t)+(r(x)u(xx))(xx)=F(x)G(t) 0, the damping coefficient mu > 0 and the temporal load G(t) > 0. As an alternative method we propose the adjoint problem approach (APA) and derive an explicit gradient formula for the Frechet derivative of the Tikhonov functional J(F)=parallel to u(.,T; F) - u(T)parallel to(2)(L2(0,l)). Comparative analysis of numerical algorithms based on SVE and APA methods are provided for the harmonic loading G(t) = cos(omega t), omega > 0, as a most common dynamic loading case. The results presented in this paper not only clearly demonstrate the key role of the damping term mu u (t) in the inverse problems arising in vibration and wave phenomena, but also allows us, firstly, to find admissible values of the final time T > 0, at which a final time measured output can be extracted, and secondly, to reconstruct the unknown spatial load F(x) in the damped Euler-Bernoulli beam equation from this measured output.