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Öğe The order of approximation by the family of integral operators with positive kernel(Inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2008) Esen, SevgiThe paper is devoted to the order of approximation of functions in generalized Lebesgue points by the family of integral operators of non-convolution types with positive kernels.Öğe The MEREC-AROMAN method for determining sustainable competitiveness levels: A case study for Turkey(Elsevier Science Inc, 2024) Kara, Karahan; Yalçın, Galip Cihan; Acar, Avni Zafer; Simic, Vladimir; Konya, Serkan; Pamucar, DraganSustainable competitiveness represents a multifaceted phenomenon encompassing economic, environmental, and social dimensions. Macro-level competitiveness strategies are formulated based on the diverse capitals possessed by individual countries, thereby giving rise to variations in the sustainable competitiveness strategies of each country. This research introduces a novel hybrid method called the method based on the removal effects of criteria (MEREC)-alternative ranking order method accounting for two-step normalization (AROMAN) for determining sustainable competitiveness levels. This study aims to assess Turkey's sustainable competitiveness position vis -`a-vis its border neighbors. Natural capital, resource efficiency and intensity, social capital, intellectual capital and innovation, economic sustainability, and governance efficiency are the Global Sustainable Competitiveness Index (GSCI) indicators. The GSCI indicators are employed as criteria for determining the sustainable competitiveness scores of countries. The findings show that the resource efficiency and intensity criterion has the highest level of significance. The sustainable competitiveness level of Turkey to its neighboring countries is elucidated based on the results. Recommendations are formulated for the development of strategies aimed at determining Turkey's position in the race for sustainable competitiveness. The introduced MEREC-AROMAN can be utilized to provide rules of thumb for other countries to improve their sustainable competitiveness. This research offers decision support for the formulation of countries' sustainable competitiveness strategies and policies, fostering awareness in the planning and establishment of regional collaborations among nations.Öğe The linear algebra of a generalized Tribonacci matrix(Ankara Univ, Fac Sci, 2023) Kızılaslan, GoncaIn this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k-th power. We also give a relation between the matrix and a matrix exponential of a special matrix.Öğe The Dirichlet-Neumann Boundary Value Problem for the Inhomogeneous Bitsadze Equation in a Ring Domain(Chiang Mai Univ, Fac Science, 2021) Gençtürk, İlkerIn this study, by using some integral representations formulas, we study solvability conditions and explicit solution of the Dirichlet-Neumann problem, an example for a combined boundary value problem, for the Bitsadze equation in a ring domain.Öğe The Complex Line (P, Q)-Integral And (P, Q)-Green's Formula(Ivane Javakhishvili Tbilisi State Univ, 2023) Gençtürk, İlker; Koca, KerimIn this study, we present the complex line (p, q)-integral and multiple (p, q)-integral by using the concept of (p, q)-calculus. The (p, q)-Green's formula and the (p, q)-Gauss formulas are obtained with appropriate conditions in a complex plane.Öğe The alternative ranking using two-step logarithmic normalization method for benchmarking the supply chain performance of countries(Elsevier Science Inc, 2024) Kara, Karahan; Yalçın, Galip Cihan; Simic, Vladimir; Baysal, Zeynep; Pamucar, DraganSupply chain performance signifies the success of countries in material and information flow within international trade activities. Countries strive to enhance their supply chain performance by increasing connectivity with partner countries and reducing dwell times at logistics hubs. In this study, the supply chain performance of countries based on international tracking indicators is examined using a multi -criteria decision -making approach. The paper encompasses two primary objectives. The first objective is the determination of the supply chain performance of countries. The second one is the development of a novel alternative ranking method. The study employs 10 supply chain key performance indicators as criteria and utilizes data from 72 countries. The data is sourced from logistics performance index reports published by the World Bank. The modified preference selection index (MPSI) is employed for criterion weighting. For the ranking of countries, a novel alternative ranking method named the Alternative Ranking using two-step LOgarithmic Normalization (ARLON) method is proposed. Through the implementation of the MPSI-ARLON hybrid method, supply chain performance and rankings of countries are computed. The findings are supported by sensitivity and comparative analyses. Furthermore, robustness tests are conducted for the ARLON method. The research concludes by presenting implications and managerial insights derived from the ARLON method.Öğe The altered Hermite matrix: implications and ramifications(Amer Inst Mathematical Sciences-Aims, 2024) Kızılaslan, GoncaMatrix theory is essential for addressing practical problems and executing computational tasks. Matrices related to Hermite polynomials are essential due to their applications in quantum relations, and spectral properties make them a valuable tool for both theoretical research and practical applications. From a different perspective, we introduced a variant of the Hermite matrix that incorporates triple factorials and demonstrated that this matrix satisfies various properties. By utilizing effective matrix algebra techniques, various algebraic properties of this matrix have been determined, including the product formula, inverse matrix and eigenvalues. Additionally, we extended this matrix to a more generalized form and derived several identities.Öğe Tauberian theorems for the weighted mean method of summability of integrals(Univ Nis, 2020) Özsaraç, Fırat; Çanak, İbrahimLet q be a positive weight function on R+ := [0, infinity) which is integrable in Lebesgue's sense over every finite interval (0, x) for 0 < x < infinity, in symbol: q is an element of L-loc(1)(R+) such that Q(x) := integral(x)(0) q(t)dt not equal 0 for each x > 0, Q(0) = 0 and Q(x) -> infinity as x -> infinity. Given a real or complex-valued function f is an element of L-loc(1) (R+), we define s(x) := integral(x)(0) f (t)dt and tau((0))(q) (x) := s(x), tau((m))(q) (x) := 1/Q(x) integral(x)(0) tau((m-1))(q) (t)q(l)di (x > 0, m = 1, 2, ...), provided that Q(x) > 0, We say that integral(infinity)(0) (x)dx is summable to L by the m-th iteration of weighted mean method determined by the function q(x), or for short, ((N) over bar, q, m) integrable to a finite number L if x ->infinity(lim) tau((m))(q) (x) = L. In this case, we write s(x) -> L((N) over bar, q, m). It is known that if the limit lim(x ->infinity) (x) = L exists, then lim(x ->infinity) tau((m))(q) (x) = L also exists. However, the converse of this implication is not always true. Some suitable conditions together with the existence of the limit lim(x ->infinity) tau((m))(q) (x), which is so called Tauberian conditions, may imply convergence of lim(x ->infinity) s(x). In this paper, one- and two-sided Tauberian conditions in terms of the generating function and its generalizations for ((N) over bar, q , m) summable integrals of real- or complex-valued functions have been obtained. Some classical type Tauberian theorems given for Cesaro summability (C, 1) and weighted mean method of summability ((N) over bar, q) have been extended and generalized.Öğe Sustainable brand logo selection using an AI-Supported PF-WENSLO-ARLON hybrid method(Pergamon-Elsevier Science Ltd, 2025) Kara, Karahan; Ergin, Elif Akagün; Yalçın, Galip Cihan; Çelik, Tuğçe; Deveci, Muhammet; Kadry, SeifedineBrands use logos to reflect their identities and convey their company character to target customers. Logos not only represent brand value but also provide various information about brands. Companies aiming to emphasize sustainable brand value also seek to showcase this aspect in their logos. Therefore, sustainable brand design and development are preferred. The focus of this research is on sustainable brand development through Artificial Intelligence-supported logo design and developing a decision support system for selecting the best logo among Artificial Intelligence-generated logos. In this study, Artificial Intelligence-supported logo design is explained, and the Multi Attribute Group Decision Making approach is adopted for identifying the best logo among the obtained logos. The Picture Fuzzy - Weights by Envelope and Slope - Alternative Ranking using Two-Step Logarithmic Normalization hybrid method is proposed for logo decision-making, combining the Weights by Envelope and Slope criterion weighting method using picture fuzzy sets with Alternative Ranking using Two-Step Logarithmic Normalization alternative ranking methods. Additionally, the Picture Fuzzy Yager Weighted Average aggregation operator based on Yager t-norm and t-conorm operations is employed. The steps of the hybrid method are outlined, and its algorithm is formulated. To test the applicability and robustness of the algorithm, sustainable logo design for an architectural firm is developed and executed as a real-case study. The research concludes that Artificial Intelligence-supported sustainable logo design can be achieved, and the hybrid method can support determining the best logo based on expert opinions. Based on the research findings, the hybrid method is recommended for sustainable logo design and selection.Öğe Surfaces of Osculating Circles in Euclidean Space(Springer Singapore Pte Ltd, 2024) Lopez, Rafael; Camcı, Çetin; Uçum, Ali; İlarslan, KazımThe aim of this paper is to define a new class of surfaces in Euclidean space using the concept of osculating circle. Given a regular curve C, the surface of osculating circles generated by C is the set of all osculating circles at all points of C. It is proved that these surfaces contain a one-parametric family of planar lines of curvature. A classification of surfaces of osculating circles is given in the family of canal surfaces, Weingarten surfaces, surfaces with constant Gauss curvature and surfaces with constant mean curvature.Öğe Space Curves Related by a Transformation of Combescure(Taylor & Francis Ltd, 2021) Çamcı, Çetin; Uçum, Ali; İlarslan, KazimIn this paper, the curves associated with the Combescure transform are discussed. With the help of the fact that these curves have a common Frenet frame, an equivalence relation is defined. The equivalence classes obtained by this equivalence relation have been examined for some special curves and it has been obtained that all curves in the equivalence class of a helix curve are also helix curves. This is also true for k-slant helix curves. The important part of this paper consists of the useful construction method to obtain a curve from the given curve a with the help of Combescure transformation. With this method, some special curves such as Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve can be obtained from any curve related by a Combescure transform. For example, we obtain an example of Mannheim curves explicitly obtained from an anti-Salkowski curve. It is not easy to find an example of Mannheim curves except circular helix in the literature. In general, the conditions for being Bertrand, Mannheim, Salkowski, anti-Salkowski or spherical curve of the curve beta obtained from the given curve alpha with the help of Combescure transformation were obtained.Öğe Spacelike Bertrand curves in Minkowski 3-space revisited(Ovidius Univ Press, 2023) Erdem, Hatice Altın; İlarslan, KazımIn the geometry of curves in E-3, if the principal normal vector field ofa given space curve phi with non-zero curvatures is the principal normalvector field of another space curve phi(& lowast;), then the curve phi is called aBertrand curve and phi(& lowast;) is called Bertrand partner of phi. These curveshave been studied in different space over a long period of time and foundwide application in different areas. Therefore, we have a great knowledgeof geometric properties of these curves. In this paper, revested resultsfor spacelike Bertrand curves with non-null normal vectors will be givenwith the previous studies on Bertrand curves in E-1(3). Follow this revestedresults, the Bertrand curve conditions of a spacelike curve are obtainedin E-1(3). In addition, new curve samples that meet the obtained conditionsare constructed and the graphs of these curves are given.Öğe Some new extensions of Darbo's fixed point theorem with application(Univ Nis, Fac Sci Math, 2024) Gençtürk, İlker; Hançer, Hatice Aslan; Altun, İshakWe present some new extensions of Darbo's fixed-point theorem with a different aspect than those available in the literature by introducing the concept of (k, L)-set contraction. The concept of (k, L)-set contraction is interesting since there is no restriction for the constant L. We also present the nonlinear Leray-Schauder type alternative for one of our results. Finally, to demonstrate the applicability, we utilize theoretical results to provide the existence of solution of an integral equation.Öğe Some Fixed-Point Theorems in Proximity Spaces with Applications(Mdpi, 2022) Qasim, Muhammad; Alamri, Hind; Altun, İshak; Hussain, NawabConsidering the omega-distance function defined by Kostic in proximity space, we prove the Matkowski and Boyd-Wong fixed-point theorems in proximity space using omega-distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions.Öğe Some Fixed Point Theorems for Multivalued Maps Satisfying an Implicit Relation on Metrically Convex Spaces(Kyungpook Natl Univ, Dept Mathematics, 2008) Altun, İshak; Türkoğlu, DuranIn this paper, we give some fixed point theorems for multivalued maps satisfying an implicit relation on metrically convex spaces. Our results extend and generalize some fixed point theorem in the literature.Öğe Some characterizations of pseudo and partially null osculating curves in Minkowski space-time(Int Electronic Journal Geometry, 2011) İlarslan, Kazım; Nesovic, EmilijaIn this paper, we characterize pseudo and partially null osculating curves of the first and second kind in Minkowski space-time E-1(4) in terms of their curvature functions. We give the necessary and sufficient conditions for pseudo and partially null curves to be osculating curves. In particular, we show that there exists a simple relationship between pseudo and partially null osculating curves and pseudo and partially null normal and rectifying curves. Finally, we obtain some explicit parameter equations of pseudo and partially null osculating curves in E-1(4).Öğe Sequential quaternions: Nestedness and applications(World Scientific Publ Co Pte Ltd, 2023) Kızılaslan, Gonca; Akkuş, İlkerIn this paper, we define a function Q which gives the sequence of partial sums of the Fibonacci quaternion sequence (Q(n)). We provide an identity about Q(k) which is the sequence obtained by applying Q to (Q(n)) k-times.Öğe Semi-parallel tensor product surfaces in semi-Euclidean space E24(Ankara Univ, Fac Sci, 2016) Yıldırım, Mehmet; İlarslan, KazımIn this article, the tensor product surfaces are studied that arise from taking the tensor product of a unit circle centered at the origin in Euclidean plane E-2 and a non-null, unit planar curve in Lorentzian plane E-1(2). Also we have shown that the tensor product surfaces in 4-dimensional semi-Euclidean space with index 2, E-2(4), satisfying the semi-parallelity condition (R) over bar (X, Y).h = 0 if and only if the tensor product surface is a totally geodesic surface in E-2(4).Öğe Sequential natural mates of Frenet curves in Euclidean 3-space(Springer Basel Ag, 2021) Camcı, Çetin; Chen, Bang-Yen; İlarslan, Kazım; Uçum, AliAssociated with a Frenet curve alpha in Euclidean 3-space E-3, there exists the notion of natural mate beta of alpha. In this article, we extend the natural mate beta to sequential natural mates {alpha(1), alpha(2), . . . , alpha(n alpha)} with alpha(1) = beta. We call each curve alpha(i), i epsilon {1, 2, . . . , n(alpha)}, the i-th natural mate. The main purpose of this article is to study the relationships between the given Frenet curve a with its sequential natural mates {alpha(1), alpha(2), . . . , alpha n(alpha)}.Öğe Reconstruction of two approximation processes in order to reproduce eax and e2ax, a>0(Element, 2021) Yılmaz, Başar; Uysal, Gümrah; Aral, AliWe propose two modifications for Gauss-Weierstrass operators and moment-type operators which fix e(ax) and e(2ax) with a> 0. First, we present moment identities for new operators. Then, we discuss weighted approximation and prove Voronovskaya-type theorems for them in exponentially weighted spaces. Using modulus of continuity in exponentially weighted spaces, we obtain some global smoothness preservation properties. We give a comparison result for Gauss-Weierstrass operators. Finally, we provide some graphical illustrations that show that modified operators perform better than classical ones.
