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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 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 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 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.Öğe Rakotch type extension of Darbo's fixed point theorem and an application(Univ Politehnica Bucharest, Sci Bull, 2024) Gençtürk, İlker; Erduran, Ali; Altun, İshakIn this paper, we present a new extension of Darbo's fixed point theorem inspired by Rakotch's contraction. We also provide the alternative version of Leray-Schauder type of our new result. In order to demonstrate the applicability of our theoretical result, we present an existence theorem based on a functional equation. Finally, we provide an illustration of our existence theorem.Öğe Quantitative type theorems in the space of locally integrable functions(Springer, 2022) Aral, Ali; Özsaraç, Fırat; Yilmaz, BasarIn this work, we introduce a new modulus of continuity for locally integrable function spaces which is influenced by the natural structure of the L-p space. After basic properties of it are given, we obtain a quantitative type theorem for the rate of convergence of convolution type integral operators and iterates of them. Their global smoothness preservation property involving the new modulus of continuity is presented. Finally, the obtained results are applied to Gauss-Weierstrass operators.Öğe Quaternionic bertrand curves in euclidean 4-space(Int Center Scientific Research & Studies, 2013) Kecilioğlu, Osman; İlarslan, KazımIn this paper, by using the similar idea of Matsuda and Yorozu [12], we prove that if bitorsion of a quatenionic curve alpha is no vanish, then there is no quaternionic curve in E-4 is a Bertrand curve. Then we define (1, 3) type Bertrand curves for quatenionic curve in Euclidean 4-space. We give some characterizations for a (1, 3) type quaternionic Bertrand curves in Euclidean 4-space by means of the curvature functions of the curve.Öğe Proximity Point Results for Generalized p-Cyclic Reich Contractions: An Application to Solving Integral Equations(Mdpi, 2023) Alamri, Hind; Hussain, Nawab; Altun, İshakThis article studies new classes of contractions called the p-cyclic Reich contraction and p-cyclic Reich contraction pair and develops certain best proximity point results for such contractions in the setting of partial metric spaces. Furthermore, the best proximity point results for p-proximal cyclic Reich contractions of the first and second types are also discussed.Öğe Presic-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations(Vilnius Univ, Inst Mathematics & Informatics, 2023) Altun, İshak; Gençtürk, İlker; Erduran, AliIn this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Presic-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.Öğe Best proximity and best periodic points for proximal nonunique contractions(Springer Basel Ag, 2021) Şahin, Hakan; Aslantaş, Mustafa; Altun, İshakTaking into account nonunique fixed point and periodic point results of Ciric (Institut Mathematique 17, 52-58, 1974) and best proximity point results in the literature, we introduce the concept of proximal nonunique contraction for nonself mappings. Then, we obtain some nonunique best proximity point theorems. Further, we describe the concept of best periodic point of nonself mappings and we present some nonunique best periodic point results. We also provide many examples to show that our new concepts are meaningful and to support our theorems. Additionally, we present a new notion for the nonself mapping H called property P-b, and then we provide some results including sufficient conditions to guarantee that H has the property P-b.Öğe Approximation by Some Baskakov-Kantorovich Exponential-Type Operators(Springer Singapore Pte Ltd, 2022) Özsaraç, Fırat; Gupta, Vijay; Aral, AliIn the present paper, we propose the modification of the Baskakov-Kantorovich operators based on mu-integral. Such operators are connected with exponential functions. We estimate moments and establish some direct results in terms of modulus of continuity.Öğe Approximation of operators related to squared Sza acute accent sz-Mirakjan basis functions(Univ Nis, Fac Sci Math, 2023) Rahman, Shagufta; Aral, Ali; Mursaleen, M.The main objective of this paper is to define a sequence of positive linear operators by means of the squared Szasz-Mirakjan basis functions. We estimate the rate of convergence in terms of the modulus of continuity and the class of Lipschitz functions. Furthermore, we have shown the comparison and convergence of these operators with the help of some illustrative graphics.Öğe Approximation Results for Hadamard-Type Exponential Sampling Kantorovich Series(Springer Basel Ag, 2023) Kurşun, Sadettin; Aral, Ali; Acar, TuncerThe present paper deals with construction of a new family of exponential sampling Kantorovich operators based on a suitable fractional-type integral operators. We study convergence properties of newly constructed operators and give a quantitative form of the rate of convergence thanks to logarithmic modulus of continuity. To obtain an asymptotic formula in the sense of Voronovskaja, we consider locally regular functions. The rest of the paper devoted to approximations of newly constructed operators in logarithmic weighted space of functions. By utilizing a suitable weighted logarithmic modulus of continuity, we obtain a rate of convergence and give a quantitative form of Voronovskaja-type theorem via remainder of Mellin-Taylor's formula. Furthermore, some examples of kernels which satisfy certain assumptions are presented and the results are examined by illustrative numerical tables and graphical representations.Öğe Approximation properties of modified Jain-Gamma operators(Vasyl Stefanyk Precarpathian Natl Univ, 2021) Erdoğan, S.; Olgun, A.In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator bymeans of themodulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.Öğe Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators(Univ Studi Catania, Dipt Matematica, 2013) Acar, Tuncer; Aral, AliIn this paper, as a generalization of Bernstein-Stancu type operators of two variable, we introduce a new positive linear operator C-n (alpha,alpha,beta,beta,) (f; x, y) called Bernstein-Stancu-Chlodowsky on a triangular domain, with mobile boundaries, which extends to [0,infinity) x [0,infinity) as n -> infinity. We give some shape properties that are preserved and also obtain weighted approximation properties of these operators.Öğe Approximation Properties of Modified Baskakov Gamma Operators(Univ Nis, 2021) Arpagus, Seda; Olgun, AliIn this paper, we have studied an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem, firste we gave the approximation properties of this operator. Secondly, we computed the rate of convergence of this operator by means of the modulus of continuity and we gave an approximation properties of weighted spaces. Finally, we studied the Voronovskaya type theorem of this operator.Öğe Approximation Properties Of Modified Gauss-Weierstrass Integral Operators In Exponential Weighted Lp Spaces(Univ Nis, 2021) Yılmaz, BaşarIn this paper, we deal with modified Gauss-Weierstrass integral operators from exponentially weighted spaces L-p,L-a (R) into L-p,L-2a (R). We give the rate of convergence in terms of weighted modulus of continuity. Moreover, we prove weighted approximation of functions belonging to the space L-p,L-a (R) by these operators with the help of a Korovkin type theorem. Finally, we give pointwise approximation of such functions by these operators at generalized Lebesgue points.Öğe An intuitionistic fuzzy-based model for performance evaluation of EcoPorts(Pergamon-Elsevier Science Ltd, 2023) Yalcin, Galip Cihan; Kara, Karahan; Toygar, Arda; Simic, Vladimir; Pamucar, Dragan; Köleoğlu, NilayThe EcoPort performance level serves as a basic indicator to determine the environmental status of a port and its achievement of certification standards. The European Sea Ports Organization has defined ten essential EcoPort criteria that contribute significantly to the assessment of EcoPort performance. The primary motivation for this study is to determine the importance of the criteria from the perspective of academics and chief officers, as well as to evaluate the EcoPort performance of six port authorities that comply with three basic certification standards for environmental management systems. The research methodology and application are conducted in four phases. In the first phase, experts, criteria, and alternative ports are identified. In the second phase, the importance levels of experts are determined using neutrosophic sets, while the criteria are weighted using the intuitionistic fuzzy weighting averaging operator. In the third phase, the alternative ranking order method ac-counting for two-step normalization (AROMAN) based on the intuitionistic fuzzy sets is introduced to evaluate the EcoPort performance of the ports. In the fourth phase, the results are supported by sensitivity analysis scenarios. The research results identified air pollution as the most critical criterion, while the Valencia Port Authority secured the highest rank in terms of EcoPort performance. Ultimately, this research contributes to the literature by developing and applying the new IF-AROMAN method for EcoPort performance evaluation.
