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https://hdl.handle.net/20.500.12587/18876

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Weighted inequalities involving Hardy and Copson operators
(Academic Press Inc Elsevier Science, 2022) Gogatishvili, Amiran; Pick, Lubos; Ünver, Tuğçe
We characterize a four-weight inequality involving the Hardy operator and the Copson operator. More precisely, given p(1), p(2), q(1), q(2) is an element of (0, infinity), we find necessary and sufficient conditions on non-negative measurable functions u(1), u(2), v(1), v(2) on (0, infinity) for which there exists a positive constant c such that the inequality (integral(infinity)(0)(integral(t)(0)f(s)(p2) v(2)(s)(p2)ds)(q2/p2) u(2)(t)(q2)dt)(1/q2) <= c(integral(infinity)(0)(integral(infinity)(t)f(s)(p1) v(1) (s)(p1) ds)(q1/p1) u(1)(t)(q1)dt)(1/q1) holds for every non-negative measurable function f on (0, infinity). The proof is based on discretizing and antidiscretizing techniques. The principal innovation consists in development of a new method which carefully avoids duality techniques and therefore enables us to obtain the characterization in previously unavailable situations, solving thereby a long-standing open problem. We then apply the characterization of the inequality to the establishing of criteria for embeddings between weighted Copson spaces Cop(p1,q1)(u(1), v(1)) and weighted Cesaro spaces Ces(p2,q2)(u(2), v(2)), and also between spaces S-q(w) equipped with the norm parallel to f parallel to(Sq(w)) = (integral(infinity)(0)[f**(t) - f*(t)](q)w(t) dt)(1/q) and classical Lorentz spaces of type Lambda. (C) 2022 Published by Elsevier Inc.
Weighted inequalities for discrete iterated kernel operators
(Wiley-V C H Verlag Gmbh, 2022) Gogatishvili, Amiran; Pick, Lubos; Ünver Yıldız, Tuğçe
We develop a new method that enables us to solve the open problem of characterizing discrete inequalities for kernel operators involving suprema. More precisely, we establish necessary and sufficient conditions under which there exists a positive constant C such that (Sigma(n is an element of z)(Sigma(n)(t = -infinity) U(i, n)a(i))(q)w(n))(1/q) <= C(Sigma(n is an element of Z)a(n)(p)v(n))(1/p) holds for every sequence of nonnegative numbers where {a(n)}(nzZ) where U is a kernel satisfying certain regularity condition, 0 < p,q <= infinity and (u(n))(nzZ) and {w(n)}(nzZ) are fixed weight sequences. We do the same for the inequality (Sigma(n is an element of z)w(n)(sup-infinity<= n U(i, n) Sigma(i)(j=-infinity) a(j)](q))(1/q) <= C(Sigma(n is an element of Z)a(n)(p)v(n))(1/p) . We characterize these inequalities by conditions of both discrete and continuous nature.
Weighted Inequalities for a Superposition of the Copson Operator and the Hardy Operator
(Springer Birkhauser, 2022) Gogatishvili, Amiran; Mihula, Zdenek; Pick, Lubos; Turcinova, Hana; Ünver, Tuğçe
We study a three-weight inequality for the superposition of the Hardy operator and the Copson operator, namely (integral(b)(a)(integral(b)(t)integral(s)(a) f(tau)p upsilon(tau)d tau)(q/p) u(s) ds)(r/q)w(t)dt)(1/r) <= C integral(b)(a) f(t) dt, in which (a, b) is any nontrivial interval, q, r are positive real parameters and p is an element of (0, 1]. A simple change of variables can be used to obtain any weighted L-p-norm with p >= 1 on the right-hand side. Another simple change of variables can be used to equivalently turn this inequality into the one in which the Hardy and Copson operators swap their positions. We focus on characterizing those triples of weight functions (u, v, w) for which this inequality holds for all nonnegative measurable functions f with a constant independent of f. We use a newtype of approach based on an innovative method of discretization which enables us to avoid duality techniques and therefore to remove various restrictions that appear in earlier work. This paper is dedicated to Professor Stefan Samko on the occasion of his 80th birthday.
Weak partial metric spaces and some fixed point results
(Univ Politecnica Valencia, Editorial Upv, 2012) Altun, İshak; Durmaz, Gonca
The concept of partial metric p on a nonempty set X was Introduced by Matt hews [8]. One of the most interesting properties of a partial metric is that p(x, x) may not be zero for x epsilon X. Also, each partial metric p on a nonempty set X generates a To topology on X. By omitting the small self-distance axiom of partial metric, Heckmann [7] defined the weak partial metric space. In the present paper, we give some fixed point results on weak partial metric spaces.
Vehicle routing software selection for last mile delivery companies using Fermatean fuzzy-based model
(Pergamon-Elsevier Science Ltd, 2024) Kara, Karahan; Yalçın, Galip Cihan; Simic, Vladimir; Gürol, Pınar; Pamucar, Dragan
Vehicle routing software (VRS) is utilized by last mile delivery (LMD) companies for route optimization. The problem of VRS selection is of paramount importance for LMD companies. In this research, a VRS selection model tailored to LMD companies is developed and proposed. This model is based on Fermatean fuzzy sets (FFS). The FFS-preference selection index (PSI) method is proposed for weighting the criteria. The FFS-alternative ranking order method accounting for two-step normalization (AROMAN) method is defined for ranking the VRS alternatives. This hybrid approach, developed as FFS-PSI-AROMAN, incorporates the FFYWA operator based on Yager t-norm and t-conorm operations as the aggregation operator to enhance the strength of aggregation operations. Additionally, an algorithm has been developed for the model. The developed model is applied through a real-life case study conducted in an LMD company operating in Turkey. An expert group is formed, criteria are defined, alternative VRS options are identified, and the proposed algorithm is employed to make the optimal VRS selection. Sensitivity analysis scenarios are created, and robustness tests are conducted to evaluate the model's reliability. Comprehensive implications for both the research and managerial insights are provided, along with recommendations for future research endeavors.
Unrestricted Tribonacci and Tribonacci-Lucas quaternions
(Bulgarian Acad Science, 2023) Kızılaslan, Gonca; Karabulut, Leyla
We define a generalization of Tribonacci and Tribonacci-Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci-Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions. Furthermore, several sum formulas and a matrix representation are obtained.
Twisted Surfaces in Semi-Euclidean 4-Space with Index 2
(Int Electronic Journal Geometry, 2024) Uçum, Ali; İlarslan, Kazım; Camcı, Çetin
In this paper, we consider the twisted surfaces in semi -Euclidean 4 -space with index 2 . We classify the twisted surface with respect to their spine curve which are non -null or null curves. So, we study the geometric properties of these surfaces. Also we obtain the family of some special surfaces such as flat surfaces, marginally trapped surfaces.
Translation hypersurfaces of semi-Euclidean spaces with constant scalar curvature
(Amer Inst Mathematical Sciences-Aims, 2023) Sağlam, Derya; Sunar, Cumali
In this paper, we present translation hypersurfaces of semi-Euclidean spaces with zero scalar curvature. In addition, we prove that translation hypersurfaces with constant scalar curvature must have zero scalar curvature in the semi-Euclidean space Rn+1 q for n >= 3.
The order of approximation by the family of integral operators with positive kernel
(Inst Mathematics & Mechanics, Natl Acad Sciences Azerbaijan, 2008) Esen, Sevgi
The 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.
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, Dragan
Sustainable 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.
The linear algebra of a generalized Tribonacci matrix
(Ankara Univ, Fac Sci, 2023) Kızılaslan, Gonca
In 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.
The Dirichlet-Neumann Boundary Value Problem for the Inhomogeneous Bitsadze Equation in a Ring Domain
(Chiang Mai Univ, Fac Science, 2021) Gençtürk, İlker
In 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.
The Complex Line (P, Q)-Integral And (P, Q)-Green's Formula
(Ivane Javakhishvili Tbilisi State Univ, 2023) Gençtürk, İlker; Koca, Kerim
In 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.
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, Dragan
Supply 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.
The altered Hermite matrix: implications and ramifications
(Amer Inst Mathematical Sciences-Aims, 2024) Kızılaslan, Gonca
Matrix 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.
Tauberian theorems for the weighted mean method of summability of integrals
(Univ Nis, 2020) Özsaraç, Fırat; Çanak, İbrahim
Let 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.
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, Seifedine
Brands 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.
Surfaces of Osculating Circles in Euclidean Space
(Springer Singapore Pte Ltd, 2024) Lopez, Rafael; Camcı, Çetin; Uçum, Ali; İlarslan, Kazım
The 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.
Supplier selection of companies providing micro mobility service under type-2 neutrosophic number based decision making model
(Pergamon-Elsevier Science Ltd, 2024) Önden, İsmail; Deveci, Muhammet; Kara, Karahan; Yalcin, Galip Cihan; Önden, Abdullah; Eker, Mert; Hasseb, Mouad
Environmental approaches play an active role in the production platform as well as in the supply chain. Studies that deal with supplier selection problems in the supply chain with a green focus have recently intensified. In this research, the supplier selection problem of companies providing last mile service, which is seen as the last step of transportation, is handled with a green focus. The supplier selection problem of these companies is differentiated according to strategic and non -strategic product groups. In this study, a green -oriented supplier selection proposal is presented for both the strategic product group and the non -strategic product group. The supplier selection problem is accepted as a multi criteria decision making problem (MCDM). Thus, the type -2 neutrosophic numbers (T2NNs) - based CRiteria Importance Through Intercriteria Correlation (CRITIC) - based Multi -Attributive Border Approximation Area Comparison (MABAC) hybrid model is applied to evaluate the green -oriented supplier. The motivation of the study is to determine the best alternative supplier type for strategic and non -strategic products groups. In this context, two cases are created, ten criteria are selected, and three supplier types are determined. Supplier types are as follows: (i) Classical suppliers, (ii) Hybrid -Classical to green centric suppliers, and (iii) Start -Ups & green centric suppliers. To devise a solution for addressing the research problem, the selection of the optimal green supplier type was accomplished through a recommended T2NNCRITIC-MABAC hybrid model. Accordingly, for both strategic and non -strategic product groups, micromobility service providers identified Hybrid -Classical to Green Centric Suppliers as the most suitable green supplier type. In addition, the findings are strengthened by creating twenty-two sensitivity analysis scenarios. In conclusion, the T2NN-CRITIC-MABAC hybrid method introduced in this study represents a methodologically diverse, fuzzy logic -based approach with practical implications for supplier selection in the micro mobility services sector. Its application and empirical testing contribute to the literature and provide valuable insights for decision -makers in the industry.
Spacelike Bertrand curves in Minkowski 3-space revisited
(Ovidius Univ Press, 2023) Erdem, Hatice Altın; İlarslan, Kazım
In 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.

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