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Article On the Lupas q-transform of Unbounded Functions(Walter de Gruyter Gmbh, 2023) Ostrovska, Sofiya; Turan, MehmetThe Lupa , s q-transform comes out naturally in the study of the Lupa , s q-analogue of the Bernstein operator. It is closely related to the Heine q-distribution which has a numerous application in q-boson operator calculus and to the Valiron method of summation for divergent series. In this paper, the Lupa , s q-transform (lambda(q)f)(z), q is an element of (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f is an element of C[0, 1] have been investigated. First, the condition for a function to possess the Lupa , s q-transform is presented. Also, results concerning the connection between growth rate of the function f (t) as t -> 1(-) and the growth of its Lupa , s q-transform (lambda(q)f)(z) as z -> infinity are established. (c) 2023 Mathematical Institute Slovak Academy of SciencesArticle Citation - WoS: 1Citation - Scopus: 2Existence of Solutions for Odd-Order Multi-Point Impulsive Boundary Value Problems on Time Scales(Walter de Gruyter Gmbh, 2022) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, Murat EymenUsing a fixed point theorem due to Schaefer, the existence of solutions for an odd-order m-point impulsive boundary value problem on time scales is obtained. The problem considered is of general form, where both the differential equation and the impulse effects are nonlinear. Illustrative examples are provided.Article Citation - WoS: 9Citation - Scopus: 9Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, KishinThe main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.Article Citation - WoS: 2Citation - Scopus: 2On the q-bernstein Polynomials of the Logarithmic Function in the Case q > 1(Walter de Gruyter Gmbh, 2016) Ostrovska, SofiyaThe q-Bernstein basis used to construct the q-Bernstein polynomials is an extension of the Bernstein basis related to the q-binomial probability distribution. This distribution plays a profound role in the q-boson operator calculus. In the case q > 1, q-Bernstein basic polynomials on [0, 1] combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of q-Bernstein polynomials in the case of q > 1. The aim of this paper is to present new results related to the q-Bernstein polynomials B-n,B- q of discontinuous functions in the case q > 1. The behavior of polynomials B-n,B- q(f; x) for functions f possessing a logarithmic singularity at 0 has been examined. (C) 2016 Mathematical Institute Slovak Academy of SciencesArticle Citation - WoS: 1Citation - Scopus: 1On the Rate of Convergence for the q-durrmeyer Polynomials in Complex Domains(Walter de Gruyter Gmbh, 2024) Gurel, Ovgu; Ostrovska, Sofiya; Turan, MehmetThe q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set D subset of C, the rate of convergence is O(q(n)) as n -> infinity. The sharpness of the obtained result is demonstrated.Article Citation - WoS: 8Effect of Austenitizing Temperatures on the Microstructure and Mechanical Properties of Aisi 9254 Steel(Walter de Gruyter Gmbh, 2021) Murathan, Omer Faruk; Davut, Kemal; Kilicli, VolkanIn this study, the effect of austenitizing temperatures and low-temperature isothermal heat treatment (below martensite start temperature) on the microstructure and mechanical properties of AISI 9254 high silicon spring steel has been investigated. Experimental studies show that ultra-fine carbide-free bainite, tempered martensite and carbon enriched retained austenite could be observed in isothermally heat-treated samples where the as-received sample consisted of fine pearlite. A high tensile strength of similar to 2060 MPa, a total elongation of similar to 8 %, and absorbed energy of 105 J were achieved in a commercial high-Si steel by austempering below the Ms temperature. A good combination of strength and ductility has been obtained in prolonged austempering below the martensite start temperature (225 degrees C) from an austenitizing temperature of 870 degrees C.Article Citation - WoS: 104Citation - Scopus: 109On Generalized Α - Ψ-Geraghty Contractions on b-metric Spaces(Walter de Gruyter Gmbh, 2020) Afshari, Hojjat; Aydi, Hassen; Karapinar, ErdalIn this paper, we consider generalized alpha - psi-Geraghty contractive type mappings and investigate the existence and uniqueness of a fixed point for mappings involving such contractions. In particular, we extend, improve and generalize some earlier results in the literature on this topic. An application concerning the existence of an integral equation is also considered to illustrate the novelty of the main result.Article Uncorrelatedness Sets of Discrete Random Variables Via Vandermonde-Type Determinants(Walter de Gruyter Gmbh, 2019) Turan, Mehmet; Ostrovska, Sofiya; Ozban, Ahmet YasarGiven random variables X and Y having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs (j, k) is an element of N-2; for which X-j and Y-kappa are uncorrelated. It is known that, broadly put, any subset of N-2 can serve as an uncorrelatedness set. This claim is no longer valid for random variables with prescribed distributions, in which case the need arises so as to identify the possible uncorrelatedness sets. This paper studies the uncorrelatedness sets for positive random variables uniformly distributed on three points. Some general features of these sets are derived. Two related Vandermonde-type determinants are examined and applied to describe uncorrelatedness sets in some special cases. (C) 2019 Mathematical Institute Slovak Academy of SciencesArticle Citation - WoS: 14Citation - Scopus: 13SOME FIXED POINT THEOREMS IN BRANCIARI METRIC SPACES(Walter de Gruyter Gmbh, 2017) Berzig, Maher; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio F.In this paper, we investigate the existence and uniqueness of a fixed point of certain contraction via auxiliary functions in the context of complete Branciari metric spaces endowed with a transitive binary relation. Our results unify and extend some existing fixed point results in the related literature.Article Citation - WoS: 1Citation - Scopus: 1Impact Behavior of Sandwich Composites With S2-glass/Epoxy and PVC Foam Under Low Velocity Loading(Walter de Gruyter Gmbh, 2025) Karakuzu, Ramazan; Sarioglu, Rifat; Kandas, HalisThe purpose of this research is to examine the absorbed energy, resistance to impact load of sandwich composite, and power exercised by impactor, experimentally. Therefore, low velocity impact tests were performed at three different energy levels for two distinct noses on sandwich composite with a PVC core and varying amounts of S2-glass layers. The vacuum-assisted resin infusion method (VARIM) was used to manufacture sandwich composites. S2-glass fabric with an areal density of 190 gm-2 and polyvinyl chloride (PVC) core material with a thickness of 10 mm were utilized. For every face sheet material, three distinct layer numbers of S2-glass fabrics were used. It is seen that composites exposed to flat impactors absorb considerably more energy than hemispherical ones.
