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Article The Inversion Results for the Limit q-bernstein Operator(Springer Basel Ag, 2018) Ostrovska, SofiyaThe limit q-Bernstein operator B-q appears as a limit for a sequence of the q-Bernstein or for a sequence of the q-Meyer-Konig and Zeller operators in the case 0 < q < 1. Lately, various features of this operator have been investigated from several angles. It has been proved that the smoothness of f is an element of C[0, 1] affects the possibility for an analytic continuation of its image B-q f. This work aims to investigate the reciprocal: to what extent the smoothness of f can be retrieved from the analytical properties of B-q f.Article Citation - WoS: 17Citation - Scopus: 27Fixed Point Theorems in New Generalized Metric Spaces(Springer Basel Ag, 2016) Karapinar, Erdal; Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; Karapınar, Erdal; Mathematics; MathematicsThe aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.Article Citation - WoS: 4Citation - Scopus: 3On Orlicz-Power Series Spaces(Springer Basel Ag, 2010) Karapinar, Erdal; Zakharyuta, VyacheslavIn this manuscript, we investigate the isomorphisms of Orlicz-Kothe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.Article Citation - WoS: 6Citation - Scopus: 5Geothermal Prospectivity of the Bigadic Basin and Surrounding Area, Nw Anatolia, Turkey, by the Spectral Analysis of Magnetic Data(Springer Basel Ag, 2021) Bilim, Funda; Aydemir, Attila; Ates, AbdullahThe Curie Point Depths (CPDs) are estimated from the spectral analysis of magnetic data in order to determine the geothermal potential of the Bigadic Basin and its surrounding region in NW Anatolia, Turkey. The estimated CPD range is from 7 to 17-18 km. The shallowest depth (7 km) lies to the north of Balikesir. The estimated geothermal gradient and heat flow values range from 33 to 80 degrees C/km, and 83 to 200 mWm(-2), respectively. All results in the study area support the previous studies from the geological or geophysical investigations for western Anatolia by other researchers. High temperatures may be resulted indirectly from the continental collision and consequent thermal relaxation and/or heating from the interiors of the Earth due to the mantle delamination or asthenospheric upwelling in response to lithospheric extension in the western Anatolia. The high heat flow and shallow CPDs can also be associated with the magmatic rocks as a consequence of the recent tectonic extension and granitoids in the studied region.Article Citation - WoS: 15Citation - Scopus: 14Generalized Transportation Cost Spaces(Springer Basel Ag, 2019) Ostrovska, Sofiya; Ostrovskii, Mikhail I.The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray et al. (Fundam Math 199(2):177-194, 2008). Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein 1 spaces. In this work, the existence of metric spaces with the following properties is proved: (1) uniformly discrete metric spaces such that transportation cost spaces on them do not contain isometric copies of l(1), this result answers a question raised by Cuth and Johanis (Proc Am Math Soc 145(8):3409-3421, 2017); (2) locally finite metric spaces which admit isometric embeddings only into Banach spaces containing isometric copies of l(1); (3) metric spaces for which the double-point norm is not a norm. In addition, it is proved that the double-point norm spaces corresponding to trees are close to l(infinity)(d) of the corresponding dimension, and that for all finite metric spaces M, except a very special class, the infimum of all seminorms for which the embedding of M into the corresponding seminormed space is isometric, is not a seminorm.Article Citation - WoS: 5Citation - Scopus: 5Geophysical Investigation of the Geothermal Potential Under the Largest Volcanic Cover in Anatolia: Kars Plateau, Ne Turkey(Springer Basel Ag, 2020) Aydemir, Attila; Bilim, Funda; Avci, Birgul; Kosaroglu, SinanIn this study, Curie-point depth (CPD), geothermal gradient, radiogenic heat production, and heat flow maps were constructed based on different thermal conductivity coefficients using magnetic anomaly data for the Kars Plateau, which has the largest volcanic cover in Turkey. The bottom depths of the magnetic crust in the research area were revealed by the CPD map for the first time in this investigation. There are two apparent magnetic anomaly trends in the study area: the first is the Horasan-Senkaya-Sarikamis-Selim-Arpacay trend in the NE-SW direction, and the other is the Hanak-Ardahan-Arpacay trend in the NW-SE direction. Two other prominent elongations extend into the Ardahan-Gole-Senkaya and Kars-Digor axes. All these trends represent mountain chains and/or stratovolcanoes in the region, and no anomalies are observed around the non-volcanic outcrops. Curie depths are shallow, up to 14 km between Horasan and Kagizman towns, and 12 km in the northwestern part of the study area. Gradient values can reach 50 degrees C km(-1) in the northwestern sector, together with the high heat flows represented by the 150 Wm(-1) K-1 contours. The deepest CPD region lies between Gole and Susuz towns, where the geothermal gradient decreases to 27 degrees C km(-1). Heat flows decrease 60 Wm(-1) K-1 in the same area. An apparent gap around the Kars Plateau was observed in previous regional heat flow maps of Turkey by other authors (who used the bottom hole temperatures of boreholes and hot springs temperatures). This gap has been accurately filled from the results of this study, and geothermal exploration areas and the geothermal potential of the Kars Plateau have thus been determined for future exploration activity on the basis of the tectonic elements and earthquake data.Article Citation - WoS: 13Citation - Scopus: 13Coincidence Point Theorems on Quasi-Metric Spaces Via Simulation Functions and Applications To g-metric Spaces(Springer Basel Ag, 2018) Lopez de Hierro, A. F. Roldan; Karapinar, E.; O'Regan, D.In this paper, we present some coincidence point results in the framework of quasi-metric spaces using contractive conditions involving simulation functions. As consequences, we are able to particularize these results to a variety of situations including G-metric spaces. The results presented in this paper generalize and extend several comparable results in the existing literature. In addition, some examples are given.Article Citation - WoS: 69Citation - Scopus: 70An Approach To Best Proximity Points Results Via Simulation Functions(Springer Basel Ag, 2017) Karapinar, Erdal; Khojasteh, FarshidIn this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.Article Citation - WoS: 17Citation - Scopus: 16The Approximation by q-bernstein Polynomials in the Case q ↓ 1(Springer Basel Ag, 2006) Ostrovska, SLet B-n (f, q; x), n = 1, 2, ... , 0 < q < infinity, be the q-Bernstein polynomials of a function f, B-n (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {B-n (f, q(n); x)} with q(n) down arrow 1 is not an approximating sequence for f is an element of C[0, 1], in contrast to the standard case q(n) up arrow 1. At the same time, there exists a sequence 0 < delta(n) down arrow 0 such that the condition 1 <= q(n) <= delta(n) implies the approximation of f by {B-n(f, qn; x)} for all f is an element of C[0, 1].Article Citation - WoS: 11Citation - Scopus: 15The q-versions of the Bernstein Operator: From Mere Analogies To Further Developments(Springer Basel Ag, 2016) Ostrovska, SofiyaThe article exhibits a review of results on two popular q-versions of the Bernstein polynomials, namely, the LupaAY q-analogue and the q-Bernstein polynomials. Their similarities and distinctions are discussed.
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