Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science
Permanent URI for this collectionhttps://hdl.handle.net/11413/6787
Browse
Browsing Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science by Language "en"
Now showing 1 - 20 of 37
- Results Per Page
- Sort Options
Publication Analytic Functions With Conic Domains Associated With Certain Generalized q-integral Operator(Korean Mathematical Society, 2023) Ahuja, Om P.; ÇETİNKAYA, ASENA; Jain, Naveen KumarIn this paper, we define a new subclass of k-uniformly starlike functions of order-gamma (0 <= gamma < 1) by using certain generalized q integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q sufficient coefficient condition, q-Fekete-Szego inequalities, q-Bieberbach De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order-gamma by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.Publication Bound on Hankel Determinants H(2)4 (F) and H(3)4 (F) for Lemniscate Starlike Functions(Honam Mathematical Soc., 2023) Kumar, Sushil; Rai, Pratima; ÇETİNKAYA, ASENAWe determine the upper bounds on fourth order Hankel de-terminants H4(2) (f) and H(3) 4 (f) for the class S*L of lemniscate starlike functions defined on the open unit disk which was introduced by Sok ' o l and Stankiewicz in [17].Publication Briot-Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function(MDPI, 2022) ÇETİNKAYA, ASENA; Cotirla, Luminita-IoanaWe define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot-Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot-Bouquet differential equations and observe that these solutions are the best dominant of the Briot-Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions.Publication Cesaro Vector Lattices and Their Ideals of Finite Elements(Springer, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R. R.For the Cesaro matrix C = (c(nm))(n,m?N), where c(nm) = (1)/(n), if n = m and c(nm) = 0 otherwise, the Cesaro sequence spaces ces(0), ces(p) (for 1 < p < 8) and cesoo are defined. These spaces turn out to be real vector lattices and with respect to a corresponding (naturally introduced) norm they are all Banach lattices, and so possess (or not possess) some interesting properties. In particular, the relations to their generating ideals c(0), t(p) and t(8) are investigated. Finally the ideals of all finite, totally finite and selfmajorizing elements in ces(0), ces(p) (for 1 < p <8) and ces(8) are described in detail.Publication Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial(MDPI, 2020) Aydoğan, S. Melike; Karahüseyin, ZelihaIn the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete-Szego problem of this subclass is also acquired. Further, some special cases of our results are designated.Publication Coefficient Inequalities for Certain Starlike and Convex Functions(Hacettepe University, 2022) Çetinkaya, Asena; Kumar, SushilIn this paper, we consider two Ma-Minda-type subclasses of starlike and convex functions associated with the normalized analytic function phi(Ne)(z) = 1 + z - z3/3 that maps an open unit disk onto the Nephroid shaped bounded domain in the right-half of the complex plane. We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes. In addition, we compute best possible estimates on third order Hermitian-To eplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.Publication Completely Monotonic Ratios of Basic and Ordinary Gamma Functions(Springer Basel AG, 2021) Berg, Christian; ÇETİNKAYA, ASENA; Karp, DmitriiObjective: In this study, it was planned to examine fatigue, well-being and life habits in children with cancer. Methods: This cross-sectional analytical study was conducted between September 2019-January 2020. "24-Hour Child Fatigue Scale", "Child Well-being Assessment" and Child Life Habit Questionnaire (LIFE-H for Children 1.0)" were administered to 20 children with cancer aged 5-15 years. Pearson's correlation coefficient was used to determine the statistical relationship between life habits, fatigue and well-being. Statistical significance level was accepted as p<0.05. Results: There were significant relationships between fatigue and personal care, shelter and mobility parameters of life habits (r=-0.66, r=0.54, r=0.45, p<0.01, respectively) and there were significant relationships between fatigue and negative emotions (r=0.46), overall life satisfaction (r=-0.52), general happiness (r=-0.49) and positive emotions (r=-0.44 *) parameters of well-being assessment. Life habits scale was found to be related with nutrition, physical fitness and communication parameters of Child Life Habit Questionnaire were found to be most related with the meaning and purpose parameter of the well-being assessment (p<0.01). There were significant relationships between positive emotions and recreation (r=0.45, p=0.04); optimism and communication (r=-0.44, p=0.04); personal care (r=-0.49, p=0, 02), social life (r=-0.46, p=0.04) and autonomy; and mobility and negative emotions (r=-0.45, p=0.04). Conclusion: Considering the relationships determined in this study, the evaluation of the children with cancer and treatment approaches can be shaped. The fact that fatigue affects all aspects of children's life reveals the importance of dealing with fatigue. It is recommended to focus on the meaning and purpose and regain autonomy for children in order to rearrange the life habits of the children and ensure their well-being.Publication Connecting Quantum Calculus and Harmonic Starlike Functions(Univ Nis., 2020) Ahuja, O. P.; ÇETİNKAYA, ASENAQuantum calculus or q-calculus plays an important role in hypergeometric series, quantum physics, operator theory, approximation theory, sobolev spaces, geometric functions theory and others. But role of q-calculus in the theory of harmonic univalent functions is quite new. In this paper, we make an attempt to connect quantum calculus and harmonic univalent starlike functions. In particular, we introduce and investigate the properties of q-harmonic functions and q-harmonic starlike functions of order alpha.Publication Covid-19 Disease Detection with Improved Deep Learning Algorithms on X-Ray Data(Institute of Electrical and Electronics Engineers Inc., 2022) ÇİÇEKLİ, NAHİDE ZEYNEP; BAYDOĞMUŞ, GÖZDE KARATAŞThe COVID-19 pandemic has brought human life to a startling halt around the world from the moment it emerged and took thousands of lives. The health system has come to the point of collapse, many people in the world have died from being infected, and many people who have survived the disease have had permanent lung damage with the spread of COVID-19 in 212 countries and regions. In this study, an answer is sought to diagnose the disease-causing virus through Artificial Intelligence Algorithms. The aim of the study is to accelerate the diagnosis and treatment process of COVID-19 disease. Enhancements were made using Deep Learning methods, including CNN, VGG16, DenseNet121, and ResNet50. For this study, the disease was detected by using X-Ray images of patients with and without COVID-19 disease, and then it was evaluated how to increase the accuracy rate with the limited available data. To increase the accuracy rate, the results of data augmentation on the image data were examined and the time complexity of the algorithms with different layers was evaluated. As a result of the study, it was seen that data augmentation increased the performance rate in all algorithms and the ResNet50 algorithm was more successful than other algorithms. © 2022 IEEE.Publication Duals of Cesaro Sequence Vector Lattices, Cesaro Sums of Banach Lattices, and Their Finite Elements(Springer Basel AG, 2023) GÖNÜLLÜ, UĞUR; Polat, Faruk; Weber, Martin R.In this paper, we study the ideals of finite elements in special vector lattices of real sequences, first in the duals of Cesaro sequence spaces ces(p) for p is an element of{0}boolean OR[1,infinity) and, second, after the Cesaro sum ces(p)(X) of a sequence of Banach spaces is introduced, where p = infinity is also allowed, we characterize their duals and the finite elements in these sums if the summed up spaces are Banach lattices. This is done by means of a remarkable extension of the corresponding result for direct sums.Publication The Effect of Loss and Optimization Functions on Bitcoin Rate Prediction in LSTM(Institute of Electrical and Electronics Engineers Inc., 2022) KIRCI, BERKE KAAN; BAYDOĞMUŞ, GÖZDE KARATAŞIn recent years, Bitcoin cryptocurrency has become a growing trend in the world. For this reason, researchers from many fields are examining various artificial intelligence models to predict Bitcoin rates. In particular, Deep Learning algorithms have been shown to outperform traditional models in predicting cryptocurrency rates. However, very few studies have examined the effect of parameters used in deep learning algorithms on the algorithm. Optimization and loss functions are very important, which affect the algorithm's ability to make a successful prediction. In this study, Long-Short Term Memory, a deep learning algorithm, is used to predict daily Bitcoin prices and the effect of optimization/loss functions on the accuracy rate is evaluated. Experimental results showed that the Long-Short Term Memory model made the best predictions as a result of working with the Adam optimization function and the Mean Square Error loss function. © 2022 IEEE.Publication Exact Sequences of BCK-Modules(Fuat Usta, 2022) ÜLKER, ALPERBCK-modules were introduced as an action of a BCK-algebra over an Abelian group. Homomorphisms of BCK-modules form an exact sequence which is called BCK-sequence. In this paper, we study homomorphisms of BCK-modules. We show that this homomorphisms have a module structure. Moreover, we show that sequences of Hom functors are BCK-sequences.Publication Faber Polynomial Expansion for a New Subclass of Bi-univalent Functions Endowed with (p,q) Calculus Operators(Fuat Usta, 2021) Ahuja, Om P.; ÇETİNKAYA, ASENAIn this paper, we use the Faber polynomial expansion techniques to get the general TaylorMaclaurin coefficient estimates for |an|, (n ≥ 4) of a generalized class of bi-univalentfunctions by means of (p,q)−calculus, which was introduced by Chakrabarti and Jagannathan. For functions in such a class, we get the initial coefficient estimates for |a2| and|a3|. In particular, the results in this paper generalize or improve (in certain cases) thecorresponding results obtained by recent researchers.Publication Fekete-SzegÖ Inequalities for q-Starlike and q-Convex Functions Involving q-Analogue of Ruscheweyh-Type Differential Operator(Palestine Polytechnic University, 2022) Soni, Amit; ÇETİNKAYA, ASENAIn the present paper, the new generalized Ma-Minda type classes of q-starlike and q-convex functions are introduced by using Ruscheweyh-type q-differential operator. Denote by SRλq (φ) the class of q-starlike functions and CRλq (φ) the class of q-convex functions associated with Ruscheweyh-type q-differential operator, where φ is the function with positive real part. By making use of these classes, we obtain initial coefficient estimates and Fekete-Szegö inequalities for the classes SRλq (φ) and CRλq (φ), respectively. © Palestine Polytechnic University-PPU 2022.Publication Generalizations for Certain Bazilevic Functions(SEAMS - Southeast Asian Mathematical Society, 2021) YAVUZ, EMEL; DAYMAZ, TUĞBA; Owa, ShigeyoshiFor analytic functions f(z) in the open unit disk U, an interesting class A(alpha, beta, gamma) is considered. The object of the present paper is to discuss some properties for f(z) in the class A(alpha, beta, gamma) and the class A(alpha, beta, infinity) for gamma -> infinity.Publication Harmonic Multivalent Functions Associated With a (P,Q)-Analogue of Ruscheweyh Operator(Turkic World Mathematical Soc., 2023) Sharma, P.; Mishra, O.; Ahuja, O. P.; ÇETİNKAYA, AYŞENURThe aim of this paper is to introduce and investigate a new class of harmonic multivalent functions defined by (p,q)-analogue of Ruscheweyh operator for multivalent functions. For this new class, we obtain a (p,q)-coefficient inequality as a sufficient con-dition. Using this coefficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic multivalent functions to its sequences of partial sums. We further consider a subclass of our new class and for which we obtain (p,q)-analogue of coefficient characterization which in fact helps us to determine its properties such as distortion bounds, extreme points, convolutions and convexity conditions. In the last section on conclusion, it is pointed out that the results obtained in this paper may also be extended to some generalized classes.Publication Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities(The National Academy of Sciences of Ukraine, 2021) ÇETİNKAYA, ASENA; Karp, Dmitrii; Prilepkina, ElenaThe main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hyper-geometric functions from the symmetries and other properties of Meijer's G function. For instance, we recover two- and three-term Thomae relations for F-3(2), give two- and three-term transformations for F-4(3) with one unit shift and F-5(4) with two unit shifts in the parameters, establish multi-term identities for general F-p(p-1) and several transformations for terminating Kampe de Feriet and Srivastava F-(3) functions. We further present a presumably new formula for analytic continuation of F-p(p-1)(1) in parameters and reveal somewhat unexpected connections between the generalized hypergeometric functions and the generalized and ordinary Bernoulli polynomials. Finally, we exploit some recent duality relations for the generalized hypergeometric and q-hypergeometric functions to derive multi-term relations for terminating series.Publication Increasing the Performance of Machine Learning-Based IDSs on an Imbalanced and Up-to-Date Dataset(IEEE, 2020) BAYDOĞMUŞ, GÖZDE KARATAŞ; Demir, Önder; ŞAHİNGÖZ, ÖZGÜR KORAYIn recent years, due to the extensive use of the Internet, the number of networked computers has been increasing in our daily lives. Weaknesses of the servers enable hackers to intrude on computers by using not only known but also new attack-types, which are more sophisticated and harder to detect. To protect the computers from them, Intrusion Detection System (IDS), which is trained with some machine learning techniques by using a pre-collected dataset, is one of the most preferred protection mechanisms. The used datasets were collected during a limited period in some specific networks and generally don & x2019;t contain up-to-date data. Additionally, they are imbalanced and cannot hold sufficient data for all types of attacks. These imbalanced and outdated datasets decrease the efficiency of current IDSs, especially for rarely encountered attack types. In this paper, we propose six machine-learning-based IDSs by using K Nearest Neighbor, Random Forest, Gradient Boosting, Adaboost, Decision Tree, and Linear Discriminant Analysis algorithms. To implement a more realistic IDS, an up-to-date security dataset, CSE-CIC-IDS2018, is used instead of older and mostly worked datasets. The selected dataset is also imbalanced. Therefore, to increase the efficiency of the system depending on attack types and to decrease missed intrusions and false alarms, the imbalance ratio is reduced by using a synthetic data generation model called Synthetic Minority Oversampling TEchnique (SMOTE). Data generation is performed for minor classes, and their numbers are increased to the average data size via this technique. Experimental results demonstrated that the proposed approach considerably increases the detection rate for rarely encountered intrusions.Publication Independent Domination Polynomial of Zero-Divisor Graphs of Commutative Rings(Springer, 2022) Gürsoy, Necla Kırcalı; ÜLKER, ALPER; Gürsoy, ArifAn independent dominating set of a graph is a vertex subset that is both dominating and independent set in the graph, i.e., a maximal independent set. Also, the independent domination polynomial is an ordinary generating function for the number of independent dominating sets in the graph. In this paper, we examine independent domination polynomials of zero-divisor graphs of the ring Z(n) where n is an element of {2p, p(2), p(alpha), pq, p(2)q, pqr) and their roots. Finally, we prove the log-concavity and unimodality of their independent domination polynomials.Publication K-Uniformly Multivalent Functions Involving Liu-Owa Q-Integral Operator(Scientific and Technological Research Council of Turkey, 2021) ÇETİNKAYA, ASENAIn this paper, we introduce q-analogue of Liu-Owa integral operator and define k-uniformly multivalent starlike functions of order gamma, (0 <= gamma < p; p is an element of N) by using Liu-Owa q-integral operator. We examine coefficient estimates, growth and distortion bounds for the functions belonging to the subclass of k-uniformly multivalent starlike functions of order gamma. Moreover, we determine radii of k- uniformly starlikeness, convexity and close-to-convexity for the functions belonging to this subclass.