Authors:Kordan OSPANOV ; Adılet YESBAYEV Abstract: We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Jınjıa LI Abstract: This paper studies the distribution of socle degrees of $R/I^{[p^e]}$ when $e$ is large, for a homogeneous ideal $I$ in a two-dimensional standard-graded normal domain $R$ in positive characteristic $p$. We prove that the distribution is very much related to the asymptotic slopes of the syzygy bundle Syz$ I $, which have been known to determine the Hilbert-Kunz multiplicity of $I$. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Yasemin BAŞCI ; Süleyman ÖĞREKÇİ , Adil MISIR Abstract: In this paper, we deal with the Hyers-Ulam-Rassias HUR and Hyers-Ulam HU stability of Hadamard type fractional integral equations on compact intervals. The stability conditions are developed using a new generalized metric GM definition and the fixed point technique by motivating Wang and Lin Ulam's type stability of Hadamard type fractional integral equations. Filomat 2014; 28 7 : 1323-1331. Moreover, our approach is efficient and ease in use than to the previously studied approaches. Finally, we give two examples to explain our main results. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Iva DOKUZOVA Abstract: A 3-dimensional Riemannian manifold equipped with a tensor structure of type 1,1 , whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e. these structures are circulant. An associated manifold, whose metric is expressed by both structures, is studied. Three classes of such manifolds are considered. Two of them are determined by special properties of the curvature tensor of the manifold. The third class is composed by manifolds whose structure is parallel with respect to the Levi-Civitaconnection of the metric. Some geometric characteristics of these manifolds are obtained. Examples of such manifolds are given PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Mohamed Mahmoud CHEMS-EDDIN ; Abdelkader ZEKHNINI , Abdelmalek AZIZI Abstract: In this paper, we investigate the unit groups, the 2-class groups, the 2-class field towers and the structures of the second 2-class groups of some multiquadratic number fields of degree 8 and 16. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:İsmet YILDIZ ; Alaattin AKYAR Abstract: In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \ a,b\ , and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \ \alpha=2^{-r}\ and order \ \alpha=2^{-r}\ type $\beta=2^{-1}$, with $r$ is a positive integer. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Tareq ALSHAMI ; Mohammed EL-SHAFEI Abstract: The desire of generalizing some set-theoretic properties to the soft set theory motivated many researchers to define various types of soft operators. For example, they redefined the complement of a soft set, and soft union and intersection between two soft sets in a way that satisfies De Morgan's laws. In this paper, we introduce and study the concepts of $T$-soft subset and $T$-soft equality relations. Then, we utilize them to define the concepts of $T$-soft union and $T$-soft intersection for arbitrary family of soft sets. By $T$-soft union, we successfully keep some classical properties via soft set theory. We conclude this work by giving and investigating new types of soft linear equations with respect to some soft equality relations. Illustrative examples are provided to elucidate main obtained results. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Ahleme BOUAKKAZ ; Rabah KHEMIS Abstract: In this paper, we consider a class of second order differential equations with iterative source term. The main results are obtained by virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green's function which allows us to prove the existence of positive periodic solutions. Finally, an example is included to illustrate the correctness of our results. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Gurnınder Sıngh SANDHU ; Didem KARALARLIOĞLU CAMCI Abstract: Let $R$ be a prime ring with center $Z R $ and an automorphism $\alpha.$ A mapping $\delta:R\to R$ is called multiplicative skew derivation if $\delta xy =\delta x y+ \alpha x \delta y $ for all $x,y\in R$ and a mapping $F:R\to R$ is said to be multiplicative generalized -skew derivation if there exists a unique multiplicative skew derivation $\delta$ such that $F xy =F x y+\alpha x \delta y $ for all $x,y\in R.$ In this paper, our intent is to examine the commutativity of $R$ involving multiplicative generalized -skew derivations that satisfy the following conditions: i $F x^{2} +x\delta x =\delta x^{2} +xF x $, ii $F x\circ y =\delta x\circ y \pm x\circ y$, iii $F [x,y] =\delta [x,y] \pm [x,y]$, iv $F x^{2} =\delta x^{2} $, v $F [x,y] =\pm x^{k}[x,\delta y ]x^{m}$, vi $F x\circ y =\pm x^{k} x\circ\delta y x^{m}$, vii $F [x,y] =\pm x^{k}[\delta x ,y]x^{m}$, viii $F x\circ y =\pm x \delta x \circ y x^{m}$ for all $x,y\in R.$ PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Çağrı KARAMAN ; Zühre TOPUZ Abstract: In this paper, we investigated a new manifold with a poly-Norden structure, which is inspired by the positive root of the equation $x^{2}-mx-1=0$. We call this new manifold as holomorphic poly-Norden manifolds. We examine some properties of the Riemann curvature tensor and give an example of this manifold. Then, we define a different connection on this manifold which is named the semisymmetric metric poly F-connection and study some properties of the curvature and torsion tensor field according to this connection. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Weı-chuan CHEN ; Yanhsıou CHENG Abstract: In this paper, we study the inverse nodal problem and the eigenvalue gap for the one-dimensional sloshing problem with the $p$-Laplacian operator. By applying the Prüfer substitution, we first derive the reconstruction formula of the depth function by using the information of the nodal data. Furthermore, we employ the Tikhonov regularization method to consider how to reconstruct the depth function using only zeros of one eigenfunction. Finally, we investigate the eigenvalue gap under the restriction of symmetric single-well depth functions. We show the gap attains its minimum when the depth function is constant. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Şuayip TOPRAKSEVEN Abstract: In this study, Lyapunov-type inequalities for fractional boundary value problems involving the fractional Caputo Fabrizio differential equation with mixed boundary conditions when the fractional order of $\beta \in 1,2]$ and Dirichlet-type boundary condition when the fractional order of $\sigma \in 2,3]$ have been derived. Some consequences of the results related to the fractional Sturm'Liouville eigenvalue problems have also been given. Additionally, we examine the nonexistence of the solution of the fractional boundary value problem. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Nihal TAŞ Abstract: In this paper, we prove new fixed-circle resp. fixed-disc results using the bilateral type contractions on a metric space. To do this, we modify some known contractive conditions called the Jaggi-type bilateral contraction and the Dass-Gupta type bilateral contraction. We give some examples to show the validity of our obtained results. Also, we construct an application to rectified linear units activation functions used in the neural networks. This application shows the importance of studying "fixed-circle problem". PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Saıd R GRACE ; Iren JADLOVSKA , Ercan TUNÇ Abstract: Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations with a superlinear neutral term to be either oscillatory or convergent to zero asymptotically. Examples illustrating the results are included and some suggestions for further research are indicated. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Yacıne HALIM ; Massaoud BERKAL , Amıra KHELIFA Abstract: In this paper we solve the following system of difference equations \begin{equation*} x_{n+1}=\dfrac{z_{n-1}}{a+by_nz_{n-1}},\quad y_{n+1}=\dfrac{x_{n-1}}{a+bz_nx_{n-1}},\quad z_{n+1}=\dfrac{y_{n-1}}{a+bx_ny_{n-1}},\quad n\in \mathbb{N}_{0} \end{equation*} where parameters $a, b$ and initial values $x_{-1},x_{0},y_{-1},y_{0},z_{-1},z_{0}$ are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Aslı Bektaş KAMIŞLIK ; Büşra ALAKOÇ , Tülay KESEMEN , Tahir KHANİYEV Abstract: We consider a classical semi-Markovian stochastic model of type $ s,S $ with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as $\Gamma g $ that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process $X t $ which represents semi-Markovian renewal reward process of type $ s,S $. We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process $X t $. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Antonıo BOCCUTO ; Kamil DEMİRCİ , Sevda YILDIZ Abstract: We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Vehbı Emrah PAKSOY Abstract: In this work we construct a cone comprised of a group of tensors hypermatrices satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Tuncay Deniz ŞENTÜRK ; Göksal BİLGİCİ , Ahmet DAŞDEMİR , Zafer ÜNAL Abstract: In this paper, we study Horadam hybrid numbers. For these numbers, we give the exponential generating function, Poisson generating function, generating matrix, Vajda's, Catalan's, Cassini's, and d'Ocagne's identities. In addition, we offer Honsberger formula, general bilinear formula, and some summation formulas for these numbers. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Erman IŞIK ; Yasemin KARA , Ekin ÖZMAN KARAKURT Abstract: Let $K$ be a totally real number field with narrow class number one and $O_K$ be its ring of integers. We prove that there is a constant $B_K$ depending only on $K$ such that for any prime exponent $p>B_K$ the Fermat type equation $x^p+y^p=z^2$ with $x,y,z\in O_K$ does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Hessam HOSSEINNEZHAD Abstract: This paper is devoted to studying the controlled dual K-g-Bessel sequences of controlled K-g-frames. In fact, we introduce the concept of dual K-g-Bessel sequences of controlled K-g-frames and then, we present some necessary and/or sufficient conditions under which a controlled g-Bessel sequence is a controlled dual K-g-frame of a given controlled K-g-frame. Subsequently, we pay attention to investigating the structure of the canonical controlled dual K-g-Bessel sequence of a Parseval controlled K-g-frame and some other related results. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Truong Dınh TU ; Thuat DO Abstract: In this work, we study max CS, min CS, max-min CS modules and their endomorphism rings. Under certain conditions e.g., related to nonsingularity and duo-ness , we prove that a module is max CS if and only if it is min CS, and that direct sums of min max CS modules is again min max CS. Finally, symmetry of max-min CS property on the endomorphism rings of max-min CS modules is investigated. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Olawale OYEWOLE ; Oluwatosın MEWOMO , Lateef JOLAOSO , Safeer Hussain KHAN Abstract: In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-$% \phi $-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space $E_1$ and a smooth, strictly convex, and reflexive Banach space $% E_2$. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our algorithm in comparison with other existing algorithms in the literature. Our results extend and improve many recent results in this direction. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Cornelıa-lıvıa BEJAN ; Şemsi Eken MERİÇ , Erol KILIÇ Abstract: The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Ufuk ÇELİK ; Nihal ÖZGÜR Abstract: We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Xıaomeng LI Abstract: Let $W^{1,2} \mathbb{R}^2 $ be the standard Sobolev space. Denote for any real number $p>2$ \begin{align*}\lambda_{p}=\inf\limits_{u\in W^{1,2} \mathbb{R}^2 ,u\not\equiv0}\frac{\int_{\mathbb{R}^{2}} \nabla u ^2+ u ^2 dx}{ \int_{\mathbb{R}^{2}} u ^pdx ^{2/p}}. \end{align*} Define a norm in $W^{1,2} \mathbb{R}^2 $ by \begin{align*}\ u\ _{\alpha,p}=\left \int_{\mathbb{R}^{2}} \nabla u ^2+ u ^2 dx-\alpha \int_{\mathbb{R}^{2}} u ^pdx ^{2/p}\right ^{1/2}\end{align*} where $0\leq\alpha2$ and $0\leq\alpha PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Şuayip YÜZBAŞI ; Gamze YILDIRIM Abstract: In this article, a collocation method based on Pell-Lucas polynomials is studied to numerically solve higher order linear Fredholm-Volterra integro differential equations FVIDE . The approximate solutions are assumed in form of the truncated Pell-Lucas polynomial series. By using Pell-Lucas polynomials and relations of their derivatives, the solution form and its derivatives are brought to matrix forms. By applying the collocation method based on equally spaced collocation points, the method reduces the problem to a system of linear algebraic equations. Solution of this system determines the coefficients of assumed solution. Error estimation is made and also a method with the help of the obtained approximate solution is developed that finds approximate solution with better results. Then, the applications are made on five examples to show that the method is successful. In addition, the results are supported by tables and graphs and the comparisons are made with other methods available in the literature. All calculations in this study have been made using codes written in Matlab. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Burcu BEKTAŞ DEMİRCİ ; Nazım AGHAYEV Abstract: Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, image and signal processing, and computer graphics. However, classical quaternions are mostly used as a representation of rotation of a vector in $3$-dimensions, and connection between its geometric interpretation and algebraic structures is still not well-developed and needs more improvements. In this study, we develop an approach to understand quaternions multiplication defining subspaces of quaternion $\mathbb{H}$, called as $\mbox{Plane} N $ and $\mbox{Line} N $, and then, we observe the effects of sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations in geometry using quaternion. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Muradiye ÇİMDİKER ; Yasin ÜNLÜTÜRK Abstract: In this study, we define a variational field for constructing a family of Frenet curvesof the length l lying on a connected oriented hypersurface and calculate the length of the variational curves due to the ED-frame field in Euclidean 4-space. And then, we derive the intrinsic equations for the variational curves and also obtain boundary conditions for this type of curves due to the ED-frame field in Euclidean 4-space. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Abdel Moneım LASHIN ; Fatma ELEMAM Abstract: In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions defined in the open unit disc. We use the Faber polynomial expansions to find upper bounds for the $n$th$~ n\geq 3 $ Taylor-Maclaurin coefficients $\left\vert a_{n}\right\vert $ of functions belong to these new subclasses with $a_{k}=0$ for $2\leq k\leq n-1$, also we find non-sharp estimates on the first two coefficients $\left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $. The results, which are presented in this paper, would generalize those in related earlier works of several authors. PubDate: Sat, 01 Aug 2020 00:00:00 +030

Authors:Sarfraz Nawaz MALIK ; Mohsan RAZA , Janusz SOKOL , Saıra ZAINAB Abstract: In this article, we define and study new domain for analytic functions which is named as cardioid domain for being of cardioid structure. Analytic functions producing cardioid domain are defined and studied to some extent. The Fekete-Szegö inequality is also investigated for such analytic functions. PubDate: Sat, 01 Aug 2020 00:00:00 +030