Cilt:71 Sayı:03 (2022)

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A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces
(Ankara Üniversitesi, 2022) Kaya, Esra; Other; Other
By using the L p ( ⋅ ) − boundedness of a maximal operator defined on homogeneous space, it has been shown that the B − maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the B − maximal operator generated by generalized translation operator under a continuity assumption on p ( ⋅ ) . It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.
A new system of generalized nonlinear variational inclusion problems in semi-inner product spacesA new system of generalized nonlinear variational inclusion problems in semi-inner product spaces
(Ankara Üniversitesi, 2022) Shaafi, Sümeera; Other; Other
In this work we reflect a new system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. By using resolvent operator technique, we offer an iterative algorithm for figuring out the approximate solution of the said system. The motive of this paper is to review the convergence analysis of a system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. The proposition used in this paper can be considered as an extension of propositions for examining the existence of solution for various classes of variational inclusions considered and studied by many authors in 2-uniformly smooth Banach spaces.
Associated curves from a different point of view in E 3
(Ankara Üniversitesi, 2022) Canlı, Davut; Other; Other
In this paper, tangent, principal normal and binormal wise associated curves are defined such that each of these vectors of any given curve lies on the osculating, normal and rectifying plane of its partner, respectively. For each associated curve, a new moving frame and the corresponding curvatures are formulated in terms of Frenet frame vectors. In addition to this, the possible solutions for distance functions between the curve and its associated mate are discussed. In particular, it is seen that the involute curves belong to the family of tangent associated curves in general and the Bertrand and the Mannheim curves belong to the principal normal associated curves. Finally, as an application, we present some examples and map a given curve together with its partner and its corresponding moving frame.
Coefficients of Randic and Sombor characteristic polynomials of some graph types
(Ankara Üniversitesi, 2022) Öz, Mehmet Sinan; Other; Other
Let G be a graph. The energy of G is defined as the summation of absolute values of the eigenvalues of the adjacency matrix of G. It is possible to study several types of graph energy originating from defining various adjacency matrices defined by correspondingly different types of graph invariants. The first step is computing the characteristic polynomial of the defined adjacency matrix of G for obtaining the corresponding energy of G. In this paper, formulae for the coefficients of the characteristic polynomials of both the Randic and the Sombor adjacency matrices of path graph Pn , cycle graph Cn are presented. Moreover, we obtain the five coefficients of the characteristic polynomials of both Randic and Sombor adjacency matrices of a special type of 3−regular graph Rn.
Combinatorial results of collapse for order-preserving and order-decreasing transformations
(Ankara Üniversitesi, 2022) Korkmaz, Emrah; Other; Other
The full transformation semigroup Tn is defined to consist of all functions from Xn={1,…,n} to itself, under the operation of composition. In \cite{JMH1}, for any α in Tn, Howie defined and denoted collapse by c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}. Let On be the semigroup of all order-preserving transformations and Cn be the semigroup of all order-preserving and decreasing transformations on Xn under its natural order, respectively. Let E(On) be the set of all idempotent elements of On, E(Cn) and N(Cn) be the sets of all idempotent and nilpotent elements of Cn, respectively. Let U be one of {Cn,N(Cn),E(Cn),On,E(On)}. For α∈U, we consider the set \imc(α)={t∈\im(α):|tα−1|≥2}. For positive integers 2≤k≤r≤n, we define U(k)={α∈U:t∈\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):∣∣⋃t∈\imc(α)tα−1|=r}. The main objective of this paper is to determine |U(k,r)|, and so |U(k)| for some values r and k.
Eigenvalue problems for a class of Sturm-Liouville operators on two different time scales
(Ankara Üniversitesi, 2022) Durna, Zeynep; Other; Other
In this study, we consider a boundary value problem generated by the Sturm-Liouville equation with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and the characteristic function of the problem on an arbitrary bounded time scale. Secondly, we prove some properties of eigenvalues and obtain a formulation for the eigenvalues-number on a finite time scale. Finally, we give an asymptotic formula for eigenvalues of the problem on another special time scale: T = [ α , δ 1 ] ⋃ [ δ 2 , β ] .
Erratum to: Zero-based invariant subspaces in the Bergman space
(Ankara Üniversitesi, 2022) Bouabddullah, Fatih; Other; Other
In this Erratum we would like to clarify statement and the proof of Theorem 2 in our paper: ”Zero-based invariant subspaces in the Bergman space Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(1) (2018), 277-285.”
Multivalent harmonic functions involving multiplier transformation
(Ankara Üniversitesi, 2022) Porwa, Saurabh; Other; Other
In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.
On difference of bivariate linear positive operators
(Ankara Üniversitesi, 2022) Ongun, Ali; Other; Other
In the present paper we give quantitative type theorems for the differences of different bivariate positive linear operators by using weighted modulus of continuity. Similar estimates are obtained via K-functional and for Chebyshev functionals. Moreover, an example involving Szasz and Szasz-Kantorovich operators is given.
On eigenfunctions of Hill's equation with symmetric double well potential
(Ankara Üniversitesi, 2022) Kabataş, Ayşe; Other; Other
Throughout this paper the asymptotic approximations for eigen- functions of eigenvalue problems associated with Hill’s equation satisfying periodic and semi-periodic boundary conditions are derived when the potential is symmetric double well. These approximations are used to determine the Green’s functions of the related problems. Then, the obtained results are adapted to the Whittaker-Hill equation which has the symmetric double well potential and is widely investigated in the literature.
On inequalities of Simpson's type for convex functions via generalized fractional integrals
(Ankara Üniversitesi, 2022) Hezenci, Fatih; Other; Other
Fractional calculus and applications have application areas in many different fields such as physics, chemistry, and engineering as well as mathematics. The application of arithmetic carried out in classical analysis in fractional analysis is very important in terms of obtaining more realistic results in the solution of many problems. In this study, we prove an identity involving generalized fractional integrals by using differentiable functions. By utilizing this identity, we obtain several Simpson’s type inequalities for the functions whose derivatives in absolute value are convex. Finally, we present some new results as the special cases of our main results.
On the maximum modulus of a complex polynomial
(Ankara Üniversitesi, 2022) Malik, Shabir; Other; Other
In this paper we impose distinct restrictions on the moduli of the zeros of p ( z ) = n ∑ v = 0 a v z v and investigate the dependence of ∥ p ( R z ) − p ( σ z ) ∥ , R > σ ≥ 1 on M α and M α + π , where M α = max 1 ≤ k ≤ n | p ( e i ( α + 2 k π ) / n ) | and on certain coefficients of p ( z ) . This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p ( 1 − w n ) , 0 < w ≤ given p ( 1 ) = 0 is considered.
On the solutions of the q-analogue of the telegraph differential equation
(Ankara Üniversitesi, 2022) Karahan, Döne; Other; Other
In this work, q-analogue of the telegraph differential equation is investigated. The approximation solution of q-analogue of the telegraph differential equation is founded by using the Laplace transform collocation method (LTCM). Then, the exact solution is compared with the approximation solution for q-analogue of the telegraph differential equation. The results showed that the method is useful and effective for q-analogue of the telegraph differential equation.
Power series methods and statistical limit superior
(Ankara Üniversitesi, 2022) Bayram, Nilay Şahin; Other; Other
Given a real bounded sequence x = ( x j ) and an infinite matrix A = ( a n j ) Knopp core theorem is equivalent to study the inequality l i m s u p A x ≤ l i m s u p x . Recently Fridy and Orhan [6] have considered some variants of this inequality by replacing l i m s u p x with statistical limit superior s t − l i m s u p x . In the present paper we examine similar type of inequalities by employing a power series method P ; a non-matrix sequence-to-function transformation, in place of A = ( a n j ) .
Role of ideals on σ -topological spaces
(Ankara Üniversitesi, 2022) Mıah, Chhapikul; Other; Other
In this writeup, we have discussed the role of ideals on σ -topological spaces. Using this idea, we have also studied and discussed two operators ( ) ∗ σ and ψ σ . We have extended this concept to a new generalized set and investigated some basic properties of these concepts using ( ) ∗ σ and ψ σ operators.
Soft semi-topological polygroups
(Ankara Üniversitesi, 2022) Davvaz, B.; Other; Other
By removing the condition that the inverse function is continuous in soft topological polygroups, we will have less constraint to obtain the results. We offer different definitions for soft topological polygroups and eliminate the inverse function continuity condition to have more freedom of action.
Some Hardy-type integral inequalities with sharp constant involving monotone functions
(Ankara Üniversitesi, 2022) SENOUCİ, Abdelkader; Other; Other
In this work, we present some Hardy-type integral inequalities for 0 < p < 1 via a second parameter q > 0 with sharp constant. This inequalities are new generalizations to the inequalities given below.
Tail dependence estimation based on smooth estimation of diagonal section
(Ankara Üniversitesi, 2022) Susam, Selim Orhun; Other; Other
This paper is mainly developed around the diagonal section which is strongly related to tail dependence coefficients as defined in Nelsen [19]. Hence, we propose a flexible method for estimating tail dependence coefficients based on the new smooth estimation of the diagonal section based on the Bernstein polynomial approximation. To assess the performance of the new estimators we conduct the Monte-Carlo simulation study. As a result of the simulation study, both estimators perform satisfactory performance. Also, the estimation methods are illustrated by real data examples.
The Minkowski type inequalities for weighted fractional operators
(Ankara Üniversitesi, 2022) Gürbüz, Mustafa; Other; Other
In this article, inequalities of reverse Minkowski type involving weighted fractional operators are investigated. In addition, new fractional integral inequalities related to Minkowski type are also established.
Timelike loxodromes on Lorentzian helicoidal surfaces in Minkowski n-space
(Ankara Üniversitesi, 2022) Demirci, Burcu Bektaş; Other; Other
In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski n -space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian helicoidal surfaces in E n 1 according to the causal characters of their meridian curves. Then, by finding general solutions, we get the explicit parametrizations of such timelike loxodromes. In particular, we investigate the timelike loxodromes on the three kinds of Lorentzian right helicoidal surfaces in E n 1 . Finally, we give an example to visualize the results.

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