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Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati
Entire Large Positive Radial Symmetry Solutions For Combined Quasilinear Elliptic System, Seshadev Padhi, Smita Pati
Turkish Journal of Mathematics
We prove the existence of entire large positive solutions to the system \begin{equation*} \begin{cases} (r^{N-1}\phi_{1}(u^{\prime}))^{\prime} = r^{N-1}P_{1}(r)f(u,v),\, \, 0 \leq r < \infty \\ (r^{N-1}\phi_{2}(v^{\prime}))^{\prime} = r^{N-1}P_{2}(r)g(u,v),\, \, 0 \leq r < \infty \\ u(0) = a, \, v(0) = b, \, u^{\prime}(0) = 0, \, v^{\prime}(0) = b, \end{cases} \end{equation*} where the functions $\phi_{i}(s) = \alpha_{i}(s^{2})s, \,\, i= 1, 2$ are odd, increasing homeomorphisms, $P_{1},P_{2}:[0,\infty)\to [0,\infty)$ are continuous, and $f,g:[0,\infty) \times [0,\infty) \to [0,\infty)$ are continuous and increasing functions.
Pre-Markov Operators, Hülya Duru, Serkan İlter
Pre-Markov Operators, Hülya Duru, Serkan İlter
Turkish Journal of Mathematics
In operator theory characterizing extreme points has been systematically studied in a convex set of linear operators from an algebra to another. This paper presents some new characterizations. We define pre-Markov operators and identify when the second adjoint of a linear positive operator being an extreme point in the collection of all Markov operators between the unital second order duals of two unital f-algebras. Moreover a characterization of extreme points is given in the collection of all contractive operators between unital f-algebras. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.
Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er
Almost Symmetric Arf Partitions, Ni̇hal Gümüşbaş Öztürk, Nesri̇n Tutaş, Naci̇ Er
Turkish Journal of Mathematics
In this paper, we introduce almost symmetric Arf partitions (for short, ASA-partitions) and using properties of partitions of positive integers, we give the number of almost symmetric Arf semigroups of genus $g$.
A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials, Nesli̇han Kilar, Yilmaz Şi̇mşek
A Special Approach To Derive New Formulas For Some Special Numbers And Polynomials, Nesli̇han Kilar, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
By applying Laplace differential operator to harmonic conjugate components of the analytic functions and using Wirtinger derivatives, some identities and relations including Bernoulli and Euler polynomials and numbers are obtained. Next, using the Legendre identity, trigonometric functions and the Dirichlet kernel, some formulas and relations involving Bernoulli and Euler numbers, cosine-type Bernoulli and Euler polynomials, and sine-type Bernoulli and Euler polynomials are driven. Then, by using the generating functions method and the well-known Euler identity, many new identities, formulas, and combinatorial sums among the Fibonacci numbers and polynomials, the Lucas numbers and polynomials, the Chebyshev polynomials, and Bernoulli and Euler …
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü
Compactness Of Soft Cone Metric Space And Fixed Point Theorems Related To Diametrically Contractive Mapping, İsmet Altintaş, Kemal Taşköprü
Turkish Journal of Mathematics
In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point …
Banach Algebra Structure On Simple Extensions, Sara El Kinani
Banach Algebra Structure On Simple Extensions, Sara El Kinani
Turkish Journal of Mathematics
We study the existence of Banach algebra structures on simple extensions of a unitary commutative Banach algebra. The link with the integrality of these extensions is studied. For any simple extension, a characterization of the existence of the Banach algebra norm making continuous the canonical injection is also given.
Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt
Symmetric Polynomials In Leibniz Algebras And Their Inner Automorphisms, Şehmus Findik, Zeynep Özkurt
Turkish Journal of Mathematics
Let $L_n$ be the free metabelian Leibniz algebra generated by the set $X_n=\{x_1,\ldots,x_n\}$ over a field $K$ of characteristic zero. This is the free algebra of rank $n$ in the variety of solvable of class $2$ Leibniz algebras. We call an element $s(X_n)\in L_n$ symmetric if $s(x_{\sigma(1)},\ldots,x_{\sigma(n)})=s(x_1,\ldots,x_n)$ for each permutation $\sigma$ of $\{1,\ldots,n\}$. The set $L_n^{S_n}$ of symmetric polynomials of $L_n$ is the algebra of invariants of the symmetric group $S_n$. Let $K[X_n]$ be the usual polynomial algebra with indeterminates from $X_n$. The description of the algebra $K[X_n]^{S_n}$ is well known, and the algebra $(L_n')^{S_n}$ in the commutator ideal $L_n'$ …
Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n
Isotropic Riemannian Submersions, Feyza Esra Erdoğan, Bayram Şahi̇n
Turkish Journal of Mathematics
In this paper, we present the notion of isotropic submersions between Riemannian manifolds. We first give examples to illustrate this new notion. Then we express a characterization in terms of O'Neill's tensor field T and examine certain relations between sectional curvatures of the total manifold and the base manifold. We also study $\lambda$-isotropic submersions with pointwise planar horizontal sections.
Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ
Games Relating To Weak Covering Properties In Bitopological Spaces, Ali̇ Emre Eysen, Selma Özçağ
Turkish Journal of Mathematics
We study topological games related to weak forms of the Menger property in bitopological spaces. In particular we investigate almost Menger game and its connections to games which are associated with the covering properties consisting of covers containing $G_\delta$ subsets.
Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad
Neutral Multivalued Integro-Differential Evolution Equations With Infinite State-Dependent Delay, Abdelaziz Mebarki, Selma Baghli Bendimerad
Turkish Journal of Mathematics
Our problem through this work is to give the existence of mild solutions for the first order class of neutral functional multivalued integro-differential evolution equations with infinite state-dependent delay using the nonlinear alternative of Frigon for multivalued contraction maps in Fréchet spaces combined with the semi-group theory.
New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek
New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
The aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving these numbers and polynomials, the Bernoulli numbers and polynomials, the Stirling numbers of the second kind, the Catalan numbers and other classes of special numbers, polynomials and functions. Some infinite series representations, including the Catalan-type numbers and combinatorial numbers, are investigated. Moreover, some recurrence relations and computational algorithms for these numbers and polynomials are provided. By implementing these algorithms in the Python programming language, we illustrate the …
Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir
Existence Results For $\Psi $-Caputo Fractional Neutral Functional Integro-Differential Equations With Finite Delay, Abdellatif Boutiara, Mohamed S. Abdo, Maamar Benbachir
Turkish Journal of Mathematics
This research article deals with novel two species of initial value problems, one of them, the fractional neutral functional integrodifferential equations, and the other one, the coupled system of fractional neutral functional integrodifferential equations, with finite delay and involving a $\psi$-Caputo fractional operator. The existence and uniqueness results are studied through Banach's contraction principle and Krasnoselskii's fixed point theorem. We also establish two various kinds of Ulam stability results for the proposed problems. Further, two pertinent examples are presented to demonstrate the reported results.
Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak
Ascending Chains Of Ideals In The Polynomial Ring, Grzegorz Pastuszak
Turkish Journal of Mathematics
Assume that $K$ is a field and $I_{1}\subsetneq ...\subsetneq I_{t}$ is an ascending chain (of length $t$) of ideals in the polynomial ring $K[x_{1},...,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by polynomials of degrees less or equal to some natural number $f(j)\geq 1$, for any $j=1,...,t$. In the paper we construct, in an elementary way, a natural number B (m,f) (depending on $m$ and the function $f$) such that ≤ (m,f)$. We also discuss some applications of this result.
$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
$Q-$Hamiltonian Systems, Bi̇lender Paşaoğlu, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this paper, we develop the basic theory of linear $q-$ Hamiltonian systems. In this context, we establish an existence and uniqueness result. Regular spectral problems are studied. Later, we introduce the corresponding maximal and minimal operators for this system. Finally, we give a spectral resolution.
Digital Hurewicz Theorem And Digital Homology Theory, Samira Sahar Jamil, Danish Ali
Digital Hurewicz Theorem And Digital Homology Theory, Samira Sahar Jamil, Danish Ali
Turkish Journal of Mathematics
In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we obtain two main results that make this homology different from already existing homologies of digital images. We prove digital analog of Hurewicz theorem for digital cubical singular homology. We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.
$Q$-Analogues Of Five Difficult Hypergeometric Evaluations, Xiaojing Chen, Wenchang Chu
$Q$-Analogues Of Five Difficult Hypergeometric Evaluations, Xiaojing Chen, Wenchang Chu
Turkish Journal of Mathematics
A nonterminating balanced $q$-series is examined by means of the modified Abel lemma on summation by parts that leads to $q$-analogues of five difficult identities for classical hypergeometric series, including three formulae conjectured by Gosper in 1977.
The Möbius Transformation Of Continued Fractions With Bounded Upper And Lower Partial Quotients, Wencai Liu
The Möbius Transformation Of Continued Fractions With Bounded Upper And Lower Partial Quotients, Wencai Liu
Turkish Journal of Mathematics
Let $h$: $x\mapsto \frac{ax+b}{cx+d} $ be the nondegenerate Möbius transformation with integer entries. We get a bound of the continued fraction of $h(x)$ by upper and lower bounds of the continued fraction of $x$.
Higher-Order Character Dedekind Sum, Mümün Can
Higher-Order Character Dedekind Sum, Mümün Can
Turkish Journal of Mathematics
In this paper, we are interested in higher-order character Dedekind sum% \[ \sum\limits_{v=0}^{ck-1}\chi_{1}\left( v\right) \mathcal{B}_{p,\chi_{2}% }\left( a\frac{v+z}{c}+x\right) \mathcal{B}_{q}\left( b\frac{v+z}% {ck}+y\right) ,\text{ }a,b,c\in\mathbb{N} \text{ and }x,y,z\in\mathbb{R}, \] where $\chi_{1}$ and $\chi_{2}$ are primitive characters of modulus $k,$ $\mathcal{B}_{p}\left( x\right) $ and $\mathcal{B}_{p,\chi_{2}}\left( x\right) $ are Bernoulli and generalized Bernoulli functions, respectively. We employ the Fourier series technique to demonstrate reciprocity formulas for this sum. Derived formulas are analogues of Mikolas' reciprocity formula. Moreover, we offer Petersson--Knopp type identities for this sum.
Star Versions Of The Hurewicz Basis Covering Property And Strong Measure Zero Spaces, Manoj Bhardwaj, Alexander Osipov
Star Versions Of The Hurewicz Basis Covering Property And Strong Measure Zero Spaces, Manoj Bhardwaj, Alexander Osipov
Turkish Journal of Mathematics
In this paper,we introduced the star version of the Hurewicz basis covering property,studied by Babinkostova, Ko?cinac, and Scheepers in 2004. The authors obtained the relationship between star-selection principles and the star version of the Hurewicz basis covering property for metrizable spaces. We also consider the star version of Hurewicz measure zero spaces and characterized these new spaces by the star-selection principle related to star-Hurewicz spaces.
Pell-Lucas Collocation Method To Solve High-Order Linear Fredholm-Volterra Integro-Differential Equations And Residual Correction, Şuayi̇p Yüzbaşi, Gamze Yildirim
Pell-Lucas Collocation Method To Solve High-Order Linear Fredholm-Volterra Integro-Differential Equations And Residual Correction, Şuayi̇p Yüzbaşi, Gamze Yildirim
Turkish Journal of Mathematics
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 …
Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab
Analytic Functions Associated With Cardioid Domain, Sarfraz Nawaz Malik, Mohsan Raza, Janusz Sokol, Saira Zainab
Turkish Journal of Mathematics
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.
Max Cs And Min Cs Modules, Truong Dinh Tu, Thuat Do
Max Cs And Min Cs Modules, Truong Dinh Tu, Thuat Do
Turkish Journal of Mathematics
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.
Dual And Canonical Dual Of Controlled K-G-Frames In Hilbert Spaces, Hessam Hosseinnezhad
Dual And Canonical Dual Of Controlled K-G-Frames In Hilbert Spaces, Hessam Hosseinnezhad
Turkish Journal of Mathematics
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.
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Paksoy
Turkish Journal of Mathematics
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.
On Ternary Diophantine Equations Of Signature $(P,P,2)$ Over Number Fields, Erman Işik, Yasemi̇n Kara, Eki̇n Özman Karakurt
On Ternary Diophantine Equations Of Signature $(P,P,2)$ Over Number Fields, Erman Işik, Yasemi̇n Kara, Eki̇n Özman Karakurt
Turkish Journal of Mathematics
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.
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
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.
$T$-Soft Equality Relation, Tareq Alshami, Mohammed El-Shafei
$T$-Soft Equality Relation, Tareq Alshami, Mohammed El-Shafei
Turkish Journal of Mathematics
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 …
The Meyer Function On The Handlebody Group, Yusuke Kuno, Masatoshi Sato
The Meyer Function On The Handlebody Group, Yusuke Kuno, Masatoshi Sato
Turkish Journal of Mathematics
We give an explicit formula for the signature of handlebody bundles over the circle interms of the homological monodromy. This gives a cobounding function of Meyer's signature cocycle on the mapping class group of a 3-dimensional handlebody, i.e. the handlebody group. As an application, we give a topological interpretation for the generator of the first cohomology group of the hyperelliptic handlebody group.