## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (203.669 recursos)

Tbilisi Mathematical Journal

1. #### Operator on Hilbert space and its application to certain multivalent functions with fixed point associated with hypergeometric function

Gbolagade, A. M.; Makinde, D. O.
By applying hypergeometric operator on Hilbert space, the author introduces a new class of meromorphic multivalent functions with an arbitrary fixed point omega. Properties such as coefficient inequalities, distortion bounds and extreme points were derived. Furthermore, the effect of this operator on functions in this class was also investigated.

2. #### Schur-convexity of the Catalan–Qi function related to the Catalan numbers

Qi, Feng; Shi, Xiao-Ting; Mahmoud, Mansour; Liu, Fang-Fang
In the paper, the authors present the Schur-convexity of the absolute of the logarithm of the Catalan–Qi function and prove the logarithmically complete monotonicity of the Catalan–Qi function.

3. #### Gabor frames on local fields of positive characteristic

Shah, Firdous A.
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply that the Gabor systems are Gabor frames is among the core problems in time-frequency analysis. In this paper, we give some simple and sufficient conditions that ensure a Gabor system $\left\{M_{u(m)b}T_{u(n)a}g=:\chi_{m}(bx)g\big(x-u(n)a\big)\right\}_{ m,n\in\mathbb N_0}$ to be a frame for $L^2(K)$. The conditions proposed are stated in terms of the Fourier transforms of the Gabor system's generating functions.

4. #### Multiplicity result for a stationary fractional reaction-diffusion equations

Ledesma, César E. Torres
In this paper, we consider the stationary fractional reaction-diffusion equations with Riemann-Liouville boundary conditions \begin{aligned} &{_{x}}D_{T}^{\alpha}({_{0}}D_{x}^{\alpha}u(x)) + {_{0}}D_{x}^{\beta}({_{x}}D_{T}^{\beta}u(x)) = f(x,u(x)),\;\;x\in (0,T),\\ &\lim_{x\to 0} {_{0}}I_{x}^{1-\alpha}u(x) = \lim_{x\to T} {_{x}}I_{T}^{1-\beta}u(x) = 0. \end{aligned} (0.1) ¶ where $0\lt \alpha , \beta \lt 1$ and $f\in C([0,T] \times \mathbb{R}, \mathbb{R})$. Under suitable conditions on the nonlinearity $f$, we study the multiplicity of weak solutions of (0.1) by using the genus in the critical point theory.

5. #### Matlis flat modules

Selvaraj, C.; Prabakaran, P.
In this paper, we introduce Matlis flat modules as a generalization of copure flat modules and give their characterizations. We prove that if $R$ is a commutative Artinian ring and $S \subset R$ is a multiplicative set, then $S^{-1}M$ is a Matlis flat $S^{-1}R$-module for any Matlis flat $R$-module $M$. Also we prove that every module has Matlis flat preenvelope over commutative Artinian rings.

6. #### Ulam-Hyers stability of undecic functional equation in quasi-$\beta$-normed spaces: Fixed point method

Ravi, K.; Rassias, J.M.; Kumar, B.V. Senthil
In this paper, we acquire the general solution of the undecic functional equation \begin{align*} & f(x+6y)-11f(x+5y)+55f(x+4y)-165f(x+3y)+330f(x+2y)\\ & \qquad\qquad -462f(x+y)+462f(x)-330f(x-y)+165f(x-2y)-55f(x-3y)\\ & \quad\qquad\qquad\qquad\qquad\qquad +11f(x-4y)-f(x-5y)=39916800f(y). \end{align*} We also obtain the generalized Ulam-Hyers stability of the above functional equation in quasi-$\beta$-normed spaces using fixed point method. Moreover, we investigate the pertinent stabilities of the above functional equation using sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms as upper bounds. We also present a counter-example for non-stability of the above functional equation in singular case.

7. #### Advances on the coefficient bounds for m-fold symmetric bi-close-to-convex functions

Jahangiri, Jay M.; Hamidi, Samaneh G.
In 1955, Waadeland considered the class of m-fold symmetric starlike functions of the form $f_{m}(z)=z+\sum_{n=1}^{\infty }a_{mn+1}z^{mn+1}$; $m\geq 1$; $|z|\lt1$ and obtained the sharp coefficient bounds $|a_{mn+1}|\leq\left[ (2/m+n-1)!\right] /\left[ (n!)(2/m-1)!\right]$. Pommerenke in 1962, proved the same coefficient bounds for m-fold symmetric close-to-convex functions. Nine years later, Keogh and Miller confirmed the same bounds for the class of m-fold symmetric Bazilevic functions. Here we will show that these bounds can be improved even further for the m-fold symmetric bi-close-to-convex functions. Moreover, our results improve those corresponding coefficient bounds given by Srivastava et al that appeared in 7(2) (2014) issue of this...

8. #### A note on closedness of algebraic sum of sets

Przybycień, Hubert
In this note we generalize the fact that in topological vector spaces the algebraic sum of closed set $A$ and compact set $B$ is closed. We also prove some conditions that are equivalent to reflexivity of Banach spaces.

9. #### Some results on uniqueness of meromorphic functions sharing a polynomial

Sahoo, Pulak; Saha, Biswajit
In this paper, with the aid of weighted value sharing we study the uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial with weight two. The result of the paper not only improves the results due to the present first author [Bull. Math. Anal. Appl., 2(2010), 106-118] and of Zhang and Xu [Comput. Math. Appl., 61(2011), 722-730], at the same time finds a possible answer of an open question posed by Zhang and Xu.

10. #### On algebraic solitons for geometric evolution equations on three-dimensional Lie groups

Wears, Thomas H.
The relationship between algebraic soliton metrics and self-similar solutions of geometric evolution equations on Lie groups is investigated. After discussing the general relationship between algebraic soliton metrics and self-similar solutions to geometric evolution equations, we investigate the cross curvature flow and the second order renormalization group flow on simply-connected, three-dimensional, unimodular Lie groups, providing a complete classification of left invariant algebraic solitons that give rise to self-similar solutions of the corresponding flows on such spaces.

11. #### The spectrum operator of $\chi^{2}$ sequence space defined by Musielak Orlicz function

Subramanian, N.; Esi, A.
In this paper we have examined various spectrum of the operator $D\left(p,q,r,s\right)$ on the sequence space $\chi^{2}$ defined by Musielak Orlicz function.

12. #### Inclusion theorems of double Deferred Cesàro means II

Patterson, Richard F.; Nuray, Fatih; Başarir, Metin
In 1932 R. P. Agnew present a definition for Deferred Cesàro mean. Using this definition R. P. Agnew present inclusion theorems for the deferred and none Deferred Cesàro means. This paper is part 2 of a series of papers that present extensions to the notion of double Deferred Cesàro means. Similar to part 1 this paper uses this definition and the notion of regularity for four dimensional matrices, to present extensions and variations of the inclusion theorems presented by R. P. Agnew in [2].

13. #### Bi-unique range sets with smallest cardinalities for the derivatives of meromorphic functions

Banerjee, Abhijit; Mallick, Sanjay
Inspired by the advent of bi-unique range sets [2], we obtain a new bi-unique range sets, with smallest cardinalities ever for the derivatives of meromorphic functions which improves all the results obtained so far in some sense including a result of Banerjee-Bhattacharjee [4]. Furthermore at the last section we pose an open question for future research.

14. #### Fractional variational approach with non-standard power-law degenerate Lagrangians and a generalized derivative operator

We extend the fractional actionlike variational approach where we substitute the standard Lagrangian by a non-standard power-law Lagrangian holding a generalized derivative operator. We focus on degenerate Lagrangians for the constructed fractional formalism where we show that non-linear oscillators with damping solutions may be obtained from degenerate non-standard Lagrangians which are linear in velocities. We explore as well the case of $2^{nd}$-order derivatives non-standard Lagrangians and we study the case where Lagrangians are linear in accelerations where damping solutions are obtained as well. It was observed that these extensions give another possibility to obtain more fundamental aspects which may have...

15. #### Chromatic number of Harary graphs

A proper coloring of a graph $G$ is a function from the vertices of the graph to a set of colors such that any two adjacent vertices have different colors, and the chromatic number of $G$ is the minimum number of colors needed in a proper coloring of a graph. In this paper, we will find the chromatic number of the Harary graphs, which are the circulant graphs in some cases.

16. #### Properties of certain new special polynomials associated with Sheffer sequences

Raza, Nusrat; Khan, Subuhi; Ali, Mahvish
In this article, the Laguerre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Certain important properties of these polynomials are established. Further, operational and integral representations for these mixed polynomials are derived.

17. #### On the generalized orthogonal stability of mixed type additive-cubic functional equations in modular spaces

El-Fassi, Iz-iddine; Kabbaj, Samir
In this paper, we establish the Hyers-Ulam-Rassias stability of the mixed type additive-cubic functional equation $$f(2x+y)+f(2x-y)-f(4x)=2[f(x+y)+f(x-y)]-8f(2x)+10f(x)-2f(-x),$$ with $x\bot y,$ where $\bot$ is the orthogonality in the sense of Rätz in modular spaces.

18. #### A generalization of $\lambda-$slant Toeplitz operators

Datt, Gopal; Aggarwal, Ritu
We compute and study the behavior of the solutions of the equation $\lambda M_{z} X = X M_{{z}^k}$, which are referred as generalized $\lambda -$slant Toeplitz operators, for general complex number $\lambda$ and $k \geq 2$.

19. #### Multipliers and convolution spaces for the Hankel space and its dual on the half space $[0,+\infty [ \times\mathbb{R}^n$

Baccar, C.
We define the Hankel space $\mathbb{H}_\mu(]0,+\infty[\times\mathbb{R}^n)$; $\mu\geqslant -\frac{1}{2}$, and its dual $\mathbb{H'}_\mu(]0,+\infty[\times\mathbb{R}^n)$. First, we characterize the space $\mathscr{M}_\mu([0,+\infty[\times\mathbb{R}^n)$ of multipliers of the space $\mathbb{H}_\mu(]0,+\infty[\times\mathbb{R}^n)$. Next, we define a subspace $\mathbb{O}'_\mu([0,+\infty[\times \mathbb{R}^n)$ of the dual $\mathbb{H'}_\mu(]0,+\infty[\times\mathbb{R}^n)$ which permits to define and study a convolution product $\ast$ on $\mathbb{H'}_\mu(]0,+\infty[\times\mathbb{R}^n)$ and we give nice properties.

20. #### Various generalized Ulam-Hyers stabilities of a nonic functional equations

Rassias, John M.; Arunkumar, M.; Sathya, E.; Namachivayam, T.
In this paper, we have established the general solution and generalized Ulam - Hyers stability of the following nonic functional equation \begin{align*} & f(x+5y)-9f(x+4y)+36f(x+3y)-84f(x+2y)+126f(x+y)-126f(x)\\ & \qquad \qquad\qquad\qquad +84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9! f(y) \end{align*} where $9! = 362880$ in a Banach Space ($\textbf{BS}$), Felbin's type Fuzzy Normed Space ($\textbf{FFNS}$) and Intuitionistic Fuzzy Normed Space ($\textbf{IFNS}$) using the standard direct and fixed point method.

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