• 제목/요약/키워드: ${\varphi}_*$-Symmetric

검색결과 9건 처리시간 0.022초

Some Geometric Properties of η-Ricci Solitons on α-Lorentzian Sasakian Manifolds

  • Shashikant, Pandey;Abhishek, Singh;Rajendra, Prasad
    • Kyungpook Mathematical Journal
    • /
    • 제62권4호
    • /
    • pp.737-749
    • /
    • 2022
  • We investigate the geometric properties of 𝜂*-Ricci solitons on α-Lorentzian Sasakian (α-LS) manifolds, and show that a Ricci semisymmetric 𝜂*-Ricci soliton on an α-LS manifold is an 𝜂*-Einstein manifold. Further, we study 𝜑*-symmetric 𝜂*-Ricci solitons on such manifolds. We prove that 𝜑*-Ricci symmetric 𝜂*-Ricci solitons on an α-LS manifold are also 𝜂*-Einstein manifolds and provide an example of a 3-dimensional α-LS manifold for the existence of such solitons.

THE FEKETE-SZEGÖ COEFFICIENT INEQUALITY FOR A NEW CLASS OF m-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS SATISFYING SUBORDINATION CONDITION

  • Akgul, Arzu
    • 호남수학학술지
    • /
    • 제40권4호
    • /
    • pp.733-748
    • /
    • 2018
  • In this paper, we investigate a new subclass $S^{{\varphi},{\lambda}}_{{\Sigma}_m}$ of ${\Sigma}_m$ consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-$Szeg{\ddot{o}}$ inequalities for this class. Also, we establish estimates for the coefficients for this subclass and several related classes are also considered and connections to earlier known results are made.

ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS

  • Hazarika, Munmun;Phukon, Ambeswar
    • 대한수학회보
    • /
    • 제48권3호
    • /
    • pp.617-625
    • /
    • 2011
  • In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions ${\Phi}_0$, ${\Phi}_1$ and ${\Phi}_2$. Here we explicitly evaluate the Schur's function ${\Phi}_3$. Using this value we find necessary and sufficient conditions under which the Toeplitz operator $T_{\varphi}$ is hyponormal, where ${\varphi}$ is a trigonometric polynomial given by ${\varphi}(z)$ = ${\sum}^N_{n=-N}a_nz_n(N{\geq}4)$ and satisfies the condition $\bar{a}_N\(\array{a_{-1}\\a_{-2}\\a_{-4}\\{\vdots}\\a_{-N}}\)=a_{-N}\;\(\array{\bar{a}_1\\\bar{a}_2\\\bar{a}_4\\{\vdots}\\\bar{a}_N}\)$. Finally we illustrate the easy applicability of the derived results with a few examples.

SHARP BOUNDS OF FIFTH COEFFICIENT AND HERMITIAN-TOEPLITZ DETERMINANTS FOR SAKAGUCHI CLASSES

  • Surya Giri;S. Sivaprasad Kumar
    • 대한수학회보
    • /
    • 제61권2호
    • /
    • pp.317-333
    • /
    • 2024
  • For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S*s(𝜑) and Cs(𝜑), respectively, the sharp bound of the nth Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

ON THE ASYMPTOTIC CONVERGENCE OF ORTHONORMAL CARDINAL REFINABLE FUNCTIONS

  • Kim, Rae-Young
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • 제12권3호
    • /
    • pp.133-137
    • /
    • 2008
  • We prove an extended version of asymptotic behavior of the orthonormal cardinal refinable functions from Blaschke products introduced by Contronei et al [2]. In fact, we show the orthonormal cardinal refinable function ${\varphi}_{k,q}$ converges in $L^p(\mathbb{R})$ ($2{\leq}p{\leq}{\infty}$) to the Shannon refinable function as ${\kappa}{\rightarrow}{\infty}$ uniforml on a class $\mathcal{Q}_{A,B}$ of real symmetric polynomials determined by positive constants $A{\leq}B$.

  • PDF

VANISHING OF CONTACT CONFORMAL CURVATURE TENSOR ON 3-DIMENSIONAL SASAKIAN MANIFOLDS

  • Bang, Keumseong;Kye, JungYeon
    • Korean Journal of Mathematics
    • /
    • 제10권2호
    • /
    • pp.157-166
    • /
    • 2002
  • We show that the contact conformal curvature tensor on 3-dimensional Sasakian manifold always vanishes. We also prove that if the contact conformal curvature tensor vanishes on a 3-dimensional locally ${\varphi}$-symmetric contact metric manifold M, then M is a Sasakian space form.

  • PDF

CERTAIN RESULTS ON CONTACT METRIC GENERALIZED (κ, µ)-SPACE FORMS

  • Huchchappa, Aruna Kumara;Naik, Devaraja Mallesha;Venkatesha, Venkatesha
    • 대한수학회논문집
    • /
    • 제34권4호
    • /
    • pp.1315-1328
    • /
    • 2019
  • The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.

LOGHARMONIC MAPPINGS WITH TYPICALLY REAL ANALYTIC COMPONENTS

  • AbdulHadi, Zayid;Alarifi, Najla M.;Ali, Rosihan M.
    • 대한수학회보
    • /
    • 제55권6호
    • /
    • pp.1783-1789
    • /
    • 2018
  • This paper treats the class of normalized logharmonic mappings $f(z)=zh(z){\overline{g(z)}}$ in the unit disk satisfying ${\varphi}(z)=zh(z)g(z)$ is analytically typically real. Every such mapping f admits an integral representation in terms of its second dilatation function and a function of positive real part with real coefficients. The radius of starlikeness and an upper estimate for arclength are obtained. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when its second dilatation has real coefficients.

ROLLING STONES WITH NONCONVEX SIDES II: ALL TIME REGULARITY OF INTERFACE AND SURFACE

  • Lee, Ki-Ahm;Rhee, Eun-Jai
    • 대한수학회지
    • /
    • 제49권3호
    • /
    • pp.585-604
    • /
    • 2012
  • In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.