• Title, Summary, Keyword: Analytic Inequalities

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SOME NEW INTEGRAL MEANS INEQUALITIES AND INCLUSION PROPERTIES FOR A CLASS OF ANALYTIC FUNCTIONS INVOLVING CERTAIN INTEGRAL OPERATORS

  • Raina, R.K.;Bansal, Deepak
    • East Asian mathematical journal
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    • v.24 no.4
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    • pp.347-358
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    • 2008
  • In this paper we investigate integral means inequalities for the integral operators $Q_{\lambda}^{\mu}$ and $P_{\lambda}^{\mu}$ applied to suitably normalized analytic functions. Further, we obtain some neighborhood and inclusion properties for a class of functions $G{\alpha}({\phi}, {\psi})$ (defined below). Several corollaries exhibiting the applications of the main results are considered in the concluding section.

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Coefficient Inequalities for Certain Subclasses of Analytic Functions Defined by Using a General Derivative Operator

  • Bulut, Serap
    • Kyungpook Mathematical Journal
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    • v.51 no.3
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    • pp.241-250
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    • 2011
  • In this paper, we define new classes of analytic functions using a general derivative operator which is a unification of the S$\breve{a}$l$\breve{a}$gean derivative operator, the Owa-Srivastava fractional calculus operator and the Al-Oboudi operator, and discuss some coefficient inequalities for functions belong to this classes.

FEKETE-SZEGÖ INEQUALITIES FOR A SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS DEFINED BY SĂLĂGEAN OPERATOR

  • BULUT, Serap
    • Honam Mathematical Journal
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    • v.39 no.4
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    • pp.591-601
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    • 2017
  • In this paper, by means of the $S{\breve{a}}l{\breve{a}}gean$ operator, we introduce a new subclass $\mathcal{B}^{m,n}_{\Sigma}({\gamma};{\varphi})$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to this class, we consider Fekete-$Szeg{\ddot{o}}$ inequalities.

GENERALIZED MINIMAX THEOREMS IN GENERALIZED CONVEX SPACES

  • Kim, Hoon-Joo
    • Honam Mathematical Journal
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    • v.31 no.4
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    • pp.559-578
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    • 2009
  • In this work, we obtain intersection theorem, analytic alternative and von Neumann type minimax theorem in G-convex spaces. We also generalize Ky Fan minimax inequality to acyclic versions in G-convex spaces. The result is applied to formulate acyclic versions of other minimax results, a theorem of systems of inequalities and analytic alternative.

On Certain Novel Subclasses of Analytic and Univalent Functions

  • Irmak, Huseyin;Joshi, Santosh Bhaurao;Raina, Ravinder Krishen
    • Kyungpook Mathematical Journal
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    • v.46 no.4
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    • pp.543-552
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    • 2006
  • The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

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UNITARILY INVARIANT NORM INEQUALITIES INVOLVING G1 OPERATORS

  • Bakherad, Mojtaba
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.889-899
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    • 2018
  • In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove $${\parallel}f(A)Xg(B){\pm}g(B)Xf(A){\parallel}_2{\leq}{\Large{\parallel}}{\frac{(I+{\mid}A{\mid})X(I+{\mid}B{\mid})+(I+{\mid}B{\mid})X(I+{\mid}A{\mid})}{^dA^dB}}{\Large{\parallel}}_2$$, where A, B, $X{\in}{\mathbb{M}}_n$ such that A, B are Hermitian with ${\sigma}(A){\cup}{\sigma}(B){\subset}{\mathbb{D}}$ and f, g are analytic on the complex unit disk ${\mathbb{D}}$, g(0) = f(0) = 1, Re(f) > 0 and Re(g) > 0.

SHARPENED FORMS OF ANALYTIC FUNCTIONS CONCERNED WITH HANKEL DETERMINANT

  • Ornek, Bulent Nafi
    • Korean Journal of Mathematics
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    • v.27 no.4
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    • pp.1027-1041
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    • 2019
  • In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H2(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

MORSE INEQUALITIES FOR MANIFOLDS WITH BOUNDARY

  • Zadeh, Mostafa Esfahani
    • Journal of the Korean Mathematical Society
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    • v.47 no.1
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    • pp.123-134
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    • 2010
  • The aim of this paper is to provide a proof for a version of the Morse inequalities for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof for it. Our proof is analytic and is based on the J. Roe account of Witten's approach to Morse Theory.