• 제목/요약/키워드: Analytic Inequalities

검색결과 53건 처리시간 0.022초

On Certain Novel Subclasses of Analytic and Univalent Functions

  • Irmak, Huseyin;Joshi, Santosh Bhaurao;Raina, Ravinder Krishen
    • Kyungpook Mathematical Journal
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    • 제46권4호
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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
    • 대한수학회논문집
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    • 제33권3호
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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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    • 제27권4호
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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
    • 대한수학회지
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    • 제47권1호
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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.

CONVEXITY OF INTEGRAL OPERATORS GENERATED BY SOME NEW INEQUALITIES OF HYPER-BESSEL FUNCTIONS

  • Din, Muhey U.
    • 대한수학회논문집
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    • 제34권4호
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    • pp.1163-1173
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    • 2019
  • In this article, we deduced some new inequalities related to hyper-Bessel function. By using these inequalities we will find some sufficient conditions under which certain families of integral operators are convex in the open unit disc. Some applications related to these results are also the part of our investigation.

SOME REMARKS OF THE CARATHÉODORY'S INEQUALITY ON THE RIGHT HALF PLANE

  • Ornek, Bulent Nafi
    • 대한수학회논문집
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    • 제35권1호
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    • pp.201-215
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    • 2020
  • In this paper, a boundary version of Carathéodory's inequality on the right half plane for p-valent is investigated. Let Z(s) = 1+cp (s - 1)p +cp+1 (s - 1)p+1 +⋯ be an analytic function in the right half plane with ℜZ(s) ≤ A (A > 1) for ℜs ≥ 0. We derive inequalities for the modulus of Z(s) function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of these inequalities is proved.

FEKETE-SZEGÖ INEQUALITIES OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS AND APPLICATIONS TO SOME DISTRIBUTION SERIES

  • SOUPRAMANIEN, T.;RAMACHANDRAN, C.;CHO, NAK EUN
    • Journal of applied mathematics & informatics
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    • 제39권5_6호
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    • pp.725-742
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    • 2021
  • The aim of this article is to estimate the coefficient bounds of certain subclasses of analytic functions. We claim that this is a novel and unique effort in combining the coefficient functional along with the new domains and the probability distributions which have not been found or are available in the literature of coefficients bounds. Here the authors analyze these bounds in the special domains associated with exponential function and sine function. Further we obtain Fekete-Szegö inequalities for the defined subclasses of analytic functions defined through Poisson distribution series and Pascal distribution series.

APPLICATIONS OF SUBORDINATION PRINCIPLE FOR ANALYTIC FUNCTIONS CONCERNED WITH ROGOSINSKI'S LEMMA

  • Aydinoglu, Selin;Ornek, Bulent Nafi
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제27권4호
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    • pp.157-169
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    • 2020
  • In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, 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.

DIFFERENTIAL INEQUALITIES ASSOCIATED WITH CARATHÉODORY FUNCTIONS

  • In Hwa, Kim;Nak Eun, Cho
    • Nonlinear Functional Analysis and Applications
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    • 제27권4호
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    • pp.773-784
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    • 2022
  • The purpose of the present paper is to estimate some real parts for certain analytic functions with some applications in connection with certain integral operators and geometric properties. Also we extend some known results as special cases of main results presented here.

SOME RESULTS ASSOCIATED WITH CERTAIN ANALYTIC AND UNIVALENT FUNCTIONS INVOLVING FRACTIONAL DERIVATIVE OPERATORS

  • Irmak, H.;Raina, R.K.
    • East Asian mathematical journal
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    • 제21권2호
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    • pp.219-231
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    • 2005
  • This paper investigates some results (Theorems 2.1-2.3, below) concerning certain classes of analytic and univalent functions, involving the familiar fractional derivative operators. We state interesting consequences arising from the main results by mentioning the cases connected with the starlikeness, convexity, close-to-convexity and quasi-convexity of geometric function theory. Relevant connections with known results are also emphasized briefly.

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