• 제목/요약/키워드: p-convex function

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p-PRECONVEX SETS ON PRECONVEXITY SPACES

  • Min, Won-Keun
    • 호남수학학술지
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    • 제30권3호
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    • pp.425-433
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    • 2008
  • In this paper, we introduce the concept of p-preconvex sets on preconvexity spaces. We study some properties for p-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of pc-convex function, $p^*c$-convex function, pI-convex function and $p^*I$-convex function.

LAZHAR TYPE INEQUALITIES FOR p-CONVEX FUNCTIONS

  • Toplu, Tekin;Iscan, Imdat;Maden, Selahattin
    • 호남수학학술지
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    • 제44권3호
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    • pp.360-369
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    • 2022
  • The aim of this study is to establish some new Jensen and Lazhar type inequalities for p-convex function that is a generalization of convex and harmonic convex functions. The results obtained here are reduced to the results obtained earlier in the literature for convex and harmonic convex functions in special cases.

s-CONVEX FUNCTIONS IN THE THIRD SENSE

  • Kemali, Serap;Sezer, Sevda;Tinaztepe, Gultekin;Adilov, Gabil
    • Korean Journal of Mathematics
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    • 제29권3호
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    • pp.593-602
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    • 2021
  • In this paper, the concept of s-convex function in the third sense is given. Then fundamental characterizations and some basic algebraic properties of s-convex function in the third sense are presented. Also, the relations between the third sense s-convex functions according to the different values of s are examined.

SVN-Ostrowski Type Inequalities for (α, β, γ, δ) -Convex Functions

  • Maria Khan;Asif Raza Khan;Ali Hassan
    • International Journal of Computer Science & Network Security
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    • 제24권1호
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    • pp.85-94
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    • 2024
  • In this paper, we present the very first time the generalized notion of (α, β, γ, δ) - convex (concave) function in mixed kind, which is the generalization of (α, β) - convex (concave) functions in 1st and 2nd kind, (s, r) - convex (concave) functions in mixed kind, s - convex (concave) functions in 1st and 2nd kind, p - convex (concave) functions, quasi convex(concave) functions and the class of convex (concave) functions. We would like to state the well-known Ostrowski inequality via SVN-Riemann Integrals for (α, β, γ, δ) - convex (concave) function in mixed kind. Moreover we establish some SVN-Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are (α, β, γ, δ)-convex (concave) functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases with respect to convexity of function.

COEFFICIENT BOUNDS FOR INVERSE OF FUNCTIONS CONVEX IN ONE DIRECTION

  • Maharana, Sudhananda;Prajapat, Jugal Kishore;Bansal, Deepak
    • 호남수학학술지
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    • 제42권4호
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    • pp.781-794
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    • 2020
  • In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.

SOME CRITERIA FOR p-VALENT FUNCTIONS

  • Yang, Dinggong
    • 대한수학회보
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    • 제35권3호
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    • pp.571-582
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    • 1998
  • The object of the present paper is to derive some sufficient conditions for p-valently close-to-convexity, p-valently starlikeness and p-valently convexity.

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FUNCTIONS SUBORDINATE TO THE EXPONENTIAL FUNCTION

  • Priya G. Krishnan;Vaithiyanathan Ravichandran;Ponnaiah Saikrishnan
    • 대한수학회논문집
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    • 제38권1호
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    • pp.163-178
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    • 2023
  • We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function p defined on the unit disc so that the function p is subordinate to the function ez. These results are applied to find sufficient conditions for the normalised analytic functions f defined on the unit disc to satisfy the subordination zf'(z)/f(z) ≺ ez.

AN EXTENSION OF SCHNEIDER'S CHARACTERIZATION THEOREM FOR ELLIPSOIDS

  • Dong-Soo Kim;Young Ho Kim
    • 대한수학회보
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    • 제60권4호
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    • pp.905-913
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    • 2023
  • Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼n+1 with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽t, and denote by Ip(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼3, the ellipsoids are the only ones satisfying Ip(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼n+1 satisfying for a constant 𝛽, Ip(t) = 𝜙(p)t𝛽. In this paper, we study the volume Ip(t) of a strictly convex and complete hypersurface in 𝔼n+1 with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼n+1 satisfying Ip(t) = 𝜙(p)t𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼n+1 satisfying Ip(t) = 𝜙(p)t𝛽.

ON SPHERICALLY CONCAVE FUNCTIONS

  • KIM SEONG-A
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제12권3호
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    • pp.229-235
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    • 2005
  • The notions of spherically concave functions defined on a subregion of the Riemann sphere P are introduced in different ways in Kim & Minda [The hyperbolic metric and spherically convex regions. J. Math. Kyoto Univ. 41 (2001), 297-314] and Kim & Sugawa [Charaterizations of hyperbolically convex regions. J. Math. Anal. Appl. 309 (2005), 37-51]. We show continuity of the concave function defined in the latter and show that the two notions of the concavity are equivalent for a function of class $C^2$. Moreover, we find more characterizations for spherically concave functions.

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