On (β, α) - Logarithmically Convex Functions in the First and Second Sense with Their Inequalities

2016 ◽  
Vol 9 (2) ◽  
pp. 39-52
Author(s):  
Abdullah Açıkel ◽  
Mevlüt Tunç
Keyword(s):  
Convex Functions ◽  
Logarithmically Convex Functions

scholarly journals Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions

Filomat ◽  
2013 ◽  
Vol 27 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Rui-Fang Bai ◽  
Qi Feng ◽  
Xi Bo-Yan
Keyword(s):  
Convex Functions ◽  
Logarithmically Convex Functions

scholarly journals On the second hankel determinant for the kth-root transform of analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Najla Alarifi ◽  
Rosihan Ali ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
The Given ◽  
Logarithmically Convex Functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying zf'(z)/f(z) is subordinate to a given analytic function ?. A sharp bound is obtained for the second Hankel determinant of the kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel determinant are also derived for the kth-root transform of several other classes, which include the class of ?-convex functions and ?-logarithmically convex functions. These bounds are expressed in terms of the coefficients of the given function ?, and thus connect with earlier known results for particular choices of ?.

scholarly journals On the fractional Hermite-Hadamard type inequalities for (α,m)-logarithmically convex functions

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1565-1580
Author(s):  
Jinrong Wang ◽  
Yumei Liao ◽  
Jian Deng
Keyword(s):  
Convex Functions ◽  
New Left ◽  
Fractional Integrals ◽  
Logarithmically Convex Functions

The purpose of this paper is to establish some refinements of Riemann-Liouville fractional Hermite-Hadamard inequalities for (?,m)-logarithmically convex functions. By using our fractional integrals identities, we present some interesting and new left type fractional Hermite-Hadamard inequalities for once and twice differentiable (?,m)-logarithmically convex functions via powerful series.

Entire and Meromorphic Functions with Asymptotically Prescribed Characteristic

1965 ◽  
Vol 17 ◽  
pp. 383-395 ◽  
Author(s):  
Albert Edrei ◽  
Wolfgang H. J. Fuchs
Keyword(s):  
Entire Function ◽  
Convex Functions ◽  
Meromorphic Functions ◽  
Image Position ◽  
Increasing Function ◽  
Logarithmically Convex Functions

If f(z) is a non-constant, entire function, then Hadamard's three-circles theorem asserts thatis a convex, increasing function of log r. Hence, by well-known properties of logarithmically convex functions,

scholarly journals On some inequalities for s-logarithmically convex functions in the second sense via fractional integrals

2014 ◽  
Vol 23 (2) ◽  
pp. 253-260
Author(s):  
MEVLUT TUNC ◽  
◽  
HAVVA KAVURMACI-ONALAN ◽  
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Logarithmically Convex Functions

In this paper, the authors establish some new Hadamard type inequalities for s-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1.1 which has been proved by Sarıkaya et al.

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