Coefficient estimates for Libera type bi-close-to-convex functions

2021 ◽  
Vol 71 (6) ◽  
pp. 1401-1410
Author(s):  
Serap Bulut
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Function Class ◽  
Upper Bounds ◽  
Coefficient Estimates

Abstract In a very recent paper, Wang and Bulut [A note on the coefficient estimates of bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 876–880] determined the estimates for the general Taylor-Maclaurin coefficients of functions belonging to the bi-close-to-convex function class. In this study, we introduce the class of Libera type bi-close-to-convex functions and obtain the upper bounds for the coefficients of functions belonging to this class. Our results generalize the results in the above mentioned paper.

scholarly journals Estimates for coefficients of certain analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3539-3552 ◽  
Author(s):  
V. Ravichandran ◽  
Shelly Verma
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Coefficient Problem ◽  
Inverse Coefficient Problem ◽  
Coefficient Bounds ◽  
Inverse Functions ◽  
Inverse Coefficient

For -1 ? B ? 1 and A > B, let S*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z)< (1+Az)/(1+Bz) (?z?<1). For -1 ? B ? 1 < A, we investigate the inverse coefficient problem for functions in the class S*[A,B] and its meromorphic counter part. Also, for -1 ? B ? 1 < A, the sharp bounds for first five coefficients for inverse functions of generalized Janowski convex functions are determined. A simple and precise proof for inverse coefficient estimations for generalized Janowski convex functions is provided for the case A = 2?-1(?>1) and B = 1. As an application, for F:= f-1, A = 2?-1 (?>1) and B = 1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z)< (1+z)/(1+Bz) (?z? < 1, -1 ? B < 1).

scholarly journals Coefficient Estimates of Bi-Starlike and Bi-Convex Functions with Respect to Symmetrical Points Associated with the Second Kind Chebyshev Polynomials

2020 ◽  
pp. 191-198
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Chebyshev Polynomials ◽  
Convex Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Symmetrical Points

In this paper, by making use the second kind Chebyshev polynomials, we introduce and study a certain class of bi-starlike and bi-convex functions with respect to symmetrical points defined in the open unit disk. We find upper bounds for the second and third coefficients of functions belong to this class.

scholarly journals Regularity properties and integral inequalities related to (k; h1; h2)-convexity of functions

2015 ◽  
Vol 53 (1) ◽  
pp. 19-35
Author(s):  
Gabriela Cristescu ◽  
Mihail Găianu ◽  
Awan Muhammad Uzair
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Local Minimizer ◽  
Upper Bounds ◽  
Integral Inequalities ◽  
Regularity Properties

Abstract The class of (k; h1; h2)-convex functions is introduced, together with some particular classes of corresponding generalized convex dominated functions. Few regularity properties of (k; h1; h2)-convex functions are proved by means of Bernstein-Doetsch type results. Also we find conditions in which every local minimizer of a (k; h1; h2)-convex function is global. Classes of (k; h1; h2)-convex functions, which allow integral upper bounds of Hermite-Hadamard type, are identified. Hermite-Hadamard type inequalities are also obtained in a particular class of the (k; h1; h2)- convex dominated functions.

scholarly journals A class of strongly close-to-convex functions

2019 ◽  
Vol 38 (6) ◽  
pp. 9-24
Author(s):  
R. K. Raina ◽  
Poonam Sharma ◽  
Janusz Sokol
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Coefficient Estimates ◽  
Special Cases ◽  
Radius Of Convexity

In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that\begin{equation*}\frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m}\end{equation*}%\begin{equation*}\left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0<m\leq 1;z\in\mathbb{U}\right) .\end{equation*}%We obtain for functions belonging to this class, the coefficient estimates, bounds, certain results based on an integral operator and radius of convexity. We also deduce a number of useful special cases and consequences of the various results which are presented in this paper.

scholarly journals Hermite–Hadamard-Type Inequalities for F -Convex Functions via Katugampola Fractional Integral

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Erhan Set ◽  
İlker Mumcu
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Function Class ◽  
Relevant Information ◽  
Fractional Integral Operator ◽  
Hadamard Inequality ◽  
Katugampola Fractional Integral

This article is organized as follows: First, definitions, theorems, and other relevant information required to obtain the main results of the article are presented. Second, a new version of the Hermite–Hadamard inequality is proved for the F-convex function class using a fractional integral operator introduced by Katugampola. Finally, new fractional Hermite–Hadamard-type inequalities are given with the help of F-convexity.

Extreme-point solutions in Markov decision processes

1983 ◽  
Vol 20 (04) ◽  
pp. 835-842
Author(s):  
David Assaf
Keyword(s):  
Convex Function ◽  
Extreme Point ◽  
Markov Decision Processes ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Decision Processes ◽  
Markov Decision ◽  
Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

scholarly journals A note on generalized convex functions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Syed Zaheer Ullah ◽  
Muhammad Adil Khan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Generalized Convex Functions

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate $(\eta _{1}, \eta _{2})$(η1,η2)-convex function and establish its Hermite–Hadamard type inequality.

Continuity of h-convex functions

2019 ◽  
Vol 12 (04) ◽  
pp. 1950059
Author(s):  
M. Rostamian Delavar ◽  
S. S. Dragomir
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Continuity Condition

In this paper, a condition which implies the continuity of an [Formula: see text]-convex function is investigated. In fact, any [Formula: see text]-convex function bounded from above is continuous if the function [Formula: see text] satisfies a certain condition which is called pre-continuity condition.

Some remarks on probability inequalities for sums of bounded convex random variables

1975 ◽  
Vol 12 (1) ◽  
pp. 155-158 ◽  
Author(s):  
M. Goldstein
Keyword(s):  
Convex Function ◽  
Exponential Convergence ◽  
Random Variables ◽  
Upper Bounds ◽  
Independent Random Variables ◽  
Probability Inequalities ◽  
Continuous Convex Function ◽  
Bounded Convex

Let X1, X2, · ··, Xn be independent random variables such that ai ≦ Xi ≦ bi, i = 1,2,…n. A class of upper bounds on the probability P(S−ES ≧ nδ) is derived where S = Σf(Xi), δ > 0 and f is a continuous convex function. Conditions for the exponential convergence of the bounds are discussed.

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