Integral representation of exponentially convex functions

1982 ◽  
Vol 34 (3) ◽  
pp. 303-306 ◽  
Author(s):  
A. A. Kalyuzhnyi
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Exponentially Convex Functions

Refinements of the majorization-type inequalities via green and fink identities and related results

2018 ◽  
Vol 68 (4) ◽  
pp. 773-788 ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić ◽  
Ana Vukelić
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Ostrowski’S Inequality ◽  
New Family ◽  
Exponentially Convex Functions ◽  
The Difference

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

scholarly journals Uniformly Alpha-Quasi-Convex Functions Defined by Janowski Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shahid Mahmood ◽  
Sarfraz Nawaz Malik ◽  
Sumbal Farman ◽  
S. M. Jawwad Riaz ◽  
Shabieh Farwa
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Janowski Functions ◽  
Convolution Properties ◽  
Inclusion Results

In this work, we aim to introduce and study a new subclass of analytic functions related to the oval and petal type domain. This includes various interesting properties such as integral representation, sufficiency criteria, inclusion results, and the convolution properties for newly introduced class.

scholarly journals New Hermite-Hadamard type inequalities for exponentially convex functions and applications

2020 ◽  
Vol 5 (6) ◽  
pp. 6874-6901 ◽  
Author(s):  
Shuang-Shuang Zhou ◽  
◽  
Saima Rashid ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Convex Functions ◽  
Exponentially Convex Functions

scholarly journals Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 807 ◽  
Author(s):  
Saima Rashid ◽  
Thabet Abdeljawad ◽  
Fahd Jarad ◽  
Muhammad Aslam Noor
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Fractional Integral ◽  
Fractional Integrals ◽  
Order Derivative ◽  
Fundamental Identity ◽  
First Order ◽  
Special Means ◽  
Exponentially Convex Functions ◽  
New Inequalities

In the present paper, we investigate some Hermite-Hadamard ( HH ) inequalities related to generalized Riemann-Liouville fractional integral ( GRLFI ) via exponentially convex functions. We also show the fundamental identity for GRLFI having the first order derivative of a given exponentially convex function. Monotonicity and exponentially convexity of functions are used with some traditional and forthright inequalities. In the application part, we give examples and new inequalities for the special means.

EXPONENTIAL CONVEXITY FOR DIVIDED DIFFERENCES RELATED TO HERMITE–HADAMARD INEQUALITIES

2012 ◽  
Vol 05 (04) ◽  
pp. 1250056
Author(s):  
Z. Pavić ◽  
J. Pečarić ◽  
A. Vukelić
Keyword(s):  
Convex Functions ◽  
Monotonicity Property ◽  
Divided Differences ◽  
Exponential Convexity ◽  
Exponentially Convex Functions

In this paper we obtain means which involve divided differences for n-convex functions. We examine their monotonicity property using exponentially convex functions.

scholarly journals Some classes of alpha-quasi-convex functions

1988 ◽  
Vol 11 (3) ◽  
pp. 497-501 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Integral Representation ◽  
Unit Disk ◽  
Convex Functions ◽  
Integral Operators ◽  
Coefficient Bounds ◽  
Class Of Functions

LetC[C,D],−1≤D<C≤1denote the class of functionsg,g(0)=0,g′(0)=1, analytic in the unit diskEsuch that(zg′(z))′g′(z)is subordinate to1+CZ1+DZ,z∈E. We investigate some classes of Alpha-Quasi-Convex Functionsf, withf(0)=f′(0)−1=0for which there exists ag∈C[C,D]such that(1−α)f′(z)g′(z)+α(zf′(z))′g′(z)is subordinate to1+AZ1+BZ′,−1≤B<A≤1. Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators.

scholarly journals Ostrowski type inequalities via some exponentially convex functions with applications

2020 ◽  
Vol 5 (2) ◽  
pp. 1476-1483
Author(s):  
Naila Mehreen ◽  
◽  
Matloob Anwar
Keyword(s):  
Convex Functions ◽  
Exponentially Convex Functions

scholarly journals Radius of Convexity of Sections of a Class of Close-to-Convex Functions of Order α

2018 ◽  
Vol 60 (1) ◽  
pp. 29-35
Author(s):  
B. Usna Banu ◽  
G. P. Youvaraj
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Coefficient Bounds ◽  
Radius Of Convexity

Abstract In this paper we study radius of convexity of sections of a class of univalent close-to-convex functions on 𝔻 = {z ∈ ℂ: |z| < 1}. For functions in this class, coefficient bounds, an integral representation and radius of convexity of nth sections have been obtained.

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