In this paper, we establish some companions of Fej,r's inequality for convex functions which generalize the inequalities of Hermite-Hadamard type from (Dragomir et al. in Univ Belgrad Publ Elek Fak Sci Math 4:3-10...
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In this paper, we establish some companions of Fej,r's inequality for convex functions which generalize the inequalities of Hermite-Hadamard type from (Dragomir et al. in Univ Belgrad Publ Elek Fak Sci Math 4:3-10, 1993).
The main object of this article is to present the sharp bounds of the third -order Hankel determinant for functions in a subclass of normalized analytic functions in the open unit disk D, which are the inverses of the...
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The main object of this article is to present the sharp bounds of the third -order Hankel determinant for functions in a subclass of normalized analytic functions in the open unit disk D, which are the inverses of the class of Ozaki type close to convex functions. Several earlier developments, which are related to our main results, are also described. (c) 2023 Elsevier Masson SAS. All rights reserved.
In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite-Hadamard inequalities for quantum integrals. The results presented in this paper are generalizat...
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In this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite-Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite-Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint-trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.
Let Delta(m) = {(t(0),..., t(m)) is an element of Rm+1 : t(i) >= 0, Sigma(m)(i=0) ti = 1} be the standard m-dimensional simplex and let circle minus not equal S subset of boolean OR(infinity)(m= 1) Delta(m). Then a...
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Let Delta(m) = {(t(0),..., t(m)) is an element of Rm+1 : t(i) >= 0, Sigma(m)(i=0) ti = 1} be the standard m-dimensional simplex and let circle minus not equal S subset of boolean OR(infinity)(m= 1) Delta(m). Then a function h: C -> R with domain a convex set in a real vector space is S-almost convex iff for all (t(0),..., t(m)) is an element of S and x(0),..., x(m). C the inequality h(t(0)x(0) + center dot center dot center dot + t(m)x(m)) <= 1 + t(0)h(x(0)) = center dot center dot center dot t(m)h(x(m)) holds. A detailed study of the properties of S-almost convex functions is made. If S contains at least one point that is not a vertex, then an extremal S-almost convex function E-S: Delta(n) -> R is constructed with the properties that it vanishes on the vertices of Delta(n) and if h: Delta(n). R is any bounded S- almost convex function with h( ek) = 0 on the vertices of. n, then h x) <= E-S(x) for all x is an element of(n). In the special case S = {(1/(m+1),..., 1/(m+ 1))}, the barycenter of Delta(m), very explicit formulas are given for E-S and (KS)(n) = sup(x is an element of Delta). E-S( x). These are of interest, as E-S and (KS)(n) are extremal in various geometric and analytic inequalities and theorems.
In this paper, firstly, Hermite-Hadamard-Fejer type inequalities for p-convex functions in fractional integral forms are built. Secondly, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities...
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In this paper, firstly, Hermite-Hadamard-Fejer type inequalities for p-convex functions in fractional integral forms are built. Secondly, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for p-convex functions in fractional integral forms are obtained. Finally, some Hermite-Hadamard and Hermite-Hadamard-Fejer inequalities for convex, harmonically convex and p-convex functions are given. Many results presented here for p-convex functions provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.
Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class F of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. functions in F are no...
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Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class F of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. functions in F are not necessarily starlike but are convex in one direction and so are close-to-convex. We prove that the sharp bounds of Script capital H3,1(f) and Script capital H3,1(f-1) for f is an element of F are all equal to 1/16. We also calculate the sharp bounds of the third Hankel determinant with entry of coefficients on the inverse of convex functions.
We present a method of proving inequalities for convex functions with use of Stieltjes integral. First, we show how some well-known inequalities can be obtained, and then we show how new inequalities and stronger vers...
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We present a method of proving inequalities for convex functions with use of Stieltjes integral. First, we show how some well-known inequalities can be obtained, and then we show how new inequalities and stronger versions of some existing results can be obtained.
Let S denote the class of analytic and univalent functions in the unit disk D = {z is an element of C : |z| < 1} of the form f (z) = z +Sigma (infinity) (n=2) a(n)z(n). For f is an element of S, the logarithmic coe...
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Let S denote the class of analytic and univalent functions in the unit disk D = {z is an element of C : |z| < 1} of the form f (z) = z +Sigma (infinity) (n=2) a(n)z(n). For f is an element of S, the logarithmic coefficients defined by log (f (z)/z) = 2 Sigma (infinity) (n=1) gamma(n)z(n), z is an element of D. In 1971, Milin [12] proposed a system of inequalities for the logarithmic coefficients of S. This is known as the Milin conjecture and implies the Robertson conjecture which implies the Bieberbach conjecture for the class S. Recently, the other interesting inequalities involving logarithmic coefficients for functions in S and some of its subfamilies have been studied by Roth [24], and Ponnusamy et al. [17]. In this article, we estimate the logarithmic coefficient inequalities for certain subfamilies of Ma-Minda family defined by a subordination relation. It is important to note that the inequalities presented in this study would generalize some of the earlier work. (c) 2024 Elsevier Masson SAS. All rights reserved.
This paper explores the class CG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen...
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This paper explores the class CG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{C}_{G}$\end{document}, consisting of functions g that satisfy a specific subordination relationship with Gregory coefficients in the open unit disk E. By applying certain conditions to related coefficient functionals, we establish sharp estimates for the first five coefficients of these functions. Additionally, we derive bounds for the second and third Hankel determinants of functions in CG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{C}_{G}$\end{document}, providing further insight into the class's properties. Our study also investigates the logarithmic coefficients of log(g(t)t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\log \left ( \frac{g(t)}{t}\right ) $\end{document} and the inverse coefficients of the inverse functions (g-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(g<^>{-1})$\end{document} within the same class.
Abstract: A normalized univalent function is called convex of bounded type if the curvature of the curve bounding the image domain of the unit disc lies between two fixed positive numbers. Sharp bounds for the...
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Abstract: A normalized univalent function is called convex of bounded type if the curvature of the curve bounding the image domain of the unit disc lies between two fixed positive numbers. Sharp bounds for the modulus of the second and the third Taylor coefficient of such functions are derived. The proof concerning the second coefficient is based on a maximum-minimum principle for locally univalent functions.
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