Isoperimetric and extremal value problem

2015 ◽  
pp. 73-80
Keyword(s):  
Extremal Value

scholarly journals Coefficient estimates of certain subclasses of analytic functions associated with Hohlov operator

2019 ◽  
pp. 2150021
Author(s):  
P. Gochhayat ◽  
A. Prajapati ◽  
A. K. Sahoo
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Sufficient Condition ◽  
Extremal Functions ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Extremal Value

A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is needed. The present paper deals with consequential functional of this type. By making use of Hohlov operator, a new subclass [Formula: see text] of analytic functions defined in the open unit disk is introduced. For both real and complex parameter, the sharp bounds for the Fekete–Szegö problems are found. An attempt has also been taken to found the sharp upper bound to the second and third Hankel determinant for functions belonging to this class. All the extremal functions are express in term of Gauss hypergeometric function and convolution. Finally, the sufficient condition for functions to be in [Formula: see text] is derived. Relevant connections of the new results with well-known ones are pointed out.

Extremal Values of the Basic Invariants of Plane Curves

2000 ◽  
Vol 09 (08) ◽  
pp. 1085-1126
Author(s):  
Jianming Yu ◽  
Jianyi Zhou ◽  
Jianzhong Pan
Keyword(s):  
Fixed Number ◽  
Plane Curves ◽  
Explicit Formulas ◽  
Double Points ◽  
Fine Structures ◽  
Extremal Values ◽  
Extremal Value

In [A2] V.I. Arnold introduced three basic invariants St, J+ and J- of plane curves and proposed some interesting conjectures concerning the extremal value of these invariants on a given set of curves. Partial answers have been obtained by O. Viro and A. N. Shumakovich. We give explicit formulas for these extremal values of sets of plane curves with fixed number of double points and of Whitney index and we determine on which curves these extremal values are attained (Theorems 3-6). Our arguments are based on understanding of the fine structures of generic curves and some surgery operations on curves.

scholarly journals The Extremal Graphs of Some Topological Indices with Given Vertex k-Partiteness

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 271 ◽  
Author(s):  
Fang Gao ◽  
Xiaoxin Li ◽  
Kai Zhou ◽  
Jia-Bao Liu
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
Extremal Graphs ◽  
Zeroth Order ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Laplacian Energy ◽  
Modified Wiener Index ◽  
Extremal Value

The vertex k-partiteness of graph G is defined as the fewest number of vertices whose deletion from G yields a k-partite graph. In this paper, we characterize the extremal value of the reformulated first Zagreb index, the multiplicative-sum Zagreb index, the general Laplacian-energy-like invariant, the general zeroth-order Randić index, and the modified-Wiener index among graphs of order n with vertex k-partiteness not more than m .

scholarly journals Application of the Strong Artin Conjecture to the Class Number Problem

2013 ◽  
Vol 65 (6) ◽  
pp. 1201-1216 ◽  
Author(s):  
Peter J. Cho ◽  
Henry H. Kim
Keyword(s):  
Class Number ◽  
Number Fields ◽  
Class Numbers ◽  
Density Result ◽  
Class Number Formula ◽  
Number Problem ◽  
Number Formula ◽  
Group A ◽  
Galois Closures ◽  
Extremal Value

AbstractWe construct unconditionally several families of number fields with the largest possible class numbers. They are number fields of degree 4 and 5 whose Galois closures have the Galois group A4; S4, and S5. We first construct families of number fields with smallest regulators, and by using the strong Artin conjecture and applying the zero density result of Kowalski–Michel, we choose subfamilies of L-functions that are zero-free close to 1. For these subfamilies, the L-functions have the extremal value at s = 1, and by the class number formula, we obtain the extreme class numbers.

scholarly journals Bilevel programs with extremal value function: global optimality

2005 ◽  
Vol 2005 (3) ◽  
pp. 419-435 ◽  
Author(s):  
Abdelmalek Aboussoror ◽  
Hicham Babahadda ◽  
Abdelatif Mansouri
Keyword(s):  
Value Function ◽  
Convex Set ◽  
Maximization Problem ◽  
Global Optimality ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bilevel Program ◽  
Bilevel Programs ◽  
Necessary And Sufficient ◽  
Extremal Value

For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to amax-minproblem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.

scholarly journals Pointwise Remez inequality

2021 ◽  
Author(s):  
B. Eichinger ◽  
P. Yuditskii
Keyword(s):  
Fixed Point ◽  
Asymptotic Solution ◽  
Lebesgue Measure ◽  
Chebyshev Polynomials ◽  
Extremal Solution ◽  
Fixed Size ◽  
Extremal Polynomials ◽  
Remez Inequality ◽  
Upper Estimate ◽  
Extremal Value

AbstractThe standard well-known Remez inequality gives an upper estimate of the values of polynomials on $$[-1,1]$$ [ - 1 , 1 ] if they are bounded by 1 on a subset of $$[-1,1]$$ [ - 1 , 1 ] of fixed Lebesgue measure. The extremal solution is given by the rescaled Chebyshev polynomials for one interval. Andrievskii asked about the maximal value of polynomials at a fixed point, if they are again bounded by 1 on a set of fixed size. We show that the extremal polynomials are either Chebyshev (one interval) or Akhiezer polynomials (two intervals) and prove Totik–Widom bounds for the extremal value, thereby providing a complete asymptotic solution to the Andrievskii problem.

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