strongly convex function
Jensen–Steffensen inequality for strongly convex functions
... of strongly convex functions are just “stronger versions” of analogous properties of convex functions (for more details, see ...for strongly convex functions (see [4] or ...is ...
12
On the quadratic support of strongly convex functions
... Strongly convex functions were introduced by Polyak ...is strongly convex, then it is bounded from below, its level sets x ∈ I : f(x) ≤ λ are bounded for each λ and f has a unique minimum on ...
6
OSTROWSKI TYPE INEQUALITIES PERTAINING STRONGLY CONVEX FUNCTIONS VIA CONFORMABLE FRACTIONAL INTEGRALS AND THEIR APPLICATIONS
... In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals.. A[r] ...
25
Majorization theorems for strongly convex functions
... the function involving the strongly convex function, prove the classical majorization theorem for majorized n-tuples by using strongly convex functions, give some applications of ...
13
10. Certain subclasses of strongly starlike and strongly convex functions defined by convolution
... 𝑧(𝐽 𝜆,𝜇 𝑐+1,𝑑 𝑓 ) ′ (𝑧) = (𝑐 + 1)𝐽 𝜆,𝜇 𝑐,𝑑 𝑓 (𝑧) − 𝑐𝐽 𝜆,𝜇 𝑐+1,𝑑 𝑓 (𝑧) , (1.15) 𝑧(𝐽 𝜆+1,𝜇 𝑐,𝑑 𝑓 ) ′ (𝑧) = (𝜇 + 1)𝐽 𝜆,𝜇 𝑐,𝑑 𝑓 (𝑧) − 𝜇𝐽 𝜆+1,𝜇 𝑐,𝑑 𝑓 (𝑧) , (1.16) 𝑧(𝐽 𝜆,𝜇 𝑐,𝑑 𝑓 ) ′ (𝑧) = 𝑑𝐽 𝜆,𝜇 𝑐,𝑑+1 𝑓 (𝑧) − (𝑑−1) 𝐽 𝜆,𝜇 𝑐,𝑑 𝑓 ...
8
New Result for Strongly Starlike Functions
... Keywords Strongly Starlike Functions, Strongly Convex Functions, Salagean Differential Operator.. Introduction Let A be the class of functions of the form ∞..[r] ...
5
On the improvement of Mocanu’s conditions
... of strongly convex functions of order β when zf (z) ∈ SS ∗ (β ...analytic function w ∈ H such that w() = , | w(z) | < and f (z) = g[w(z)] for z ∈ D ⊆ g( D ...
10
Beyond the Regret Minimization Barrier: Optimal Algorithms for Stochastic Strongly-Convex Optimization
... stochastic convex optimization were obtained using this online-to-batch reduction, and thus these rates were equal to the average regret of the corresponding online convex optimization ...general ...
24
INEQUALITIES VIA STRONGLY (p; h)-HARMONIC CONVEX FUNCTIONS
... the function is a convex function, if and only if, it satisfies the integral inequality, which is known as the Hermite-Hadamard ...arbitrary function, one can obtain a wide class of ...
14
On Lower and Upper Bounds in Smooth and Strongly Convex Optimization
... and strongly convex ...and strongly convex functions in a natural way by substituting ∇f (x) for Ax + b, while preserving the original conver- gence properties to a large ...and ...
51
On the multivalency of certain analytic functions
... and strongly convex functions of order α, ...of strongly starlike and strongly convex functions of order α was introduced in [] and [] with their geometric ...and convex ...
9
Optimality for \(E\mbox{ }[0,1]\) convex multi objective programming problems
... where the above inequalities hold because f , g are E-[, ] convex at x ∗ with respect to the same E (see Theorem . in []). Thus, x ∗ is the minimizer of f (x) under the constraint g(x) ≤ , which implies that ...
18
Compensated convex transforms and geometric singularity extraction from semiconvex functions
... of convex functions) [13] have been used in many opti- misation problems ...distance function and the squared distance ...of convex/concave and semiconvex/semiconcave functions have been studied ...
25
On geodesic strongly E convex sets and geodesic strongly E convex functions
... geodesic strongly E-convex sets and geodesic strongly E-convex ...geodesic strongly E-convex sets are also ...in convex analysis and related optimization ...
10
Convex function and its secant
... Theorem 3.4. Let µ be a positive measure on R . Let I ⊆ R be an interval, and let f : I → R be an integrable convex function. Let [a, b] ⊆ I be a bounded closed subinterval so that the set S = I \ (a, b) ...
15
On approximation and energy estimates for delta 6 convex functions
... 6-convex function. We derive some basic prop- erties of the delta 6-convex function under certain ...6-convex function by smooth ones and derive weighted energy estimates for the ...
9
Characterizations of some near continuous functions and near open functions
... O-neighborhood, weakly continuous function, O-continuous function, strongly O-continuous function, almost strongly O-continuous function, weakly S-continuous function, weakly open functi[r] ...
6
Analytic Functions Related with Mocanu Class
... Lemma 1.4. [29] Let ε be a positive measure on [0, 1] . Let g be a complex-valued function defined on ∆×[0, 1] such that g (., t) is analytic in ∆ for each t ∈ [0, 1] and g (z, .) is ε-integrable on [0, 1] for all ...
10
A survey of Algorithms and Analysis for Adaptive Online Learning
... online convex optimization that includes Dual Averaging, Mirror Descent, FTRL, and FTRL-Proximal, recovering and sometimes improving regret bounds from many earlier ...
50
On the definition of a close to convex function
... the extremal solution of a coefficient problem to omit an open set when there are.. competing functions such as Fz in the same class that do not omit any open set..[r] ...
8