Let E be a Banach space and (J_{q}) be a generalized duality mapping.
For q > 1,a mapping J q : X → 2 X ∗ is said to be a generalized duality mapping if it is defined by J q ( x ) = { f ∗ ∈ X ∗ : 〈 x, f ∗ 〉 = ∥ x ∥ q, ∥ f ∗ ∥ = ∥ x ∥ q − 1 }, ∀ x ∈ X.
Furthermore, we utilize two partitioning schemes due to Mond and Weir [7] and Yang [18], in conjunction with the generalized versions of the new classes of second-order invex functions introduced in (Verma and Zalmai [10]) to formulate six generalized parameter-free duality models for principal problem (P) and prove appropriate duality theorems.
Using a direct nonparametric approach, in this paper, we have formulated six generalized second-order parameter-free duality models for a discrete minmax fractional programming problem and established numerous duality results using a variety of generalized ((mathcal {F},beta,phi,rho,theta,m -sounivexity assumptions.
2, we utilize a partitioning scheme due to Mond and Weir [7], and formulate two general second-order parameter-free duality models for (P) and prove weak, strong, and strict converse duality theorems using various generalized ((mathcal {F},beta,phi,rho,theta,m -sounivexity assumptions.
For mRNA expression arrays, a generalized linear model for microarray by limma (Bioconductor [ 32]) was used.
*Estimated by a generalized linear model for the binomial family with a log link.
A correction factor can then be calculated from a generalized linear model for each individual spot.
Using this tactic, Tuten and August 10 developed a generalized "bidimensional model for service industries".
Mardia (1975) proposed a generalized von Mises Fisher model for paired angles (θ1, θ2).
