If F is an involution and φ a suitable collineation, then φ ◦ F ◦ φ−1 is an involution; this form includes well-known conjugacies and new conjugacies, including aleph, beth, complementary, and anticomplementary. If Z(U) is the self-isogonal cubic with pivot U , then φ carries Z(U) to a pivotal cubic. Particular attention is given to the Darboux and Lucas cubics, D and L, and conjugacy-preservin...

In this paper, new concepts of monotonicity, namely (Φ, ρ)-monotonicity, (Φ, ρ)-pseudo-monotonicity and (Φ, ρ)-quasi-monotonicityare introduced for functions defined in Banach spaces. Series of necessary conditions are also given that relate (Φ, ρ)-invexity and generalized (Φ, ρ)-invexity of the function with (Φ, ρ)monotonicity and generalized (Φ, ρ)-monotonicity of its gradient.

Let Φ be an irreducible crystallographic root system with Weyl group W and coroot lattice Q̌, spanning a Euclidean space V . Let m be a positive integer and AmΦ be the arrangement of hyperplanes in V of the form (α, x) = k for α ∈ Φ and k = 0, 1, . . . ,m. It is known that the number N(Φ, m) of bounded dominant regions of AmΦ is equal to the number of facets of the positive part ∆ m + (Φ) of the...

The purpose of this paper is to introduce the class (a,b,c)-modified enriched Kannan pair mappings (T,S) in setting Banach space that includes mappings, contraction and nonexpansive some other mappings. Some examples are presented support concepts introduced herein. We establish existence common fixed point such pair. also show problem studied herein well posed. A convergence theorem for Krasno...

We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...