which, for invertible φ can also be expressed as, EX ≤ φ−1(E φ(X)) The term φ−1 ( E φ(X) ) can be seen as a generalized mean value [2],[1, ch.3]. The Lp norms (E|X|p)1/p for example fit this framework. The notion of convexity was generalized by B. Jessen in [2] to compare two functions in terms of the means defined by them. An increasing function φ is defined to be convex with respect to anothe...

Abstract. In this paper, we introduce three new broad classes of secondorder generalized convex functions, namely, (F , b, φ, ρ, θ)-sounivex functions, (F , b, φ, ρ, θ)-pseudosounivex functions, and (F , b, φ, ρ, θ)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized (F , b, φ, ρ, θ)-sounivexity assumptio...

In this paper, we introduce the notion of generalized (α, φ, ψ)- Geraghty contractive type mappings in setup Sb-metric spaces and α-orbital admissible with respect to φ. Furthermore, fixed-point theorems for such complete are proven without assuming subadditivity ψ. Some examples provided supporting our main results. Also, gave an application integral equations as well Homotopy.

Let Φ be a finite root system of rank n and let m be a positive integer. It is proved that the generalized cluster complex ∆m(Φ), introduced by S. Fomin and N. Reading, is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. This statement was conjectured by V. Reiner. More precisely, it is proved that the simplicial complex obtained from ∆m(Φ) by removing any subset of its vertex set of cardinal...

We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ : A→ C be a linear map such that φ(1) = 1 and (φ(a))2 + (φ(b))2 = 0 for all a, b in A satisfying ab = ba and a2 + b2 is invertible. Then φ(ab) = φ(a)φ(b) for all a, b in A. Similar resu...

Theorem 3.2 A consequence system (L,`) enjoys Craig interpolation with respect to an L-function var, if (i) there is a Craig generalized translation schema from (L,`) to another consequence system (L′,`′) with respect to var and an L′-function var′; (ii) (L′,`′) enjoys Craig interpolation with respect to var′. Proof: Let (h1, h2, h) be a Craig generalized translation schema from (L,`) to (L′,`′...

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...