For every action φ ∈ Hom(G, Autk(K)) of a group G on commutative ring K we introduce two abelian monoids. The monoid Cliffk(φ) consists equivalence classes strongly G-graded algebras type up to Clifford system extensions K-central algebras. $${{\cal C}_k}(\phi )$$ equivariance homomorphisms from the Picard groups (generalized collective characters). Furthermore, for such there is an exact seque...

Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized compo...

Branciari [1] obtained a fixed point result for a single mapping satisfying an analogue of Banach’s contraction principle for an integral-type inequality. The second author [3] proved two fixed point theorems involving more general contractive conditions. In this paper, we establish a general principle, which makes it possible to prove many fixed point theorems for a pair of maps of integral ty...

A pyramid of n-dimensional generalized maps is a hierarchical data structure. It can be used, for instance, in order to represent an irregular pyramid of n-dimensional images. A pyramid of generalized maps can be built by successively removing and/or contracting cells of any dimension. In this paper, we define generalized orbits, which extend the classical notion of receptive fields. Generalize...

Let F2 be a free group of rank 2. We prove that there is an algorithm that decides whether or not, for given two elements u, v of F2, u and v are translation equivalent in F2, that is, whether or not u and v have the property that the cyclic length of φ(u) equals the cyclic length of φ(v) for every automorphism φ of F2. This gives an affirmative solution to problem F38a in the online version (h...

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...

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

Abstract. Let Fn be a free group of rank n ≥ 2. Two elements g, h in Fn are said to be translation equivalent in Fn if the cyclic length of φ(g) equals the cyclic length of φ(h) for every automorphism φ of Fn. Let F (a, b) be the free group generated by {a, b} and let w(a, b) be an arbitrary word in F (a, b). We prove that w(g, h) and w(h, g) are translation equivalent in Fn whenever g, h ∈ Fn ...

In this paper, we introduce the concepts of qpb-cyclic-Banach contraction mapping, qpb-cyclic-Kannan mapping and qpb-cyclic β-quasi-contraction mapping and establish the existence and uniqueness of fixed point theorems for these mappings in quasi-partial b-metric spaces. Some examples are presented to validate our results. c ©2016 All rights reserved.

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...