Volume 46, Issue 2

The paper deals with the following problems concerning pseudo-ordered denumerable fields: (i) a connection between Fermat’s two squares theorem and the unique pseudo-order in a finite field; (ii) properties of a proper pseudo-order determined by any prime number in the field of rational numbers; (iii) existence of a proper pseudo-order in every subfield of the sequence used to obtain the field of constructible numbers; (iv) some brief of applications of the latter pseudo-orders to construct new algebraic and geometric structures. In particular, we extend the known construction of finite nearfields or quasifields given by e.g. W. A. Pierce or P. Dembowski – to infinite cases.

The aim of this paper is to define generalized ( m , n )-Jordan centralizers and to prove that on a prime ring with nonzero center and char ( R ) ≠ 6 mn ( m + n )( m +2 n ) every generalized ( m , n )-Jordan centralizer is a two-sided centralizer.

We classify vector sheaves (an abstraction of vector bundles) by means of a universal Grassmann sheaf. This is done in three steps. Given a sheaf of unital commutative and associative algebras 𝒜, we first construct the k -th Grassmann sheaf 𝒢 𝒜 ( k , n ) of 𝒜 n , whose sections induce vector subsheaves of 𝒜 n of rank k . Next we show that every vector sheaf (a locally free 𝒜-module) over a paracompact space is a subsheaf of 𝒜 ∞ . In the last step, the foregoing considerations lead to the construction of a universal Grassmann sheaf 𝒢 𝒜 ( n ), whose global sections classify vector sheaves of rank n over a paracompact space. Note that a homotopy classification is not applicable in this context.

In this paper, we prove the arcwise connectedness of the solution set of a nonclosed, nonconvex Fredholm type, Riemann–Liouville integral inclusion of fractional order.

This paper focuses on a generalized linear operator I m which is a combination of both differential and integral operators. Involving this operator, a class TS k ( I m ; α , β ) (⊆ TS ( I m ; α , β )) with respect to k -symmetric points is defined. Results based on coefficient inequalities and bounds for this class are obtained. Various integral representations and some consequent results for TS ( I m ; α , β ) class are also determined. Further, results on partial sums are discussed.

In this paper, we deal with sequence spaces inclusion equations (SSIE), which are determined by an inclusion where each term is a sum or a sum of products of sets of the form χ a ( T ) and χ f ( x ) ( T ) where f maps U + to itself, and χ ∈ { s 0 , s ( c ) , s }, the sequence x is the unknown and T is a given triangle. Here, we determine the set of all sequences x with positive entries such that χb″⊂χa+χx′$\chi _b'' \subset \chi _a + \chi _x^\prime $, and χa+χx′⊂χb″$\chi _a + \chi _x^\prime \subset \chi _b''$ where χ , χ′ , χ ″ ∈ { s 0 , s ( c ) , s }. We are led to study, among other things, the inclusion equations sx(c)+sb0(Δ)⊂sb$s_x^{(c)} + s_b^0 (\Delta ) \subset s_b $ and sx0+sb0(Δ)⊂sb$s_x^0 + s_b^0 (\Delta ) \subset s_b $ where Δ is the operator of first differences defined by Δξ n = ξ n − ξ n −1 for n ≥ 1 with ξ 0 = 0. The first (SSIE) leads to determine the set of all sequences x such that y n / x n → l and Δ z n / b n → 0 implies y n + z n = O ( b n ) ( n → ∞). These results generalize some of the results given in [1].

In the paper, there has been constructed the ∇-model of the Bittner operational calculus for the backward difference ∇ u ( k ) = u ( k ) − u ( k − 1) in the space of two-sided sequences. A form of the Taylor’s formula has been derived. Applying the operation ∇ b u ( k ) = u ( k ) − b ( k ) u ( k − 1), the ∇-model has been generalized.

In this paper, we have introduced a generalised Kannan type contraction. It has been established that such mappings necessarily have fixed points in a complete partially ordered metric space. The fixed point is unique under some additional conditions. The result is illustrated with an example. The work is in the line of research in fixed point theory on ordered metric structures.

The boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.

We define a semi-symmetric semi-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a semi-symmetric semi-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

Solving a certain functional equation, we find all invariants of a pair of directions in n -dimensional pseudo-Euclidean geometry of index one 𝔼1n\font\msbm=MTMIB${\msbm E}_1^n $. In ( n − 1)-dimensional space we construct a model for these directions by means of concepts characteristic of Euclidean geometry. Because it is a pseudo-orthogonal group, not orthogonal, that operates in this model, the distance between two points and the measure of an angle are not invariants. Using these changeable quantities we construct invariant quantities.

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized ϕ -weak contraction, Appl. Math. Lett. 22(2009), 75-78] and [D. Dorić, Common fixed point for generalized ( ψ , ϕ )-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900] to prove a common fixed point theorem for four mappings satisfying generalized weak contractive condition (see Filomat 24:2 (2010), 1–10). In this paper, we generalize this theorem by using the concept of common property (E.A). Our result generalizes and unifies several existing results involving generalized weak contractive conditions. We study also well-posedness of a related fixed point problem.

In this paper, we present a common fixed point theorem by altering distances for a contractive condition of integral type in partial metric spaces.

In this paper, we introduce and study the notions of upper and lower rarely s -precontinuous multifunctions which are a generalization of weakly s -precontinuous multifunctions due to Ekici and Park [3].

The aim of the present paper is to obtain common fixed point theorems under a strict contractive condition by assuming minimal commutativity conditions. Our theorems extend the results due to Pant and Pant [4]. In the setting of our results, we also provide pair of mappings which ensures the existence of a common fixed point; however, both the mappings are discontinuous at the common fixed point. We, thus, provide one more answer to the problem of Rhoades [10]. In the last section, we apply our results to solve an eigenvalue problem.

In [8], Császár introduced some generalized open sets in generalized topological spaces, namely, μ -semi-open, μ -preopen, μ-β -open, and μ-α -open. The primary purpose of this paper is to study some new properties and characterizations of these concepts as we also introduce and study a new generalized open set in generalized topological spaces, namely, μ-b -open. We also investigate some relationships between these concepts.

In this paper, we present conditions which are equivalent to the Darboux property for non-constant polynomials in Golomb’s and Kirch’s topologies on the set of positive integers.