Abstract

In the present paper, we introduce a new class of meromorphic functions defined by means of the Hadamard product of Cho-Kwon-Srivastava operator and we define here a similar transformation by means of an operator introduced by Ghanim and Darus. We investigate a number of inclusion relationships of this class. We also derive some interesting properties of this class.

Keywords: Subordination; meromorphic function; Cho-Kwon-Srivastava operator; Choi-Saigo-Srivastava operator; Hadamard product; integral operator.

MSC: 30C45, 30C50

Abstract

In this paper, we introduce new generalized Hausdorff operators. They include many famous operators as special cases. We obtain necessary and sufficient conditions for these operators to be bounded on the weighted Herz spaces. The corresponding new operator norm inequalities are obtained. They are significant improvements and generalizations of many known results. Several open problems are formulated.

Keywords: Hausdorff operator; weighted Herz space; norm inequality.

MSC: 26D10, 47A30

Abstract

The object of the present paper is to study $N(k)$-quasi Einstein manifolds. Existence of $N(k)$-quasi Einstein manifolds are proved by two non-trivial examples. Also a physical example of an $N(k)$-quasi-Einstein manifold is given. We study an $N(k)$-quasi-Einstein manifold satisfying the curvature conditions $\tilde Z(\xi ,X)\cdot S=0$, $P(\xi ,X)\cdot\tilde Z=0$, $\tilde Z(\xi,X)\cdot P=0$, $\tilde Z(\xi,X)\cdot C=0$ and $P(\xi,X)\cdot C=0$. Finally, we study Ricci-pseudosymmetric $N(k)$-quasi-Einstein manifolds.

Keywords: Quasi Einstein manifold; $N(k)$-quasi Einstein manifold; projective curvature tensor; concircular curvature tensor; conformal curvature tensor; Ricci-pseudosymmetric manifold.

MSC: 53C25

Abstract

In this paper, we take up Taylor means to study the degree of approximation of $f\in H(\alpha,p)$ space in the generalized Hölder metric and obtain a general theorem which is used to obtain a few more results that improve upon some earlier results obtained by Mohapatra, Holland and Sahney [J. Approx. Theory 45 (1985), 363--374] in $L_p$-norm, Mohapatra and Chandra [Math. Chronicle 11 (1982), 89--96] in Hölder metric and Chui and Holland [J. Approx. Theory 39 (1983), 24--38] in sup-norm.

Keywords: Generalized Hölder metric; Taylor mean; degree of approximation.

MSC: 41A25, 42A10, 40G10

Abstract

Coincidence point theorems for hybrid pairs of single valued and multivalued mappings on an arbitrary nonempty set have been proved. As an application of our main result, the existence of common solutions of functional equations arising in dynamic programming are discussed.

Keywords: Coincidence point; orbitally complete space; common fixed point.

MSC: 47H09, 47H10, 54H25

Abstract

In this article we introduce the notion of $\cal{I}$-convergence and $\cal{I}$-Cauchyness of double sequences in the topology induced by random $2$-normed spaces and prove some important results.

Keywords: $t$-norm; random $2$-normed space; ideal convergence; ideal Cauchy sequences; $F$-topology.

MSC: 40A35, 46A70, 54E70

Abstract

In this paper, we give some characterizations of spaces with locally countable network and some characterizations of $sn$-symmetric (or Cauchy $sn$-symmetric) spaces with locally countable $sn$-networks by compact images (or $\pi$-images) of locally separable metric spaces.

Keywords: Network; $cs^*$-network; $sn$-network; weak base; locally countable; sequence-covering; $1$-sequence-covering; weak-open; compact map; $\pi$-map.

MSC: 54C10, 54D65, 54E40, 54E99

Abstract

In this paper, we introduce some spaces of double difference sequences of fuzzy numbers defined by a sequence of modulus functions $F=(f_{k,l})$. We also make an effort to study some topological properties and prove some inclusion relations between these spaces.

Keywords: Fuzzy numbers; modulus function; double sequence spaces

MSC: 40A05, 40D25

Abstract

Let $H$ be a Hilbert space and $B(H)$ the algebra of all bounded linear operators on $H$. In this paper, we study the class of operators $A\in B(H)$ with closed range such that $AA^{+}-A^{+}A$ is invertible, where $A^{+}$ is the Moore-Penrose inverse of $A$. Also, we present new relations between $(AA^{*}+A^{*}A)^{-1}$ and $(A+A^{*})^{-1}$. The present paper is an extension of results from [J. Benítez and V. Rakočević, Appl. Math. Comput. 217 (2010) 3493--3503] to infinite-dimensional Hilbert space.

Keywords: Moore-Penrose inverse; idempotent; orthogonal projection; positive operator.

MSC: 47A05

Abstract

In this brief note we present two infinite families of equivalences of the Continuum Hypothesis, as follows: $\bullet$ For every fixed $n \geq 2$, the Continuum Hypothesis is equivalent to the following statement: ``There is an $n$-dimensional real normed vector space $E$ including a subset $A$ of size $\aleph_1$ such that $E \setminus A$ is not path connected''. $\bullet$ For every fixed $T_1$ first-countable topological space $X$ with at least two points, the Continuum Hypothesis is equivalent to the following statement: ``There is a point of the Tychonoff product $X^{\mathbb{R}}$ with a fundamental system of open neighbourhoods $B$ of size $\aleph_1$''.

Keywords: Continuum Hypothesis; path connected subsets; normed spaces; $T_1$ spaces; product topology; function spaces.

MSC: 03E50, 54A35, 54B10, 54C30

Abstract

In this paper, we prove a general fixed point theorem in S-metric spaces which is a generalization of Theorem~3.1 from [S. Sedghi, N. Shobe, A. Aliouche, Mat. Vesnik 64 (2012), 258--266]. As applications, we get many analogues of fixed point theorems from metric spaces to S-metric spaces.

Keywords: S-metric space.

MSC: 54H25, 54E99