Introduction. Several authors have proved theorems of the type: The "structure" of a certain class of transformations defined on a "suitable" space A to a fixed "suitable" space B "determines" the space A. As examples, we have: Banach [3, p. 170, see also 6, 7, 13] i The Banach space of all real, continuous functions defined on a compact metric space A "determines" A. Eidelheit [5, see also 2, ...

We provide some new results on the weak convergence of sequences or nets lying in L,((T, & r), X) = L,(p, X), 1 <p < co, i.e., the space of equivalence classes of X-valued (X is a Banach space) Bochner integrable functions on the finite measure space ( r, z, I”). Our theorems generalize in several directions recent resuls on weak sequential convergence in L,(p, X) obtained by M. A. Khan and M. ...

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...

The articles [6], [1], [4], [5], [2], and [3] provide the notation and terminology for this paper. Let O1 be an ordered affine space. Then Λ(O1) is an affine space. Let O1 be an ordered affine plane. Then Λ(O1) is an affine plane. We now state several propositions: (1) There exists a real linear space V and there exist vectors u, v of V such that for all real numbers a, b such that a · u + b · ...

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

On $\mathscr{L}-$ fuzzy normed spaces, which is the generalization of notion lacunary statistical convergence for double sequences a convergence, are studied and developed in this paper. In addition, definitions Cauchy completeness related theorems given on spaces. Also, relationship Cauchyness boundedness with respect to norm shown.

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that  the category $L$-$mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.