In this article, we define and study a family of modified Baskakov type operators based on a parameter . This family is a generalization of the classical Baskakov sequence. First, we prove that it converges to the function being approximated. Then, we find a Voronovsky-type formula and obtain that the order of approximation of this family is . This order is better than the order of the classical Baskakov sequence  whenever . Finally, we apply our sequence to approximate two test functions and analyze the numerical results obtained.

In this paper we introduce a new class of operators on Hilbert space. We
call the operators in this class, n,m- powers operators. We study this class
of operators and give some of their basic properties.

Antimagic labeling of a graph  with  vertices and  edges is assigned the labels for its edges by some integers from the set , such that no two edges received the same label, and the weights of vertices of a graph  are pairwise distinct. Where the vertex-weights of a vertex  under this labeling is the sum of labels of all edges incident to this vertex, in this paper, we deal with the problem of finding vertex antimagic edge labeling for some special families of graphs called strong face graphs. We prove that vertex antimagic, edge labeling for strong face ladder graph , strong face wheel graph ,  strong face fan graph , strong face prism graph  and finally strong face friendship graph .

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact

In this paper, we define two operators of summation and summation-integral of q-type in two dimensional spaces. Firstly, we study the convergence of these operators and then we prove Voronovskaya- type asymptotic formulas for these operators.

In this paper the concepts of weakly (resp., closure, strongly) Perfect Mappings are defined and the important relationships are studied: (a) Comparison between deferent forms of perfect mappings. (b) Relationship between compositions of deferent forms of perfect mappings. (c) Investigate relationships between deferent forms of perfect mappings and their graphs mappings.

In this paper we have made different regular graphs by using block designs. In one of our applicable methods, first we have changed symmetric block designs into new block designs by using a method called a union method. Then we have made various regular graphs from each of them. For symmetric block designs with  (which is named finite projective geometry), this method leads to infinite class of regular graphs. With some examples we will show that these graphs can be strongly regular or semi-strongly regular. We have also propounded this conjecture that if two semi-symmetric block designs are non-isomorphic, then the resultant block graphs of them are non-isomorphic, too.

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.