In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

The family of q-Konhauser matrix polynomials have been extended to Konhauser matrix polynomials. The purpose of the present work is to show that an extension of the explicit forms, generating matrix functions, matrix recurrence relations and Rodrigues-type formula for these matrix polynomials are given, our desired results have been established and their applications are presented.

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree''s K-functional for the bivariate Szasz-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szasz-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bogel continuous functions.

In this paper we introduce and consider a new class of variational inequalities with four operators. This class is called the extended general mixed quasi variational inequality. We show that the extended general mixed quasi variational inequality is equivalent to the mixed point problem. We use this alternative equivalent formulation to discuss the existence of a solution of extended general mixed quasi variational inequality and also develop several iterative methods for solving extended general mixed quasi variational inequality and its variant forms. We consider the convergence analysis of the proposed iterative methods under appropriate conditions. We also introduce a new class of resolvent equation, which is called the extended general implicit resolvent equation and establish an equivalent relation between the extended general implicit resolvent equation and the extended general mixed quasi variational inequality. Some special cases are also discussed.

The fundamental relation on a fuzzy hyperring is de-fined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this pa-per, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Even-tually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transi-tive.

We introduce at e-covers of modules and define e­perfect rings as a generalization of perfect rings. We prove that a ring is right perfect if and only if it is semilocal and right e-perfect which generalizes a result due to N. Ding and J. Chen. Moreover, in the light of the fact that a ring R is right perfect if and only if at covers of any R-module are pro-jective covers, we study on the rings over which at covers of modules are (generalized) locally projective covers, and obtain some characterizations of (semi) perfect, A-perfect and B-perfect rings.