We study permuting tri-derivations in -rings and give an example.

This paper proves the following results: Let be a transcendental entire function, and let be a positive integer. If , then assumes every finite nonzero value infinitely often. Also the case when f is a transcendental meromorphic function has been considered and some results are obtained.

We prove the following results: (1) Let R be a strongly euclidean semiring. Then an ideal A of is a partitioning ideal if and only if it is a subtractive ideal. (2) A monic ideal M of R[], where R is a strongly euclidean semiring, is a partitioning ideal if and only if it is a subtractive ideal.

In the present paper, we give the applications of the optimum bound for Bernstein basis functions. It is noted that using the optimum bound the main results of Aniol and Taberska [Ann. Soc. Math. Pol. Seri, Commentat. Math., 30(1990), 9-17], [Approx. Theory and its Appl. 11:2(1995), 94-105] and V. Gupta [Soochow J. Math., 23(1)(1997) 115-118] can be improved which were not pointed out earlier.

The semicontinuous quasi-uniformity is known to be one of the most important examples of transitive quasi-uniformities. The aim of this paper is to show that various facts in classical topology connected with the semicontinuous quasi-uniformity and semicontinuous real functions may be easily extended to pointfree topology via a construction introduced by the authors in a previous paper. Several consequences are derived.

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T.

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term >, where the functions and are real-valued continuous functions defined on with > and > for .

We characterize those commutative semigroups S such that every non-isomorphic homomorphic image of S has smaller cardinality than S. We also characterize commutative groups with the same property.

Applications of Weyl fractional -integral operator to various generalized basic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper. Certain interesting special cases have also been deduced.

(Left or Right) Weakly commutative semigroups are described. Relationships of weakly commutative semigroups and (l- or r-) Archimedean semigroups are discussed. The structure theorems of weakly commutative semigroups and weakly commutative abundant semigroups are shown.

Let and be any positive integers, let the ring of integers of modulo , let the group of all by nonsingular matrices over and let the order of . In this paper, can be computed by the following investigation: First, for any relatively prime positive integers and , is isomorphic to . Secondly, for any positive integer and any prime , , and so for the prime factorization of , .

In this paper, we investigate and characterize the class of A-semirings. A characterization of the Thierrin radical of a proper ideal of an A-semiring is given. Moreover, when P is a Q-ideal in the semiring R, it is shown that P is primary if and only if R/P is nilpotent.

In this paper, we study nonoscillatory solutions of a class of second order nonlinear neutral delay differential equations with positive and negative coefficients. Some sufficient conditions for existence of nonoscillatory solutions are obtained.

We present a concept of negative definite functions on a commutative normal hypercomplex system (Q, ) with basis unity. Negative definite functions were studied in [5] and [4] for commutative groups and semigroups respectively. The definition of such functions on Q is a natural generalization of that defined on a commutative hypergroups.

We classify centroaffine minimal surfaces with constant curvature metric under some natural conditions on the cubic differentials.