The authors begin by presenting a brief survey of the various useful methods of solving certain integral equations of Fredholm type. In particular, they apply the reduction techniques with a view to inverting a class of generalized hypergeometric integral transforms. This is observed to lead to an interesting generalization of the work of E. R. Love [9]. The Mellin transform technique for solving a general Fredholm type integral equation with the familiar H-function in the kernel is also considered.

A continuous selection and a coincidence theorem are proved in H-spaces which generalize the corresponding results of Ben-El-Mechaiekh-Deguire-Granas, Browder, Ko-Tan, Lassonde, Park, Simon and Takahashi to noncompact and/or nonconvex settings. By applying the two theorems, some intersection theorems concerning sets with H-convex sections are obtained which generalize the corresponding results of Fan, Lassonde and Shih-Tan to H-spaces. Some applications to minimax principle are given.

A Bochner-Martinelli-Koppelman type integral formula with weight factors is derived on complete intersection submanifolds of domains of Cn.

The group near-ring constructed from a right near-ring R and a group G is studied in the special case where the near-ring is distributively generated. In particular, results concerning homomorphisms of near-rings or of groups and the augmentation ideal are obtained which resemble closely those obtained for group rings.

The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In an earlier paper, we characterize this lattice as a complete lattice. Let m be an uncountable regular cardinal. The lattice L of all m-complete congruence relations of an m-complete lattice K is an m-algebraic lattice; if K is bounded, then the unit element of L is m-compact. Our main result is the converse statement: For an m-algebraic lattice L with an m-compact unit element, we construct a bounded m-complete lattice K such that L is isomorphic to the lattice of m-complete congruence relations of K. In addition, if L has more than one element, then we show how to construct K so that it will also have a prescribed automorphism group. On the way to the main result, we prove a technical theorem, the One Point Extension Theorem, which is also used to provide a new proof of the earlier result.

In this note a characterization of semigroups with atomistic consruence lattices, given for weakly reductive semigroups, is generalized to arbitrary semigroups. Also, it is shown that there is a complete congruence on the congruence lattice of such a semigroup that decomposes it into a disjoint union of intervals of the partition lattice.

Let 1≤p <∞ and 1/p+1/q = 1. If φ ∈ Lq, we denote by Tφ the functional defined on the Hardy space Hp by . A function f in Hp, which satisfies Tpφ(f) = ‖Tpφ‖ and ‖f‖p ≤ 1, is called an extremal function. Also, φ is called an extremal kernel when ‖φ‖q =‖Tpφ‖. In this paper, using the results in the case of p = 1, we study extremal kernel and extremal functions for p > 1.

Properties of the Lebesgue function associated with interpolation at the equidistant nodes , are investigated. In particular, it is proved that the relative maxima of the Lebesgue function are strictly decreasing from the outside towards the middle of the interval [0, n], and upper and lower bounds, and an asymptotic expansion, are obtained for the smallest maximum when n is odd.

We define an equivalence relation on the class of torsion-free abelian groups under which two groups are equivalent ifevery pure subgroup of one has a non-zero image in the other, and each has a non-zero image in every torsion-free factor of the other.

We study the closure properties of the equivalence classes, and the structural properties of the class of all equivalence classes. Finally we identify a class of groups which satisfy Krull-Schmidt and Jordan-Hölder properties with respect to the equivalence.

We give a transcendence measure of special values of functions satisfying certain functional equations. This improves an earlier result of Galochkin, and gives a better upper bound of the type for such a number as an S-number in the classification of transcendental numbers by Mahler.

If R has 1 in the stable range, then any two presentations f, g: p→ M of an R-module M by a finitely generated projective p are right equivalent, that is, f = gh for some automorphism h of P. The convers is also true.