A strong maximum modulus theorem for maximal function algebras

A Strong Maximum Modulus Theorem for Maximal Function Algebras

On the Structure of Maximum Modulus Algebras

i.e., if every fER attains its maximum modulus on C. As a matter of convenience, we shall, in this paper, abbreviate "maximum modulus algebra on K" to "ilf-algebra." Examples of Af-algebras which come to mind immediately are (a) the algebra ft consisting of all functions which are continuous on K and analytic in U, (b) any subalgebra of ft, (c) any algebra (B which is equivalent to an algebra o...

The Multilinear Strong Maximal Function

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear m...

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

A strong convergence theorem for solutions of zero point problems and fixed point problems

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.