Compactness of Certain Mappings

EXISTENCE OF FIXED POINTS OF CERTAIN CLASSES OF NONLINEAR MAPPINGS

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

On certain subclasses of univalent $p$-harmonic mappings

Inthis paper, the main aim is to introduce the class $mathcal{U}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p$ and $mathcal{U}_p(lambda,alpha,beta,k_0)capmathcal {T}_p^0$, andinvestigate the properties of the mappings in these classes. First,we give a sufficient condition for mappings to be in $mathcal{U}_p(l...

A Characterization of Certain Quasi-open Mappings

On Boundedness and Compactness of a Certain Class Kernel Operators

New conditions of Lp[0,∞)−Lq[0,∞) boundedness and compactness for the operator f → w(x) R b(x) a(x) k(x, y)f(y)v(y)dy with locally integrable weight functions v, w and a positive continuous kernel k(x, y) from Oinarov’s type class are obtained for 1 < p, q <∞.

Compactness Methods for Hölder Estimates of Certain Degenerate Elliptic Equations

In this paper we obtain the interior C regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local L estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method.