Mohamed-Aziz Taoudi

Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations

We present some new common fixed point theorems for a pair of nonlinear mappings defined on an ordered Banach space. Our results extend several earlier works. An application is given to show the usefulness and the applicability of the obtained results.

Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces

We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.

Fixed Point Theorems for ws-Compact Mappings in Banach Spaces

We present new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii, Leray-Schauder, Rothe, Altman, Petryshyn, and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results.

Fixed point theorems for convex-power condensing operators relative to the weak topology and appli- cations to Volterra integral equations

In this paper we present new fixed point theorems for weakly sequentially continuous mapping which are convex-power condensing relative to a measure of weak noncompactness. Our fixed point results extend and improve several earlier works. As an application, we investigate the existence of weak solutions to a Volterra integral equation.

FIXED POINT THEOREMS FOR GENERAL CLASSES OF MAPS ACTING ON TOPOLOGICAL VECTOR SPACES

We present new fixed point theorems for multivalued -admissible maps acting on locally convex topological vector spaces. The considered multivalued maps need not be compact. We merely assume that they are weakly compact and map weakly compact sets into relatively compact sets. Our fixed point results are obtained under Schauder, Leray–Schauder and Furi-Pera type conditions. These results are useful in applications and extend earlier works.

Measures of Weak Noncompactness and Fixed Points

The interaction between measures of weak noncompactness and fixed point theory is really strong and fruitful. In particular, measures of weak noncompactness play a significant role in topological fixed point problems. The purpose of this chapter is to exhibit the importance of the use of measures of weak noncompactness in topological fixed point theory and to demonstrate how the theory of measures of weak noncompactness will be applied in integral and partial differential equations. The theory of measures of weak noncompactness was initiated by De Blasi in the paper [28], where he introduced the first measure of weak noncompactness. De Blasi’s measure can be regarded as a counterpart of the classical Hausdorff measure of noncompactness. Unfortunately, it is not easy to construct formulas which allow to express the measure of weak noncompactness in a convenient form. For this reason, measures of weak noncompactness have been axiomatized [12] allowing thus several authors to construct measures of weak noncompactness in several Banach spaces [7, 11, 47, 48]. Measures of weak noncompactness have been successfully applied in operator theory, differential equations and integral equations. In particular, they enabled several authors to dispense with the lack of weak compactness in many practical situations. The material is far from exhausting the subject and basically we do not go into profound applications.

Fixed Point Theorems with Applications to the Solvability of Operator Equations and Inclusions on Function Spaces

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia 2Department of Mathematical Analysis, University of Valencia, Spain 3Centre Universitaire Polydisciplinaire, Kelaa des Sraghna, Morocco 4Universite Cadi Ayyad, Laboratoire de Mathematiques et de Dynamique de Populations, Marrakech, Morocco 5Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy