IntroductionIn this paper we present some fixed point theorems for multi-valued functions (m.v. functions for short), generalizing well-known results (Chapter 2).Next, in Chapter 3, we consider continuous solutions of equation (3.1). First we characterize the continuous solutions of this equation, and then we give some theorems on extending continuous solutions.Chapter 4 contains theorems on the existence of continuous solutions when this equation is of order n, i.e. if the set of indices is finite.The last chapter shows how we can apply the results of Chapters 3 and 4 to a double functional inequality (5.1).In this paper we denote all m.v. function by capital letters.
CONTENTSIntroduction.....................................................................................................................................................................................................51. Some properties of multi-valued functions...................................................................................................................................................52. Fixed-point theorems for multi-valued functions.........................................................................................................................................113. On the characterization and extension of continuous solutions of functional equation with multi-valued functions...................................174. On the existence of continuous solutions of functional equations of n-th order with multi-valued functions..............................................215. On the continuous solutions of a functional inequality...............................................................................................................................25References.....................................................................................................................................................................................................28
@book{bwmeta1.element.zamlynska-25c76834-835d-42e8-a810-527a245ceeb2,
author = {Roman W\k egrzyk},
title = {Fixed-point theorems for multi-valued functions and their applications to functional equations},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1982},
zbl = {0521.54034},
language = {pl},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-25c76834-835d-42e8-a810-527a245ceeb2}
}
Roman Węgrzyk. Fixed-point theorems for multi-valued functions and their applications to functional equations. GDML_Books (1982), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-25c76834-835d-42e8-a810-527a245ceeb2/