# Fixed-point theorems for multi-valued functions and their applications to functional equations

• Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1982

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## Abstract

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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

## How to cite

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Roman Węgrzyk. Fixed-point theorems for multi-valued functions and their applications to functional equations. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1982. <http://eudml.org/doc/268403>.

@book{RomanWęgrzyk1982,
author = {Roman Węgrzyk},
keywords = {characterization and extension of continuous solutions of functional equation with multi-valued functions; existence of continuous solutions of functional equations of nth order with multi-valued functions; continuous solutions of functional inequality},
language = {pol},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Fixed-point theorems for multi-valued functions and their applications to functional equations},
url = {http://eudml.org/doc/268403},
year = {1982},
}

TY - BOOK
AU - Roman Węgrzyk
TI - Fixed-point theorems for multi-valued functions and their applications to functional equations
PY - 1982
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
LA - pol
KW - characterization and extension of continuous solutions of functional equation with multi-valued functions; existence of continuous solutions of functional equations of nth order with multi-valued functions; continuous solutions of functional inequality
UR - http://eudml.org/doc/268403
ER -

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