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

Seria
Rozprawy Matematyczne tom/nr w serii: 201 wydano: 1982
Zawartość
Warianty tytułu
Abstrakty
EN

Introduction
In 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.
EN

CONTENTS
Introduction.....................................................................................................................................................................................................5
1. Some properties of multi-valued functions...................................................................................................................................................5
2. Fixed-point theorems for multi-valued functions.........................................................................................................................................11
3. On the characterization and extension of continuous solutions of functional equation with multi-valued functions...................................17
4. On the existence of continuous solutions of functional equations of n-th order with multi-valued functions..............................................21
5. On the continuous solutions of a functional inequality...............................................................................................................................25
References.....................................................................................................................................................................................................28
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 201
Liczba stron
28
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCI
Daty
wydano
1982
Twórcy
Bibliografia
  • [1] K. Baron, Continuous solutions of a functional equation of n-th order, Aeq. Math. 9 (1973), pp. 257-259.
  • [2] K. Baron, Note on the existence of continuous solutions of a functional equation of n-th order, Ann. Polon. Math. 30 (1974), pp. 77-80.
  • [3] K. Baron, Note on continuous solutions of a functional equation, Aeq. Math. 11 (1974), pp. 267-269.
  • [4] K. Baron, On extending of solutions of functional equation, Aeq. Math. 13 (1975), pp. 285-288.
  • [5] K. Baron, On extending of solutions of functional equations in a single variable, Recueil des travaux de l'Institut Math, Nouvelle série, No. 1 (9) (1976), pp. 23-24.
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  • [13] H. M. Ko, Fixed points theorems for point to set mappings and the set of fixed points, Pacific J. Math. 42 (1972), pp. 369-379.
  • [14] M. Kuczma, Functional equations in a single variable, PWN, Monografie Mat. 46, Warszawa 1968.
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  • [21] E. Michael, A selection theorem, Proc. Amer. Math. Soc. 17 (1966), pp. 1404-1406.
  • [22] S. B. Nadler jr., Multivalued contraction mappings, Pacific J. Math. 30 (1969), pp. 475-488.
  • [23] E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), pp. 459-465.
  • [24] S. Reich, Fixed points of contractive functions. Boll. Un. Math. Ital. (4) 5 (1972), pp. 26-42.
  • [25] H. H. Schaefer, Topological vector spaces, New York 1966.
  • [26] C. Shiau, K. K. Tan and C. S. Wong, Quasi-nonexpansive multi-valued maps and selections, Fund. Math. 87 (1975), pp. 109-119.
  • [27] W. J. Thron, Sequences generates by iteration, Trans. Amer. Math. Soc. 96 (1960), pp. 38-53.
  • [28] C. S. Wong, Fixed point theorems for point to set mappings, Canad. Math. Bull. 17 (4) (1974).
Języki publikacji
PL, FR, EN, RU
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-25c76834-835d-42e8-a810-527a245ceeb2
Identyfikatory
ISBN
83-01-02068-7
ISSN
0012-3862
Kolekcja
DML-PL
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