Measures of noncompactness and related properties

2018 ◽  
pp. 128-146
Author(s):  
Kazimierz Goebel ◽  
Stanisław Prus
Keyword(s):  
Uniform Convexity ◽  
Measures Of Noncompactness

Attempts to classify properties of the ball B, or the space X, utilizing the notion of measures of noncompactness are presented. They are connected with the Kadec–Klee property. Measures of noncompactness are used to generalize the notion of uniform convexity and smoothness.

scholarly journals Measures of noncompactness in modular spaces and fixed point theorems for multivalued nonexpansive mappings

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
T. Domínguez Benavides ◽  
P. Lorenzo Ramírez
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Geometric Property ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniform Convexity ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Measures Of Noncompactness ◽  
Modular Spaces

AbstractThis paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems for multivalued nonexpansive mappings in modular spaces.

scholarly journals Modulus of nearly uniform smoothness and Lindenstrauss formulae

1995 ◽  
Vol 37 (2) ◽  
pp. 143-153 ◽  
Author(s):  
Tomás Domínguez Benavides
Keyword(s):  
Banach Space ◽  
Strong Relationship ◽  
Uniform Convexity ◽  
Measures Of Noncompactness ◽  
Conjugate Space ◽  
Uniform Smoothness ◽  
Image Position ◽  
Smooth Space

AbstractThe Lindenstrauss formulawhich states a strong relationship between the (Clarkson) modulus of uniform convexity δx of a Banach space X and the modulus of uniform smoothness px* of the conjugate space X*, is well known. Following the idea of the definitions of nearly uniform smooth space by S. Prus and modulus of uniform smoothness we define a modulus of nearly uniform smoothness and prove some Lindenstrauss type formulae concerning this modulus and the modulus of nearly uniform convexity for some measures of noncompactness.

On Random Uniform Convexity

2012 ◽  
Vol 14 (1) ◽  
pp. 23
Author(s):  
Xiaolin ZENG
Keyword(s):  
Uniform Convexity

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

scholarly journals Measures of Noncompactness in Regular Spaces

2014 ◽  
Vol 57 (4) ◽  
pp. 780-793 ◽  
Author(s):  
Nina A. Erzakova
Keyword(s):  
Measures Of Noncompactness ◽  
Geometric Characteristics ◽  
Measurable Functions

AbstractPrevious results by the author on the connection between three measures of noncompactness obtained for Lp are extended to regular spaces of measurable functions. An example is given of the advantages of some cases in comparison with others. Geometric characteristics of regular spaces are determined. New theorems for (k,β)-boundedness of partially additive operators are proved.

Measures of Noncompactness

2019 ◽  
pp. 229-284
Author(s):  
Eberhard Malkowsky ◽  
Vladimir Rakočević
Keyword(s):  
Measures Of Noncompactness
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