Strongly Generated Banach Spaces and Measures of Noncompactness

1998 ◽  
Vol 191 (1) ◽  
pp. 197-214 ◽  
Author(s):  
Markus Kunze ◽  
Georg Schlüchtermann
Keyword(s):  
Banach Spaces ◽  
Measures Of Noncompactness

scholarly journals An existence theorem for solutions of an integro-differential equation in Banach spaces

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Initial Value Problem ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Integro Differential Equation ◽  
Local Solutions

AbstractThe paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.

A new approach to measures of noncompactness of Banach spaces

2018 ◽  
Vol 240 (1) ◽  
pp. 21-45 ◽  
Author(s):  
Lixin Cheng ◽  
Qingjin Cheng ◽  
Qinrui Shen ◽  
Kun Tu ◽  
Wen Zhang
Keyword(s):  
Banach Spaces ◽  
Measures Of Noncompactness ◽  
New Approach

scholarly journals SOLVABILITY FOR A CLASS OF NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR IN BANACH SPACES

2020 ◽  
pp. 693
Author(s):  
Choukri Derbazi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Laplacian Operator ◽  
Measures Of Noncompactness ◽  
Hadamard Fractional Differential Equations ◽  
Fractional Differential

This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the Caputo-Hadamard fractional-order with $\mathrm{p}$-Laplacian operator in Banach spaces. The arguments are based on M\"{o}nch's fixed point theorem combined with the technique of measures of noncompactness. An example is also presented to illustrate the effectiveness of the main results. 

scholarly journals Set quantities and Tauberian operators

2001 ◽  
Vol 6 (7) ◽  
pp. 431-440
Author(s):  
Sergio Falcon ◽  
Kishin Sadarangani
Keyword(s):  
Nonlinear Analysis ◽  
Banach Spaces ◽  
Euclidean Distance ◽  
Normed Spaces ◽  
Measures Of Noncompactness ◽  
Classical Geometry

The concept of convexity plays an important role in the classical geometry of normed spaces and it is frequently used in several branches of nonlinear analysis. In recent years some papers that contain generalizations of the concept of convexity with the help of the measures of noncompactness have appeared. The Tauberian operators were introduced by Kalton and Wilansky (1976) and they appear in the literature with the aim of responding to some questions related with the summability and the factorization of operators; in the preservation by isomorphisms in Banach spaces, and so forth. In this paper we make the study of the Tauberian operators, not starting from the Euclidean distance, but by means of general set quantities.

On the aronszajn property for a differential equation of fractional order in Banach spaces

2011 ◽  
Vol 61 (4) ◽  
Author(s):  
Aldona Dutkiewicz
Keyword(s):  
Differential Equation ◽  
Banach Spaces ◽  
Fractional Order ◽  
Topological Properties ◽  
Measures Of Noncompactness ◽  
Solution Sets

AbstractIn this paper we investigate some topological properties of solution sets of a differential equation of fractional order in Banach spaces. Our assumptions and proofs are expressed in terms of measures of noncompactness.

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.

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