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 Nonlinear sequential fractional differential equations in partially ordered spaces

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4577-4586 ◽  
Author(s):  
Hossein Fazli ◽  
Juan Nieto
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
New Approach ◽  
Partially Ordered ◽  
Fractional Differential ◽  
Partially Ordered Spaces ◽  
Sequential Fractional Differential Equations ◽  
Ordered Banach Spaces

In this paper, some new partially ordered Banach spaces are introduced. Based on those new partially ordered Banach spaces and applying some fixed point theorems, we present a new approach to the theory of nonlinear sequential fractional differential equations. An example illustrating our approach is also discussed.

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.

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 Homogeneous operators and essential complexes

1989 ◽  
Vol 31 (1) ◽  
pp. 73-85 ◽  
Author(s):  
F.-H. Vasilescu
Keyword(s):  
Banach Spaces ◽  
Small Perturbations ◽  
New Approach ◽  
Non Linear ◽  
Homogeneous Mappings ◽  
The Stability ◽  
Homogeneous Operators ◽  
Fredholm Complexes ◽  
Gap Topology

The aim of this work is to present a new approach to the concept of essential Fredholm complex of Banach spaces ([10], [2]; see also [11], [4], [6], [7] etc. for further connections), by using non-linear homogeneous mappings. We obtain some generalized homotopic properties of the class of essential Fredholm complexes, in our sense, which are then applied to establish its relationship with similar concepts. We also prove the stability of this class under small perturbations with respect to the gap topology.

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