We give now a list of three important examples of measures of noncompactness which arise over and over in applications. A measure of noncompactness in the space of functions with tempered increments on the halfaxis and its applications. Ultimately, the solutions to a system of nonlinear functional integral equations by the. This book offers a comprehensive treatment of the theory of measures of noncompactness. Measure of noncompactness and application to stochastic. N is a measure of noncompactness in our terminology if nx is the family of all precompact subsets of x. The degree of noncompactness of a set is measured by means of functions called measures of noncompactness. A measure of noncompactness essential norm for maximal functions and potential operators defined on homogeneous groups is. We define and study in detail the three main and most frequently used mncs.
The notion of measure of noncompactness is one of the most useful ones. Easily integrate our pdf measuring tools into your application or workflow. Measures of noncompactness in metric fixed point theory. Several topics in these notes can be found either in texts on measures of noncompactness see akprsj, bg or in books on metric fixed point theory see gk1, sm, z. Measure of super weak noncompactness in some banach. Our fixed point results are obtained under a weak topology and measure of weak noncompactness. Measures of noncompactness are very useful tools in banach spaces. Speed business processes and let employees work anywhere with allnew adobe acrobat dc products and adobe document cloud.
Compactness in measure and measure of noncompactness. The concept of a measure of noncompactness is very. Measure of weak noncompactness, some new properties in fredholm theory, characterization of the schechter essential spectrum and application to transport operators. Adobe adobe acrobat reader dc download free pdf viewer. Weighted estimates of a measure of noncompactness for.
Application of measure of noncompactness to infinite systems of. Measure of super weak noncompactness in some banach sequence. Pdf on may, 2020, aleksandar kostic published measures of noncompactness on wdistance spaces find, read and cite all the research you need on researchgate. In functional analysis, two measures of noncompactness are commonly used. Lx, y is compact if the closure of t ux is compact, where ux is the unit closed ball in x. Application of measure of noncompactness to a cauchy problem. Pdf hausdorff measure of noncompactness in some sequence. Sequence spaces and measures of noncompactness with. Axioms free fulltext measure of noncompactness for. Open access hausdorff measure of noncompactness in some sequence spaces of a triple band matrix ali karaisa correspondence.
Measure of noncompactness and application to stochastic differential equations. On the applications of measure of noncompactness to the existence of solutions for fractional difference equations, results math. Measure of open sets approximate from within by polygons measure of compact sets approximate from outside by opens outer and inner measures. Advances in nonlinear analysis via the concept of measure. Pdf a measure of noncompactness in the space of functions.
Pdf in this chapter, we present a survey of theory and applications of measures of noncompactness. Our aim in this paper is to present results of existence of fixed points for. In this research article, we introduce a new class of hybrid langevin equation involving two distinct fractional order derivatives in the caputo sense and riemannliouville fractional integral. It enables accurate measurement of the distance and angle between two points on a page. Applications of the hausdorff measure of noncompactness in some sequence spaces of weighted means. Caratheodory solutions of sturmliouville dynamic equation. In this paper an axiomatic approach to the notion of a measure of weak noncompactness is presented. To compute the hausdorff measure of noncompactness of a bounded subset of the bk space. Several properties of the defined measures are given. Pdf measures of noncompactness in metric fixed point.
Because of the important role of the measure of noncompactness in fixed point. Similar problem for partial sums of the fourier series is studied. Mathematics free fulltext the technique of quadruple fixed. May 15, 2019 the following definition of a measure of noncompactness given in. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixedpoint theory.
A family of measures of noncompactness in the locally. Now, assume that is a banach algebra and is a measure of noncompactness on satisfying. Pdf measures of noncompactness in metric fixed point theory. Further facts concerning measure of noncompactness and their properties may be found in. Yerzakova, the measure of noncompactness of sobolev embeddings, integral equations operator theory,19, no. Basso financial derivatives pricing, applications, and mathematics by. Pdf compactness by the hausdorff measure of noncompactness. The technique of measures of noncompactness in banach. Do everything you can do in acrobat reader, plus create, protect, convert and edit your. The investigation is based on a new fixed point result which is a generalization of the well known darbos fixed point theorem.
Pdf generalized measures of noncompactness of sets and. On the application of measure of noncompactness to the. Some remarks on measures of noncompactness and retractions. Abstract we investigate the solutions of functionalintegral equation of fractional order in the setting of a measure of noncompactness on realvalued bounded and. Nov 01, 2019 one of the properties of the measure of noncompactness is x. Measures of noncompactness in banach spaces, lecture notes in pure and applied mathematics 60, marcel dekker, new york and basel, 1980 with k. Solvability of nonlinear quadratic integral equation by using. Pdf applications of measure of noncompactness and operator.
Dec 01, 20 abstract this paper is devoted to study the existence of solutions of a cauchy type problem for a nonlinear fractional differential equation, via the techniques of measure of noncompactness. Mathematics free fulltext the technique of quadruple. Measures of noncompactness in what follows we will give a brief description of measures of noncompactness and condensing oper. Pdf weighted estimates of a measure of noncompactness. Advances in nonlinear analysis via the concept of measure of. Definition of lebesgue measurable for sets with finite outer measure remove restriction of finite outer measure rn, l, lambda is a measure space, i. Hausdorff measure of noncompactness in some sequence spaces of a triple band matrix. Pdf weighted estimates of a measure of noncompactness for. Let x, d be a metric space and d be a bounded subset of x. Pdf measures of noncompactness and their applications.
Many other topics have come from papers where the authors of this volume have published the results of their research over the last ten years. The leading pdf viewer to print, sign, and annotate pdfs. Request pdf on nov 1, 2020, mohsen rabbani and others published measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations find. In this chapter we consider the basic notions connected with measures of noncompactness mncs for brevity and condensing or densifying operators. Sep 21, 2009 in this paper, we prove the existence of solutions for a boundary value problem of fractional differential equations. For simplicity, we consider only the following three measures of noncompactness. Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of. We also illustrate our results through some concrete examples to the memory of professor lj. The technique relies on the concept of measures of noncompactness and monchs fixed point theorem. A family of measures of noncompactness in the locally sobolev. Convexification of super weakly compact sets and measure of super weak noncompactness, preprint, 2020. A condensing or densifying operator is a mapping under which the image of any set is in a certain sense more compact than the set itself. Measures of noncompactness and condensing operators. Pdf solvability of fractional dynamic systems utilizing.
Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the banach sequence spaces n. The hausdorff measure of noncompactness the hausdorff measure of noncompactness was defined by goldenstein, gohberg and markus in 1957, later. Jun 25, 2008 a measure of noncompactness essential norm for maximal functions and potential operators defined on homogeneous groups is estimated in terms of weights. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented.
By using re,n,p measure of noncompactness and under a generalization of the compactness assumptions, we prove an existence. By a free ultrafilter we understand a system u of subsets of an infinite set. Download free acrobat reader dc software, the only pdf viewer that lets you read, search, print, and interact with virtually any type of pdf file. Oct 28, 2020 download pdf measure it for free pdf measure it is an acrobat plugin tool, it enables accurate measurement of the distance and angle between two points on a page. Download fulltext pdf download fulltext pdf read fulltext. To measure a distance, click anywhere on a pdf page to set a. Measure of noncompactness of a new space of tempered. Weighted estimates of a measure of noncompactness for maximal. Download free designing control loops for linear and switching power supplies a tutorial guide book by christophe p. The kuratowski measure of noncompactness of d ad is defined as the infimum of positive numbers e such that d can be covered by a finite number of sets of diameter not greater than e. By clicking the download acrobat reader button, you acknowledge that you have read and accepted all of the terms and conditions. Moreover, studying the equivalence of measures of super weak noncompactness, we investigate the axiomatic definition and formulate a new measure which is not equivalent to the measure now we study the relationship between the super weakly compact set in. Fixed point free maps of a closed ball with small measures of. Many other topics have come from papers where the authors of this volume have published the results of.
The notion of measure of noncompactness is one of the most useful ones available and has many applications. Measure of weak noncompactness and real interpolation of. Measures of noncompactness in metric fixed point theory j. Axioms free fulltext measure of weak noncompactness and. They are widely used in fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and so on 28. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Functional integral equations measure of noncompactness. In some cases, we conclude that there is no weight pair for which these operators acting between two weighted lebesgue spaces are compact. Fixed point free maps of a closed ball with small measures. Measure of weak noncompactness, some new properties in fredholm theory, characterization of the schechter essential spectrum and application to transport.
Moreover, we provide a few concrete realizations of the accepeted axiomatic system in some banach spaces. Supported by threepoint boundary conditions, we discuss the existence of a solution to this boundary value problem. The basic properties of the hausdorff measure of noncompactness can be found in 6 and 15. Text is available under the creative commons attributionsharealike license. Existence results for abstract semilinear evolution differential inclusions with nonlocal. The main result is less restrictive than those given in the literature. This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. Compactness by the hausdorff measure of noncompactness. Lecture notes measure and integration mathematics mit. The basic properties of the hausdorff measure of noncompactness can be found in 5, for example if q, q1 and q2 are bounded subsets of a metric space x, d, then. Axioms free fulltext measure of weak noncompactness.
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