On rates of convergence in metric fixed point theory. Banas, measures of noncompactness in the space of continuous tempered functions, demonstr. Metric fixed point theory mathematics stack exchange. Pdf applications of measure of noncompactness to coupled. Online reading fixed point theory in ordered sets and. Measures of noncompactness in metric fixed point theory by j m ayerbe toledano, t dominguez benavides and g lopez acedo no static citation data no static citation data cite. Lopez acedo, measures of noncompactness in metric fixed point theory, birkhaser, basel, 1997. Measures of noncompactness in metric fixed point theory core. Some fixed point results via measure of noncompactness. Multivalued fixed point theorems in terms of weak topology. Pure mathematics research article a family of measures. Since then, the fixed point theory became a major branch of topology and afterwards it consistently became a major theme of the research. Cone metric spaces and xed point theorems for contractive mappings. He successively extended the schauder fixed point theorem to the setting of.
In particular, the technique of measure of noncompactness is a very useful tool for studying the existing solutions of integral equations and differential equations. Measures of weak noncompactness are formulae that quantify different characterizations of weak compactness in banach spaces. A natural extension of the study of contractions is the limiting case when the lipschitz constant is allowed to equal one. These geometrical numbers are useful in the study of measures of noncompactness, some of which are interesting quantities in fixed point theory, in chapter 1, we give some definitions and km. Chiming chen, erdal karapinar, some fixed point results via measure of noncompactness, journal of nonlinear sciences and applications, 10 2017, no. Some new generalization of darbos fixed point theorem.
Measure of weak noncompactness and fixed point theorems in. Topics in metric fixed point theory cambridge studies in. Measures of noncompactness in metric fixed point theory. It is intended to be especially useful to those who might not have ready access to other sources, or to groups of people with diverse mathematical backgrounds. This text is primarily an introduction to metric spaces and fixed point theory. Poincares analysis motivation, l e j brouwers fixed point theorem came into the world. For any bounded subset d of r2 with the radial metric, we have ad 2 wd and 0d wd. Introduction and preliminaries the concept of measures of noncompactness was rst devised by kuratowski. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or settheoretic branch of the theory. Those results were obtained by the author and his coworkers during last years with some help of the technique of measures. Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Read generalizing the kreinrutman theorem, measures of noncompactness and the fixed point index, journal of fixed point theory and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Conevalued measures of noncompactness nguyen bich huy, nguyen huu khanh and vo viet tri department of mathematics, ho chi minh city university of pedagogy. Stability of the fixed point property for nonexpansive mappings j.
A fixed point theorem for bmetric space swati agrawal, k. In some sense the theory is a farreaching outgrowth of banachs contraction mapping principle. This site is like a library, use search box in the widget to get ebook that you want. Free download fixed point theory in ordered sets and applications book now is available, you just need to subscribe to our book vendor, fill the registration form and the digital book copy will present to you. Click download or read online button to get fixed point theory and graph theory book now. Theory of nonlinear operators, akademieverlag, berlin 1974, 1556. Measures of noncompactness in metric fixed point theory j. Qureshi and jyoti nema oriental college of technology bhopal, m. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. The following theorem states, roughly speaking, that in the space r2 with the radial metric the situation concerning the measures of noncompactness is similar as in the case of r2 with the river metric.
Generalization of darbos xed point theorem and application. Under the assumptions of corollary 5, we have, by virtue remark 3, that sequence tx, converges to the unique fixed point of i. For a bounded subset s of a metric space x, the kuratowski measure of noncompactness is defined as 9. The goal is to develop, in a selfcontained fashion, those results in this theory which involve the use of measures of noncompactness. Concerning the metric branch, the most important metric fixed point result is the banach contraction principle. Our results generalize some recent theorems given in petrusel and rus the theory of a metric fixed point theorem for multivalued operators, proc. Advances and applications on free shipping on qualified orders. The journal of fixed point theory and applications jfpta provides a publication forum for an important research in all disciplines in which the use of tools of fixed point theory plays an essential role. Request pdf on researchgate measures of noncompactness in metric fixed point theory as we have seen in chapter i, compactness plays an essential. In this talk, we present a brief survey of theory and applications of measures of noncompactness. The purpose of this paper is to study the existence of fixed points by using measures of weak noncompactness. Pdf compactness and measures of noncompactness in metric.
This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory. Cone metric and cone normed spaces were introduced in the middle of the 20th century by using an ordered banach space instead of the set of real numbers, as the codomain for a metric 9,10. On the measures of noncompactness in some metric spaces dariusz bugajewski and ewa grzelaczvk received march 1997 abstract. On measures of noncompactness in banach spaces dmlcz.
Buy measures of noncompactness in metric fixed point theory operator theory. G lopez acedo this book is devoted to metric fixed point theory. Geometrical coefficients and measures of noncompactness. In this section we show an application of our results to fixed point theory in hyperconvex metric spaces.
An introduction to metric spaces and fixed point theory includes an extensive bibliography and an appendix which provides a complete summary of the concepts of set theory, including zorns lemma, tychonoffs theorem, zermelos theorem, and transfinite induction. Coupled and mixed coupled hybrid fixed point principles in. They are widely used in fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and so on 28. On densifying and related mappings and their applications in nonlinear functional analysis. Bidholi, via prem nagar, dehradun uttarakhand, india. Rezapour, some xed point results in tvscone metric spaces, fixed point theory, 1420, no. Our approach is based on the partial kuratowskii measure of noncompactness with maximum property and is somewhat different from the approach of coupled hybrid. Moreover for bounded sets h of a banach space e we consider the worst distance k h of the weak. Since 1965 considerable effort has been done to study the.
The approaches for constructing measure of noncompactness in a general metric or linear space are described, along with the classical results for existence of. Our fixed point results are obtained under a weak topology and measure of weak noncompactness. Handbook of metric fixed point theory william a kirk. Measures of noncompactness are very useful tools in banach spaces. The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Fixed point theorems econ 2010 fall 20 fixed point theory serves as an essential tool for various branches of mathematical analysis and its applications. Existence of fixed points and measures of weak noncompactness. Fixed point theorem, measure of noncompactness, darbos xed point theorem. These remarks are based on a talk the writer gave at the 11th international conference in fixed point theory and applications, held at galatasaray university in istanbul, turkey, july 2024, 2015. 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. An introduction to metric spaces and fixed point theory. This book aims to offer the mathematical community an accessible, selfcontained account which can be used as an introduction to the subject and its development.
They represent selected thoughts on a career in research, largely devoted to metric fixed point theory, that has spanned over 50 years. Further, we prove a fixed point theorem on the family of measures of noncompactness in lp loc. Some results on existence and approximation in metric fixed point. This thesis develops further the uses of proof mining in metric xed point theory, and investigates some e ective and quantitative aspects of metric xed point theory with the help of proof mining. Vietoris fractions and fixed points for setvalued maps. In this paper we calculate the hausdorff and the kuratowski mea sure of noncompactness for any bounded subsets of the space r2 with the river metric or with the radial metric. Journal of fixed point theory and applications home.
One of the generalizations of metric spaces is the partial metric space in which selfdistance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. P india abstract the aim of this paper to obtain completeness and uniqueness of fixed point theorem on bmetric space. The interplay between the geometry of banach spaces and fixed point theory has been very strong and fruitful. A family of measures of noncompactness in the locally. In particular, the technique of measure of noncompactness is a very useful tool for studying the existing solu. Pure mathematics research article a family of measures of. Due to importance of topology in fixed point theory, we discuss some topological structures in bquasi metric family as. Situations in which measures of noncompactness arise in the study of fixed point theory usually involve the study of either condensing mappings or kset. Some common fixed point theorems in partial metric spaces. Many problems in pure and applied mathematics reduce to a problem of common fixed point of some selfmapping operators which are defined on metric spaces. As an application, we investigate the existence of entire solutions for some classes of nonlinear functional integral equations of convolution type associated with the new family of measures of noncompactness. Applications of measure of noncompactness to coupled fixed points and systems of integral equations article pdf available in miskolc mathematical notes 191. Metric fixed point theory is a powerful tool for solving several problems in various parts of mathematics and its applications. Later on, we provide an existence principle for solutions for a nonlinear integral equation.
Metric fixed point results concerning measures of noncompactness t. Concerning the metric branch, the most important metric. Metric fixed point theory has proved a flourishing area of research for many mathematicians. Another measure of noncompactness is called hausdor measure of noncompactness which has been introduced by. Request pdf handbook of metric fixed point theory fixed point theory has two main branches.
Measure of nonhyperconvexity and fixed point theorems. Loosely speaking, there are three main approaches in this theory. The classical measures of noncompactness are discussed and their properties are compared. A family of measures of noncompactness in the locally sobolev. Ninth international conference on fixed point theory and its applications, changhua, taiwan, july 1622, 2009, 161175, 2010. Topics in metric fixed point theory cambridge studies in advanced mathematics 28 n.
Online reading fixed point theory in ordered sets and applications book are very easy. These spaces have applications in approximation theory 9,10, in xed point theory and theory of di erential equations in banach spaces 1. However many necessary andor sufficient conditions for the existence of such points involve a mixture of algebraic order theoretic or topological properties of mapping or its domain. Preface vii introduction 1 i the fixed point theorems of brouwer and schauder 5 1 the fixed point theorem of brouwer and applications 6 2 the fixed point theorem of schauder and applications 10 ii measures of noncompactness 17 1 the general notion of a measure of noncompactness 18 2 the kuratowski and hausdorff measures of noncompactness 20 3 the. Handbook of metric fixed point theory springerlink. Some fixed point theorems in generating space of bquasi.
In particular, geometrical properties play key roles in metric fixed point problems. Apr 28, 2010 read generalizing the kreinrutman theorem, measures of noncompactness and the fixed point index, journal of fixed point theory and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Some fixed point theorems in metric and banach spaces. Oreganfixed point theory for weakly contractive maps with. 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.
A comprehensive, basic level introduction to metric spaces and fixed point theory an introduction to metric spaces and fixed point theory presents a highly selfcontained treatment of the subject that is accessible for students and researchers from diverse mathematical backgrounds, including those who may have had little training in mathematics beyond calculus. Fixed point theorems via conenorms and conevalued measures of noncompactness nguyen bich huy, nguyen huu khanh and vo viet tri department of mathematics, ho chi minh city university of pedagogy. Introduction to metric fixed point theory in these lectures, we will focus mainly on the second area though from time to time we may say a word on the other areas. Lopez, metric fixed point results concerning measures of noncompactness, handbook of metric fixed point theory, kluwer acad. Oreganfixedpoint theory for weakly sequentially continuous mappings. Nov 24, 2015 these remarks are based on a talk the writer gave at the 11th international conference in fixed point theory and applications, held at galatasaray university in istanbul, turkey, july 2024, 2015. The notion of the measure of noncompactness of a subset of a metric space was introduced by kurato wski 11 as a way to generalize canto rs intersection theorem.
Remarks on some fixed point theorems for hyperconvex metric. This thesis studies various measures of noncompactness and some geometrical coefficients in metric or bauach spaces. Recent advances on metric fixed point theory this book consists of the proceedings of the international workshop on metric fixed point theory which was held at the university of seville, 2529 september, 1995. Those results were obtained by the author and his coworkers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of darbo type.
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