Now we establish a fixed point theorem for a weaknonexpansive multivalued mapping. Introduction and preliminaries fixed point theory plays one of the important roles in nonlinear analysis. This result is extended by kubiaczyk1996 from single valued to. Sur les operations dans les ensembles abstraits et leur application aux equations integrales. The banach fixed point theorem is also called the contraction mapping theorem, and it is in general use to prove that an unique solution to a given equation exists. Pdf new fixed point theorems on order intervals and.
Nielsen theory is a branch of mathematical research with its origins in topological fixed point theory. Fixedpoint theorems using theorem 6 of ky fan io and lemma 1 below, we establish a number of fixedpoint theorems for certain upper demicontinuous mappings which are defined on closed convex sets and which satisfy condition l, i. Common fixed point theorems in cone banach spaces 2 ii x n n. Pdf common fixed point theorems in cone banach spaces. The prototype of theorems in this class is the brouwer fixed point theorem. Some new common fixed point theorems under strict contractive. Our results im prove some recent results contained in imdad and ali jungcks common fixed point theorem and e. Recently nieto and rodriguezlopez 9, 11, ran and reurings 12 and petrusel and rus presented some new results for contractions in partially ordered metric spaces. New common fixed point theorems for multivalued maps. C is nonexpansive and satisfies a conditional fixed point property, then the fixedpoint set of t is a nonexpansive retract of c. Let c be a weakly compact subset of a banach space x and t. Mizoguchitakahashi s xed point theorem with,r functions, abstract and applied analysis,vol. Fixed point theorems for multivalued contractive mappings in bmetric space u. The results on fixed point theorems are generalizations of the recent results of choudhury and maity b.
In this paper,we prove a xed point theorem for multivalued contractive mappings in bmetric spaces. September17,2010 1 introduction in this vignette, we will show how we start from a small game to discover one of the most powerful theorems of mathematics, namely the banach. In the present paper we will establish some fixed point and common fixed point theorem in 2 banach space taking rational expression for 1,2,3 mappings. Further fixed point results on g metric spaces fixed.
Please comment if you need me to reproduce the latter proof here. Common fixed point theorems in nonarchimedean normed. Fixedpoint theorems for multivalued noncompact inward maps. To prove the fixed point theorem, we follow the idea of a class of im plicit functions initiated by popa 8, because it covers several contractive conditions rather than one. Fixed point theorems for multivalued contractive mappings in bmetric space.
This doesnt seem intuitive to me the way some other problems do. Some fixed point theorem for expansive type mapping in. Theorems of hsiang and torn dieck suggest that theorem a should generalize to a class of compact lie groups. Fixed point theorems in generalized partially ordered g. Many existence problems in economics for example existence of competitive equilibrium in general equilibrium theory, existence of nash in equilibrium in game theory. Its central ideas were developed by danish mathematician jakob nielsen, and bear his name the theory developed in the study of the socalled minimal number of a map f from a compact space to itself, denoted mff. Pdf new fixed point theorems on order intervals and their. Some fixed point theorems for quadratic quasicontractive. On the variations of some well known fixed point theorem. On the variations of some well known fixed point theorem in. Recently erdal karapinar, billur kayamakcalan and kenan tas 19 improved and extend the coupled fixed point of ayedi et al. Dynamic properties of the dynamical system sfnmx, sfnmf 20 views since. Some fixed point theorems in b metriclike spaces fixed.
Here, we remark that a common xed point for the mappings exists even if the conditions of the above theorem are not satis ed. C c is nonexpansive and satisfies a conditional fixed point property, then the fixedpoint set of t is a nonexpansive retract of c. Fixed point theorem 75 iii if every cauchy sequence in x is convergent, then x. Josephs collegeautonomous, tiruchirappalli620 002,india. Fixed point theorems using theorem 6 of ky fan io and lemma 1 below, we establish a number of fixed point theorems for certain upper demicontinuous mappings which are defined on closed convex sets and which satisfy condition l, i. Contraction conditions using comparison functions on b.
Fixed point theorems on multi valued mappings in bmetric. A common fixed point theorem for multivalued mappings. With pdf merger you can merge your multiple pdf files to a single pdf file in matter of seconds. Moreover, for such spaces, we prove matkowskis fixed point theorem. Common fixed point theorem governed by implicit relation. For this let f 6 be the set of all realvalued continuous functions f 6t1 w 6. Fixed point theorems for generalized weakly contractive mappings 217 t. Some common coupled fixed point theorems for generalized contraction in bmetric space. Suppose there exists for which for all, and for all. Fixed point theory and nonexpansive mappings springerlink. Its central ideas were developed by danish mathematician jakob nielsen, and bear his name. Fixed point theory originally aided in the early developement of di erential equations. We choose any xo e x and define the iterative sequence xn by 2 clearly, this is the sequence of the images of xo under repeated.
We also apply the method to two other fixed point theorems, a generalization of tarskis theorem to chaincomplete posets and bourbakiwitts. The concept of b metric spaces was introduced by bakhtin 21 in 1989, who used it to prove a generalization of the banach principle in spaces endowed with such kind of. Department of mathematics, sri sankara arts and science college, enathur, kanchipuram631 561,india. Anyway, the proof of theorem 2 applies banachs fixed point theorem, just like what exercise 5 asks to. This result is used to generalize a theorem of belluce and kirk on the existence of a common fixed point of a finite family of commuting. This results o ers a generalization of swati agarawal,k. In 1962, edelstein 1 proved the following fixed point theorem. It can be easily observed that these are significant improvement of some of the wellknown classical result dealing with. Maity, coupled fixed point results in generalized metric spaces, math. Fixed point theorems for multivalued contractive mappings in. A fixed point theorem for setvalued quasicontractions in bmetric spaces. We also show that continuity of any mapping is not needed for the. This paper aims to present some fixed point theorems on metric spaces. X satisfying the above inequality is said to be weakly contractive with respect to fand if fis the identity mapping, t is said to be weakly contractive.
New common fixed point theorems for multivalued maps singh. The following example shows that the largest class we can expect consists of extensions of finite pgroups by tori. This theorem has fantastic applications inside and outside mathematics. Jan 27, 2018 we give a characterization of complete vgeneralized metric spaces in terms of the fixed point property. Fixedpoint theorems for multivalued mappings in modular. Among other directions, the theory now addresses certain geometric properties of sets and the banach spaces that contain them. Fixed point theorems for multivalued nonself almost. In the case of twogeneralized metric spaces, we obtain a characterization of uniform continuity in terms of the distance function between two sets. And then a new staionary point theorem for multivalued maps is given. Presented to the society, january 24, 1977 under the title fixed point theorems for multivalued pycompact mappings. In article 2 vasile berinde, generalized contractions in quasimetric spaces, 1993, no.
A fixed point theorem for multivalued maps in symmetric. Fixed point theorems for multivalued nonself almost contractions in banach spaces endowed with graphs j. Recently, isufati 5, proved fixed point theorem for contractive type condition with rational expression in dislocated quasimetric spaces. The theory developed in the study of the socalled minimal number of a map f from a compact space to itself, denoted mf f. In mathematics, the banachcaccioppoli fixedpoint theorem is an important tool in the theory of metric spaces. Let abe a nonempty compact convex subset of a hausdor. Moreover, the method of lower and upper solutions is. A note on fixed point results in complexvalued metric spaces. In this paper, using the concept of wdistances on a metric space, we. To prove our claim, we give following counter example where the conditions 1. A fixed point corresponds to a point at which the g. Coupled fixed point theorems in complex valued metric. Our pdf merger allows you to quickly combine multiple pdf files into one single pdf document, in just a few clicks. Fixed point theorems formultivalued meirkeeler set.
Fixed point theorems fixed point theorems concern maps f of a set x into itself that, under certain conditions, admit a. A common fixed point theorem for multivalued mappings through. Finally, we give an application of our result for weakly. Common fixed point theorems in nonarchimedean normed space. Fixed point theorems on multi valued mappings in bmetric spaces. Also, there have been developed studies on approximate fixed point or on qualitative aspects of numerical procedures for approximating fixed points see, for example 19, 20. It seems to me i should be able to find a number of counterexamples.
A contraction of x also called a contraction mapping on x is a. The great difficulty in talking about nonalgorithmic phenomena is that although we can say what it is in general terms that they do, it is impossible by their very nature to describe how they do it. The banach fixed point theorem is a very good example of the sort of theorem that the author of this. Coupled fixed point theorems in gbmetric space satisfying. It seems that exercise 5 calls for the reader to construct a proof similar to that of theorem 2. Fixed point theorems for generalized multivalued mappings in bmetric space u.
Fixed point theorems for nonseparating plane continua and related results the brouwer fixed point theorem implies that the 2cell has the. Results dealing with a fixed point for a map need not be continuous on a metric space, which improves a famous classical result, has been presented here, wherein the convergence aspect is duly addressed. This concept is a very useful tool in functional analysis, such as in metric fixed point theory and operator equation theory in banach spaces. On new extensions of darbos fixed point theorem with. The closure of g, written g, is the intersection of all closed sets that fully contain g.
Research article a fixed point theorem for multivalued. Prove fixed point theorem using the mean value theorem. This concept is further extended to tripled fixed point by berinde and borcut 2011 and to quadrupled fixed point by karapinar. Fixed point theorems for multivalued contractive mappings. Fixed point results for rational type contraction in. Fixed point theorems for general contractive mappings with wdistances in metric spaces wataru takahashi, ngaiching wong, and jenchih yao abstract. Many existence problems in economics for example existence of competitive equilibrium in general equilibrium theory, existence of nash in equilibrium in game theory can be formulated as xed point problems.
The banach fixed point theorem for contraction mappings has been generalized and extended in many directions. A common fixed point theorem for multivalued mappings through tweak commutativity i. Fixed points and stationary points for multivalued maps in. Department of mathematics, sri sankara arts and science college, enathur, kanchipuram631 561. Fixed point theorems for planar or onedimensional continua throughoutthissection,a continuum means a compact connected metric space. Note that our result does not assure the uniqueness of a fixed point, as illustrated in the above example. In this paper we have obtained some fixed point theorems on b metric space which is an extension of a fixed point theorem by hardy and reich 20. Generalized common fixed point theorems in complex valued. Coupled fixed point theorem on partially ordered gmetric. In this paper, we prove a fixed point theorem and a common fixed point theorem for multi valued mappings in complete bmetric spaces. This thesis contains results from two areas of analysis. Combines pdf files, views them in a browser and downloads. Fixed point theorems for two new classes of multivalued.
In 2008, aage and salunke 4 proved some results on fixed point in dislocated quasimetric spaces. The existence of solutions is deduced from a recent fixed point theorem valid for operators defined on suitable cones of banach spaces. Coupled fixed point theorems in complex valued metric spaces. Since then large number of research papers came out about coupled fixed point. Common fixed point theorem governed by implicit relation and. C of the above theorem are not satis ed but there is a common xed point for the maps. Also we prove a common fixed point theorem for commuting. Common fixed point theorems for a new class of multivalued maps are obtained, which generalize and extend classical fixed point theorems of nadler and reich and some recent suzuki type fixed point theorems. In this section we shall prove two fixed point theorems. Various application of fixed point theorems will be given in the next chapter. Suantai 2 1 department of mathematics and statistics, faculty of science and technology thailand, chiang mai rajabhat university, chiang mai 50300, thailand. Jul 21, 2015 recently, the concept of bmetriclike spaces which is a generalization of metriclike spaces and bmetric spaces and partial metric spaces was introduced in.
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