The main purpose of this paper is to give some new common fixed point theorems under strict contractive conditions for mappings satisfying a new property. Some common fixed point theorems for contraction type. While proving this result, we utilize definition 1. Our results im prove some recent results contained in imdad and ali jungcks common fixed point theorem and e.
Common fixed point theorems in complete metric and. Some common fixed point theorems for fuzzy maps under. Very recently, roldanlopezdehierro and shahzad introduced the notion of r. Common fixed point theorems of integral type contraction. Common fixed point theorems on weakly contractive and. Common fixed point theorems in fuzzy metric spaces. Some common fixed point theorems satisfying meirkeeler. The last theorem extends known results on compatible maps to. L 0,1 and s and t be weakly compatible mappings of x into itself. Pdf common fixed point theorems in digital metric spaces jyoti antil academia. Sufficient conditions for the existence of a common fixed point for generalized nonlinear. Abstract in this paper, we prove some common fixed point results for two mappings satisfying contraction conditions in complete bmetric spaces.
Common fixed point theorems for compatible mappings article pdf available in international journal of mathematics and mathematical sciences 193 january 1996 with 150 reads how we measure. Pdf common fixed point theorems for compatible mappings. Eslamian, fixed point theorems for suzuki generalized nonexpansive multivalued mappings in banach spaces, fixed point theory and applications, vol. Common fixed point theorems on fuzzy metric spaces. Common fixed point theorems in intuitionistic fuzzy metric. In this paper several common fixed point theorems for four continuous mappings in menger and metric spaces are proved. Some recent results are discussed as special cases.
In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. Common fixed point theorems on fuzzy metric spaces using. Common fixed point theorems under r,\mathcal scontractivity conditions. Acknowledgments the authors would like to express their sincere appreciation to the referees for their very helpful suggestions and many kind. We present some fixed point theorems and common fixed point theorems which generalize and unify previous known results. Fixed and common fixed point theorems in metric spaces saleh a. Some common fixed point theorems in generalized metric spaces manoj kumar,1,2 pankaj kumar,3 and sanjay kumar4 1department of mathematics, delhi institute of technology and management, gannaur 1101, sonipat, india 2guru jambheshwar university of science and technology, hisar 125001, india 3department of mathematics, guru jambheshwar university of science and technology, hisar. Common fixed point theorems for multivalued mappings. Our results improve and generalize the main results of mihet in mihet, 2010 and many fixed point theorems in fuzzy metric spaces. Obtained results extend and generalize wellknown comparable results in the literature. Recent progress in fixed point theory and applications 2015. Subsequently, a number of new xed common xed point theorems for mappings in metric spacespartial metric spaces have been. Pdf in the present paper, we establish a common fixed point theorem for four selfmappings of a complete 2metric space using the weak commutativity.
Pdf we introduce the notions of the w function and s function, and then we prove two common fixed point theorems in complete generalized metric spaces. Our main results extend, generalize and fuzzify some known results in fuzzy metric spaces, probabilistic metric spaces and uniform spaces. Common fixed point theorems for a finite family of. Further, using two corollaries of the main result theorem 2. Fixed and common fixed point theorems in metric spaces. Common fixed point theorems in modified intuitionistic.
Jungck initiated the concept of weakly compatible maps to study common fixed point theorems. In this paper, we prove some common fixed point the orems for four maps in complete metric spaces. Some common fixed theorems which generalize the result of hicks. Some fixed point and common fixed point theorems in 2. In this paper we study and generalize some common fixed point theorems in compact and hausdorff spaces for a pair of commuting mappings with new contraction conditions. School of mathematics and s ystems science, shenyang normal university, shenyang 110034, china. We prove some common fixed point theorems for four mappings in those spaces. 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. Common fixed point theorems of gregus type for weakly compatible. Common fixed point theorems for multivalued mappings in. The study of common fixed points satisfying contractive type conditions has been a very active field of research activity.
In this paper, we prove some common fixed point theorems for a finite family of multivalued and singlevalued mappings operating on ordered banach spaces. After that a series of articles have been dedicated to the improvement of fixed point theory. Generalization of common fixed point theorems for two mappings. Some fixed point and common fixed point theorems in 2banach spaces a. Journal of inequalities and applications common fixed point theorems for multivalued mappings in complexvalued metric spaces akbar azam 0 jamshaid ahmad 0 poom kumam 1 0 department of mathematics, comsats institute of information technology, chack shahzad, islamabad, 44000, pakistan 1 department of mathematics, faculty of science, king mongkuts university of technology. Our results modify the results of seong hoon cho 16. These theorems are versions of some known results in.
X\rightarrow x\ is a point \x\in x\ for which \kxlxx\. We also give some examples to illustrate our results. Our results extend, generalize, and unify several known results in the literature. Some common fixed point theorems for generalized nonlinear.
Two examples related to our results are also given. In this paper we prove common fixed point theorems for six mappings in fuzzy metric space. We prove some common fixed point theorems for contractions in 0complete partial metric spaces. Pdf new coincidence and common fixed point theorems. Fixed point theorems fixed point theorems concern maps f of a set x into itself that, under certain conditions, admit a. Some examples are included which show that the generalization is proper. Common fixed point theorems for mappings under clrs. Pdf in this paper, we establish a common fixed point theorem for a family of self setvalued mappings on a compact and convex set in a locally convex. Further, we first formulate the definition of weakly commuting and rweakly commuting mappings in.
Meanwhile, two examples are presented to support our results. Pdf general common fixed point theorems and applications. Common fixed point theorems for mappings satisfying ea. The most general common fixed point theorems for four mappings, say a, b, s and t of a metric space xd, use either a.
Common fixed points for multivalued mappings in complex valued metric spaces with applications ahmad, jamshaid, klineam, chakkrid, and azam, akbar, abstract and applied analysis, 20. Dwijendra and yumnam rohen abstract in this paper we prove some common fixed point theorems for compatible mappings of type a in fuzzy metric spaces. Pdf common fixed point theorems for mappings satisfying. Some common fixed point theorems for mappings and multivalued mappings. Pdf some common fixed point theorems for mappings and. We prove the existence and uniqueness of a common fixed point of two selfmappings under certain conditions. In this paper, we have proved some common fixed point theorems for a pair of mappings satisfying certain rational contraction condition in the frame work of bicomplex valued metric space x, d.
Coincidence points and common fixed points for expansive type. Almezel department of mathematics university of tabuk p. The purpose of this paper, using the idea of intuitionistic fuzzy set due to atanassov 2, we define the notion of intuitionistic fuzzy metric spaces see, 1 due to kramosil and michalek 17 and jungcks common fixed point theorem 11 is generalized to intuitionistic fuzzy metric spaces. It is well known that banachs fixed point theorem for contraction mappings is one of the pivotal results in analysis. In 15, huang and zhang introduced the concept of cone metric spaces. Annual international interdisciplinary conference, aiic common fixed point theorems for commuting mappings on a quasimetric space luljeta kikina 0 asoc. Recently, suzuki in 2008 obtained a generalization of banach contraction principle.
Our results extend and generalize many results in the literature on fixed point theory and lead to existence theorems for a system of integral inclusions. Pdf common fixedpoint theorems in complete generalized. The results presented in this paper include the generalization of some fixed point theorems of fisher, jungck, mukherjee, pachpatte and sahu and sharma. The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of d oric and lazovic 2011 for a multivalued map on a. A common fixed point of a pair of selfmapping \k,l.
In recent years, some interesting common fixed point theorems for contractive type mappings have been reported in the literature, e. In the present paper we prove some fixed point and common fixed point theorems in 2banach spaces for new rational expression. Coupled coincidence point theorems for new types of mixed monotone multivalued mappings in partially ordered metric spaces klanarong, chalongchai and suantai, suthep, abstract and applied. In this paper, we give a fixed point theorem and some results for mappings satisfying e. Some generalizations of fixed point theorems and common. Moreover, a and s have a unique common fixed point in x provided that the pair a, s is weakly compatible. Common fixed point theorems in menger spaces 43 h e i. Common fixed point theorems for four mappings on cone. Notice that here the operators need not commute with. Two common fixed point theorems have been proved by using minimal type commutativity and contractive conditions. Let be an arbitrary point in and let be an iteration of type krasnoselskimann generated by 1.
Common fixed point theorems for pairs of mappings in d. A common fixed point theorem of a gregus type on convex cone metric spaces. Pdf common fixed point theorems in a complete 2metric space. These mappings are assumed to satisfy some generalizations of. Some common fixed point theorems in generalized metric. Common fixed point theorems in digital metric spaces asha rani, kumari jyoti, asha rani department of mathematics, srm university, haryana, sonepat 1001, india. Some common fixed point theorems in partial metric spaces. General common fixed point theorems and applications.
We prove a common fixed point theorem of gregus type for four mappings satisfying a contractive condition of integral type in metric spaces using the concept of. In 2008, altun and turkoglu 4 proved two common fixed point theorems. Common fixed point theorems in digital metric spaces ijser. Banach type contractive condition of the form 1 d ax by hm x y h. We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of kramosil and michalek and in the sense of george and veeramani by using the new property and give some examples. Generalized common fixed point theorems in complex valued. Motivated by aforementioned articles, we establish common fixed point.
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