Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions

We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.K. Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A).     

A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type

In this paper, we proved a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type and a property (E.A) introduced in [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188]. Our theorem generalizes Theorem 2.2 of [M. Aamri, D. El Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-Notes 3 (2003) 156-162] and Theorem 2 of [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188].     

类距离空间中关于循环映射的公共不动点定理

在0-σ-完备的类距离空间中,证明了一类循环压缩映射的公共不动点定理,其中压缩条件包含了二元变距离函数.结果改正并推广了Akram等人最近的结果.     

非相容映象的公共不动点定理

本文研究了度量空间中非相容自映象对.利用非相容映象的性质和压缩条件得到一类映象的公共不动点定理,其结果推广了相关文献中的结论.     

Approximation of common fixed points of weakly compatible pairs using the Jungck iteration

We show that the Jungck iteration scheme can be used to approximate the common fixed points of some weakly compatible pairs of generalized quasicontractive operators defined on metric spaces. The existence of coincidence points are also discussed for those pair of maps. The results are generalizations of well known results of the convergence of Picard iterations for single self maps of Banach spaces. In particular, the results improve, generalize and extend the recent results of Berinde [V. Berinde, A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Applied Mathematics and Computation 213 (2009) 348-354] and answers the open question posed in the paper.     

Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type

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 weak compatibility which generalizes Theorem 2 of [A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378] and other papers. We prove also common fixed point theorems of Gregus type using a strict contractive condition of integral type, a property (E.A) and a common property (E.A) introduced by [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188] and [W. Liu, J. Wu, Z. Li, Common fixed points of single-valued and multi-valued maps, Int. J. Math. Math. Sci. 19 (2005) 3045-3055], respectively.     

Compatible mappings of type (B) and common fixed point theorems in Saks spaces

In this paper we first introduce the concept of compatible mappings of type (B) and compare these mappings with compatible mappings and compatible mappings of type (A) in Saks spaces. In the sequel, we derive some relations between these mappings. Secondly, we prove a coincidence point theorem and common fixed point theorem for compatible mappings of type (B) in Saks spaces.     

Almost biased mappings and almost compatible mappings are equivalent under some condition

The concepts of almost biased mappings and almost compatible mappings are introduced. Some variants of these concepts are also discussed. A common fixed point theorem for a pair of almost I-biased mappings in metric spaces is proved under certain condition. In the sequel, it is shown that almost biased mappings and almost compatible mappings are equivalent under some condition.     

Fixed point theorems for generalized weakly contractive mappings

We prove a fixed point theorem for a generalized weakly contractive mapping and a fixed point theorem for a pair of weakly contractive mappings. We also show that these mappings satisfy properties P and Q.     

Best proximity point theorems for contractive mappings

This article is concerned with some new best proximity point theorems for principal cyclic contractive mappings, proximal cyclic contractive mappings, and proximal contractive mappings. As a consequence, an interesting fixed point theorem, due to Edelstein, for a contractive mapping is obtained from all those best proximity point theorems.     

Fixed Points of Mappings Satisfying a Weakly Contractive Type Condition

In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak(k, k/) contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T_1 : X γ Y → X and T_2: X γ Y → Y be two operators which satisfy weak(k, k/) contractive type condition. Using T_1 and T_2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γ Y.We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings(T_1, T_2) satisfying weak(k, k/)contractive type condition on X γ Y and from this pair, we also obtain two self mappings S_1 and S_2 on X and Y respectively with unique fixed points.     

Contractive type non-self mappings on metric spaces of hyperbolic type

Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of ?iri? [L.B. ?iri?, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. ?iri?, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.     

Fixed point and (DS)-weak commutativity condition in intuitionistic fuzzy metric spaces

The aim of this paper is to show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic fuzzy metric spaces without assuming continuity of any mappings. To prove the result we use new commutativity condition for mappings weaker than compatibility of mappings.     

COMMON FIXED POINT THEOREMS FOR THREE MAPS IN DISCONTINUOUS Gb-METRIC SPACES

In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or Gb-metric. In this paper, we prove a common fixed point theorem for three mappings in Gb-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result.     

Coincidence and fixed points in symmetric spaces under strict contractions

Some common fixed point theorems due to Aamri and El Moutawakil [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188] and Pant and Pant [R.P. Pant, V. Pant, Common fixed points under strict contractive conditions, J. Math. Anal. Appl. 248 (2000) 327-332] proved for strict contractive mappings in metric spaces are extended to symmetric (semi-metric) spaces under tight conditions. Some related results are derived besides discussing illustrative examples which establish the utility of results proved in this note.     

广义概率A—proper 映象的拓扑度及其不动点定理

本文建立了M—PN 空间中广义概率A-proper 映象的拓扑度及其不动点定理。它是广义A—proper 映象及其不动点定理的推广。     

Common fixed points for discontinuous mappings in fuzzy metric spaces

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

Some Fixed Point Results for a Sequence of Mappings on G-Metric Space

In the setting of generalized metric spaces, so called G-metric spaced introduced by Z. Mustafa and B. Sims in 2006, some fixed point results for mappings with contractive iterate at a point and common fixed point results for infinite family of self mappings will be presented. The results are generalizations of well known results in the metric space. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

偏距离空间上四个映射的公共不动点的存在性与唯一性

该文证明了偏距离空间上满足广义非线性压缩型的四个映射的公共不动点定理.最后,举例说明了该文压缩条件确实改进了目前一些文献中压缩条件.