General Contractive Condition Research Articles

Conditions of regularity in cone metric spaces

In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included.

On a General Contractive Condition for Cyclic Self‐Mappings

This paper is concerned with p(≥2)‐cyclic self‐mappings in a metric space (X, d), with Ai ⊂ X, T(Ai)⊆Ai+1 for i = 1, 2, …, p, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed points and best proximity points is discussed as well as the convergence to them of the iterates generated by the self‐mapping from given initial points.

Gregus‐Type Common Fixed Point Theorems for Tangential Multivalued Mappings of Integral Type in Metric Spaces

The concept of tangential for single‐valued mappings is extended to multivalued mappings and used to prove the existence of a common fixed point theorem of Gregus type for four mappings satisfying a strict general contractive condition of integral type. Consequently, several known fixed point results generalized and improved the corresponding recent result of Pathak and Shahzad (2009) and many authors.

Fixed points of occasionally weakly compatible maps satisfying general contractive conditions of integral type

In this paper, two common fixed point theorems for four occasionally weakly compatible maps satisfying a contractive condition of integral type are obtained. Our results improve some results especially Theorem 2.1 of [3] and Theorem 1 of [1].

Fixed Point of TF-contractive Single-valued Mappings

In this paper, we study the existence of fixed points for mappings defined on complete metric space (X,d) satisfying a general contractive inequality depended on another function. This conditions is analogous of Banach conditions and general contraction condition of integral type.

Coincidence and fixed points for hybrid tangential maps

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

Random solution of random multivalued operator inclusions

Abstract Sufficient conditions for a random solution of random operator inclusions involving random multivalued operators satisfying a general contractive condition are obtained. A simultaneous random solution of the system of two random operator inclusions is also derived.

Comparison of Contract General Conditions between United States and China

In light of the fact that construction projects are expensive, complex, and time-consuming undertakings, a well-written contract that specifies each participant’s duties and obligations is required. Furthermore, a well-written contract with regard to business practice differences between the United States and China is unquestionably needed by American owners, design firms, and construction companies conducting business in China. In response to this industry need, general conditions of construction contracts commonly used in the United States (AIA-A201) and China (GF-1999-0201) have been analyzed and compared. The findings of this research reveal that the content of subclauses in AIA-A201 and GF-1999-0201 is different in several ways. These differences may have been caused by cultural, historical, geographical, political, and language variations that exist between the American and Chinese construction markets. Understanding these differences could help U.S. companies stay competitive and profitable in China.

Some results on the continuous dependence of the fixed points for Kirk-type iterative processes in Banach space

In this paper, we shall establish some results pertaining to the continuous dependence of the fixed points in a Banach space setting for Kirk and two Kirk-type iterative processes using two general contractive conditions. Our results are new extensions of some of the results of Berinde (Iterative approximation of fixed points, CUB PRESS 22 SRL, Editura Efemeride, Baia Mare, 2002; Iterative approximation of fixed points, Springer, Berlin 2007), Rus (Generalized contractions and applications, Cluj University Press, Cluj Napoca , 2001), Zeidler (Nonlinear functional analysis and its applications-Fixed point theorems, Springer, New York, 1986) and the recent results of the author Olatinwo (Fixed Point Theory 10(1):151–157, 2009). See also the recent results of Berinde and Pacurar (Fixed Point Theory 9(1):23–34, 2008), Rus (Fixed Point Theory 9(2):541–559, 2008), Rus and Rus (Stud Univ Babes-Bolyai Math 43:79–83, 1998), Rus and Muresan (Data dependence of the fixed points set of some weakly Picard operators, Tiberiu Popoviciu Sem, Cluj-Napoca, pp. 201–208, 2000).

Common Fixed Point Theorem for Non-Self Mappings Satisfying Generalized Ćirić Type Contraction Condition in Cone Metric Space

We prove common fixed point theorem for coincidentally commuting nonself mappings satisfying generalized contraction condition of Ciric type in cone metric space. Our results generalize and extend all the recent results related to non-self mappings in the setting of cone metric space.

Two Fixed‐Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type in the Modular Space

First we prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive inequality of integral type. Then we generalize fixed‐point theorem for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974).

Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces

The probabilistic version of the classical Banach Contraction Principle was proved in 1972 by Sehgal and Bharucha-Reid [V.M. Sehgal, A.T. Bharucha-Reid, Fixed points of contraction mappings on PM spaces. Math. Syst. Theory 6, 97–102]. Their fixed point theorem is further generalized by many authors. In the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems. However, the problem to prove the probabilistic versions of the very important generalization of the Banach Contraction Principle, obtained in 1969 by Boyd and Wong [D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Am. Math. Soc. 20 (1969) 458–464], who proved the fixed point theorem for a self-mapping of a metric space, satisfying the very general nonlinear contractive condition, is unsolved in these days. Similarly, as in the metric space case, to prove a fixed point theorem for a mapping, satisfying the general probabilistic nonlinear contractive condition, it was necessary to find a new approach, substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition, introduced by Sehgal and Bharucha-Reid and further used by many authors. So, the problem to obtain a truthful probabilistic version of the Banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years. We have solved this problem in this paper.

NECESSARY AND SUFFICIENT CONDITIONS FOR COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACE

The aim of this paper is to provide a necessary and su cient condition for the existence of a common xed point of three maps f; g and T in a complete fuzzy metric space under a general contractive condition. A common xed point theorem for a pair of weakly biased mappings, which is more general than weakly compatible mappings is also proved. |||||||||||||||

Gregus type fixed point results for tangential mappings satisfying contractive conditions of integral type

The notion of pair-wise tangential mappings, which is a generalization of mappings satisfying (E.A) property, is introduced and used to prove a common fixed point theorem of Gregus type for a quadruple of self mappings of a metric space satisfying a strict general contractive condition of integral type. Our main result generalizes a recent result of A. Djoudi, A. Alioche [Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (2007), 31-45].

Common Fixed Point Theorems for Weakly Compatible Maps Satisfying a General Contractive Condition

We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type.

Common fixed point theorems for maps under a contractive condition of integral type

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007–4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149–153].

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).

Fixed Points of Weakly Contractive Maps and Boundedness of Orbits

We discuss weakly contractive maps on complete metric spaces. Following three methods of generalizing the Banach contraction principle, we obtain some fixed point theorems under some relatively weaker and more general contractive conditions.

Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type

AbstractWe prove a fixed point theorem for weakly compatible maps satisfying a general contractive condition of integral type.

Coincidence Points and Invariant Approximation Results for Multimaps

Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved. © 2006 Springer-Verlag Berlin Heidelberg.