Nonlinear Contractive Condition Research Articles

Coupled Coincidence Point Results for (ψ, α, β)‐Weak Contractions in Partially Ordered Metric Spaces

In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. (2011). Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.

(DS)-WEAK COMMUTATIVITY CONDITION AND COMMON FIXED POINT IN INTUITIONISTIC MENGER SPACES

The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.

Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces

The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.

Common fixed point theorems involving two pairs of weakly compatible mappings in [formula omitted]-metric spaces

We establish common fixed point theorems involving two pairs of weakly compatible mappings satisfying nonlinear contractive conditions in K -metric spaces. The presented theorems generalize, extend and improve many existing results in the literature.

Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems

AbstractWe establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.

Coupled Random Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces

Let (X, ≤) be a partially ordered set and suppose there is a metric d on X such that (X, d) is a complete separable metric space and (Ω, Σ) be a measurable space. In this article a pair of random mappings F: Ω × (X × X) → X and g: Ω × X → X, where F has a mixed g-monotone property on X, and F and g satisfy the non-linear contractive condition (5) below, are introduced and investigated. Two coupled random coincidence and coupled random fixed point theorems are proved. These results are random versions and extensions of recent results of Lakshmikantham and Ćirić [V. Lakshmikantham and Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal.—Theor. 70(12) (2009): 4341–4349] and include several recent developments.

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.

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.

Non-self mappings satisfying non-linear contractive condition with applications

The concept of non-self mappings satisfying a new non-linear contractive type condition is introduced, and coincidence and common fixed point theorems in metric spaces of hyperbolic type are proved. Presented theorems generalize and improve recent theorems of Imdad and Kumar [M. Imdad, S. Kumar, Rhoades-type fixed-point theorems for a pair of nonself mappings, Comput. Math. Appl. 46 (2003), 919–927] and several others theorems. One example is constructed to show that our theorems are genuine generalizations of the above mentioned results of Imdad and Kumar and several others.

Common fixed point theorems for families of weakly compatible maps

In this paper the existence and approximation of a unique common fixed point of two families of weakly compatible self-maps on a complete metric space are investigated. An example is presented to show that our results for the mappings considered satisfying non-linear contractive type conditions are genuine generalizations of the recent result for metric spaces [B. Singh, S. Jain, A fixed point theorem in Menger space through weak compatibility, J. Math. Anal. Appl. 301 (2005) 439–448, Theorem 3.3] and many other known results.

A common fixed point theorem for R-weakly commuting mappings in probabilistic spaces with nonlinear contractive conditions

Abstract This paper presents a common fixed point theorem for a family of R -weakly commuting mappings satisfying nonlinear type contractive conditions. This result improves and unifies previous results due to O’Regan and Saadati [D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008) 86–93]. Also, the following results will be probabilistic versions and improvements of the results given in [D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Am. Math. Soc. 20 (1969) 458–464; G. Jungck, Commuting maps and fixed points, Am. Math. Month. 83 (1976) 261–263; R.P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994) 436–440] and many other.

Common fixed point theorems in intuitionistic fuzzy metric spaces and [formula omitted]-fuzzy metric spaces with nonlinear contractive condition

The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2004;22:1039–46] and L -fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L -fuzzy metric spaces. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458–64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436–40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261–3]. Some examples and comments according to the preceding results are given.