Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
نویسندگان
چکیده
The existence of fixed point in partially ordered sets has been studied and investigated recently in 1–13 and references therein. Since the various contractive conditions are important in metric fixed point theory, there is a trend to weaken the requirement on contractions. Nieto and Rodrı́guez-López in 8, 10 used Tarski’s theorem to show the existence of solutions for fuzzy equations and fuzzy differential equations, respectively. The existence of solutions for matrix equations or ordinary differential equations by applying fixed point theorems are presented in 2, 6, 9, 11, 12 . In 3, 13 , the authors proved some fixed point theorems for a mixed monotone mapping in a metric space endowed with partial order and applied their results to problems of existence and uniqueness of solutions for some boundary value problems. In 2006, Bhaskar and Lakshmikantham 2 first proved the following interesting coupled fixed point theorem in partially ordered metric spaces.
منابع مشابه
Coupled fixed point on ordered cone metric spaces with application in integral equations
Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis, 72(2010) 2259-2261.], showed that the fixed point results in the setting of cone...
متن کاملCOUPLED FIXED POINT THEOREMS FOR GENERALIZED Φ-MAPPINGS SATISFYING CONTRACTIVE CONDITION OF INTEGRAL TYPE ON CONE METRIC SPACES
In this paper, we unify, extend and generalize some results on coupled fixed point theorems of generalized φ- mappings with some applications to fixed points of integral type mappings in cone metric spaces.
متن کاملCoupled coincidence point theorems for maps under a new invariant set in ordered cone metric spaces
In this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. In fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. Some examples are provided to verify the effectiveness and applicability of our results.
متن کاملCoupled coincidence point and common coupled fixed point theorems in complex valued metric spaces
In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illus...
متن کاملCoupled fixed point theorems involving contractive condition of integral type in generalized metric spaces
In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We f...
متن کاملFixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the set...
متن کامل