[PDF] Top 20 3. Coupled fixed point theorems in partially ordered metric spaces

... fixed point for contraction type mappings in partially ordered metric spaces and aplications have been considered recently by many authors (see, for details, [2], [3], [4], [5], ... See full document

... a point verifying the related conditions above is a coupled (respectively, tripled, quadrupled) fixed point of F due to Gnana Bhaskar and Lakshmikantham [] (respectively, Berinde and Borcut [], ... See full document

... common coupled fixed point theorems for two hybrid pairs of mappings satisfying an implicit relation under the conditions of weakly commuta- tivity and w−compatibility on a complete ... See full document

... tripled fixed point for single valued mappings in partially ordered metric ...tripled fixed point of single-valued mappings in partially ordered ... See full document

... Later on, Lakshmikantham and Ciríc [8] proved coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces..[r] ... See full document

... unique coupled point of coincidence of F and ...unique coupled common fixed ...another coupled coincidence point of F and ... See full document

... Example 2.3. Let X = [0, ∞) be equipped with the b-metric-like d(x, y) = (x + y) 2 for all x, y ∈ X , where b = 2. Define a relation on X by x y iff y ≤ x, the functions f , g : X → X by f x = ln(1 + 13 x ) and f ... See full document

... Corollary 2.8. Let (X, v) be a partially ordered set and suppose there exists a cone metric d in X such that the cone metric space (X, d) is complete. Suppose F : X × X −→ X be a continuous ... See full document

... some coupled fixed point theorems which has attracted the attention of many researchers ...on coupled fixed ...several coupled common fixed point ... See full document

... Corollary 3.5. Let (X , ≤) be a partially ordered set and suppose that there is a G−metric on X such that (X , G) is a complete G-metric space. Let F : X × X → X and g: X → X be two mappings ... See full document

... approximation theorems, a natural question in this direction is whether it is possible to guarantee the existence of approximate solution that is ...the point to be explored is whether one can find an ... See full document

... in partially ordered sets has been con- sidered in [, ], where some applications to matrix equations are ...in partially ordered sets and applied to study ordinary differential ... See full document

... fixed point problems for isotone mappings are easier than that of mixed monotone ...fixed point theorems for a k-variable isotone mapping, which include the unidimensional, coupled, tripled, and ... See full document

... a partially ordered set satisfying condition (??) and sup- pose that there exists a metric d in X such that (X, d) is a complete metric ... See full document

... of coupled fixed point of a mapping F : X × X → X was introduced by Gnana Bhaskar and Lakshmikantham in ...many coupled fixed point results in different spaces such as ... See full document

... hand, fixed-point theory has developed rapidly in metric spaces endowed with a partial ...many fixed-point theorems in ordered metric ...common ... See full document

... a coupled fixed point in partially ordered metric spaces,also discussed some problems of the uniqueness of a coupled fixed point and applied their ... See full document

... Example 2.4. Let E R 2 , P {x, y ∈ R 2 : x, y ≥ 0} ⊆ R 2 , and X 0, 1. Define d : X×X → E with dx, y |x − y|, |x − y|. Then X, d is a complete cone metric space. Consider the mapping F : X × X → X with Fx, y x ... See full document

... celebrated theorems of the fixed point theory such as the Banach contrac- tion mapping principle [] from the point of view of ...in partially ordered metric ...in ordered ... See full document

... reducing coupled fixed point results in (ordered) metric spaces to the respective results for mappings with one variable, even obtaining more general ...common coupled ... See full document