Contraction Mappings In Metric Spaces Research Articles

Coupled Common Fixed Points of Contractive Mappings in Metric Spaces

Coupled Common Fixed Points of Contractive Mappings in Metric Spaces

Fixed point theorems for nonlinear weakly [formula omitted]-contractive mappings in metric spaces

The purpose of this paper is to present some fixed point and coupled fixed point theorems for a nonlinear weakly C -contraction type mapping in metric and ordered metric spaces. Also, an example is given to support our results. Our results generalize several well-known results from the current literature.

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.

Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120). Also, we establish the following new fixed point theorem. Suppose ϕ : R + → R + is a contractive gauge function in the sense that for any ε > 0 there exists δ > ε such that ε < t < δ implies ϕ ( t ) ⩽ ε , and suppose T is a continuous and asymptotically regular selfmapping on a complete metric space ( X , d ) satisfying the following: (i) d ( Tx , Ty ) ⩽ ϕ ( D ( x , y ) ) for all x , y ∈ X , and (ii) d ( Tx , Ty ) < D ( x , y ) for all x , y ∈ X with x ≠ y , where D ( x , y ) = d ( x , y ) + γ . [ d ( x , Tx ) + d ( y , Ty ) ] with γ ⩾ 0 . Then T has a unique fixed point and all of the Picard iterates of T converge to this fixed point. This result includes those of Jachimski (Equivalent conditions and the Meir–Keeler type theorems, J. Math. Anal. Appl. 194 (1995) 293–303), Matkowski (Fixed point theorems for contractive mappings in metric spaces, Cas. Pest. Mat. 105 (1980) 341–344) and others.

Generalization of istratescu's theorem on contractive mappings in metric spaces

In this paper we consider mappings T:X→X of metric spaces, satisfying the condition: , where ω is some right semicontinuous function. We prove that if ω is a nondecreasing function, ω(π) 0, π−ω(π)→∞ as π→∞, , then the map T has a fixed point ξ and $$\mathop {\lim }\limits_{n \to \infty } T_x^n = \xi$$ for any pointx∈X. Interesting examples are given.

Fixed point theorems for contractive mappings in metric spaces

Fixed point theorems for contractive mappings in metric spaces

A Common Fixed Point Theorem for a Sequence of Multivalued Mappings

Recently, fixed point theorems for multivalued contraction mappings in metric spaces were obtained by many authors ( [5] , [2] , [7] , [1] , [4] , [6] , etc) . On the other hand, Dube [3] proved a theorem on common fixed points of two multivalued mappings. In this paper, we shall give a common fixed point theorem for a sequence of multivalued mappings satisfying some conditions in complete metric spaces. In our theorem, we shall obtain an extension of the result of Itoh [4] to the case of a sequence of multivalued mappings.

Multi-valued contraction mappings in metric spaces

Some fixed point theorems for multi-valued contraction mappings in metric spaces, related to a fixed point theorem due to T. Zamfirescu [6], [5], are presented.

Multi-valued contraction mappings in metric spaces

Multi-valued contraction mappings in metric spaces