The common fixed point of single-valued generalized φf-weakly contractive mappings

AbstractFixed point and coincidence results are presented for single-valued generalized φf-weakly contractive mappings on complete metric spaces (X,d), where φ:[0,∞)→[0,∞) is a lower semicontinuous function with φ(0)=0 and φ(t)>0 for all t>0 and f:E→X is a function such that E⊆X is nonempty and closed. Our results extend previous results given by Rhoades (2001) [1] and by Zhang and Song (2009) [2]

On The Fixed-Point Property of Unital Uniformly Closed Subalgebras of <inline-formula> <graphic file="1687-1812-2010-268450-i1.gif"/></inline-formula>

Abstract Let be a compact Hausdorff topological space and let and denote the complex and real Banach algebras of all continuous complex-valued and continuous real-valued functions on under the uniform norm on , respectively. Recently, Fupinwong and Dhompongsa (2010) obtained a general condition for infinite dimensional unital commutative real and complex Banach algebras to fail the fixed-point property and showed that and are examples of such algebras. At the same time Dhompongsa et al. (2010) showed that a complex -algebra has the fixed-point property if and only if is finite dimensional. In this paper we show that some complex and real unital uniformly closed subalgebras of do not have the fixed-point property by using the results given by them and by applying the concept of peak points for those subalgebras.</p

Common Fixed Point of Multivalued Generalized <inline-formula> <graphic file="1687-1812-2010-708984-i1.gif"/></inline-formula>-Weak Contractive Mappings

Fixed point and coincidence results are presented for multivalued generalized -weak contractive mappings on complete metric spaces, where is a lower semicontinuous function with and for all . Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969), and Daffer and Kaneko (1995).</p

On the existence and approximation of fixed points for Ciric type contractive mappings

Click on the link to view the abstract.Quaestiones Mathematicae 37(2014), 179-18

Common Fixed Point of Multivalued Generalized &#x03C6;-Weak Contractive Mappings

Fixed point and coincidence results are presented for multivalued generalized &#x03C6;-weak contractive mappings on complete metric spaces, where &#x03C6;:[0,+&#x221E;)&#x02192;[0,+&#x221E;) is a lower semicontinuous function with &#x03C6;(0)=0 and &#x03C6;(t)&#x003E;0 for all t&#x003E;0. Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969), and Daffer and Kaneko (1995)

On the existence and approximation of fixed points for Ćirić type contractive mappings

Let (X, d) be a complete convex metric space, and C be a nonempty, closed and convex subset of X. We consider Ćirić type contractive self-mappings T of C satisfying: for all x, y ∈ C, where 0 \u3c a \u3c 1, a + b = 1, and c ≥ 0. We give a simple proof to an extension of Ćirić\u27s fixed point theorem [4] and Gregus’ fixed point theorem [9], and present some results on the approximation of fixed points. In particular, we show that the least upper bound of c for T to have a fixed point is , which is therefore independent of a and b

On the maximal ideal space of extended analytic Lipschitz algebras

Let X be a compact, plane set and let K be a compact subset of X. We introduce new classes of Lipschitz algebras Lip(X, K, &#945), lip(X, K, &#945), consisting of those continuous functions f on X such that f|K &#949 Lip(K, &#945), lip(K, &#945), and their analytic subalgebras LipA(X, K, &#945) = Lip(X, K, &#945) &#8745 A(X, K) and lipA(X, K, &#945) = lip(X, K, &#945) &#8745; A(X, K), where 0 < &#945 &#8804; 1 and A(X, K) is the algebra of all continuous complex-valued functions on X, which are analytic on the interior of K. We show that the maximal ideal spaces of these extended Lipschitz algebras coincide with X.Quaestiones Mathematicae 30(2007), 349–35

A fixed point of generalized <it>T</it> _<it>F</it>-contraction mappings in cone metric spaces

Abstract In this paper, the existence of a fixed point for TF -contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X &#8594; X is a one to one and closed graph function and F : P &#8594; P is non-decreasing and right continuous, with F -1(0) = -0} and F(tn ) &#8594; 0 implies tn &#8594; 0. Our results, extend previous results given by Meir and Keeler (J. Math. Anal. Appl. 28, 326-329, 1969), Branciari (Int. J. Math. sci. 29, 531-536, 2002), Suzuki (J. Math. Math. Sci. 2007), Rezapour et al. (J. Math. Anal. Appl. 345, 719-724, 2010), Moradi et al. (Iran. J. Math. Sci. Inf. 5, 25-32, 2010) and Khojasteh et al. (Fixed Point Theory Appl. 2010). MSC(2000): 47H10; 54H25; 28B05.</p