Search results for "Fixed point"
showing 10 items of 347 documents
MR2684111 Kadelburg, Zoran; Radenović, Stojan; Rakočević, Vladimir Topological vector space-valued cone metric spaces and fixed point theorems. Fixed…
2011
Recently, Huang and Zhang [\emph{Cone metric spaces and fixed point theorems of contractive mappings}, J. Math. Anal. Appl., \textbf{332} (2007), 1468 -1476] defined cone metric spaces by substituing an order normed space for the real numbers and proved some fixed point theorems. Let $E$ be a real Hausdorff topological vector space and $P$ a cone in $E$ with int\,$P\neq \emptyset$, where int\,$P$ denotes the interior of $P$. Let $X$ be a nonempty set. A function $d : X \times X\to E$ is called a \emph{tvs}-cone metric and $(X, d)$ is called a \emph{tvs}-cone metric space, if the following conditions hold: (1) $\theta \leq d(x, y)$ for all $x, y \in X$ and $d(x, y)= \theta$ if and only if $x…
MR3269340 Reviewed O'Regan, Donal Lefschetz type theorems for a class of noncompact mappings. J. Nonlinear Sci. Appl. 7 (2014), no. 5, 288–295. (Revi…
2015
Lefschetz fixed-point theorem furnishes a way for counting the fixed points of a suitable mapping. In particular, the Lefschetz fixed-point theorem states that if Lefschetz number is not zero, then the involved mapping has at least one fixed point, that is, there exists a point that does not change upon application of mapping. ewline Let $f={f_q}:E o E$ be an endomorphism of degree zero of graded vector space $E={E_q}$. Let $ ilde{E}=E setminus {x in E : f^n(x)=0, mbox{ for some }n in mathbb{N}}$. Define the generalized Lefschetz number $Lambda(f)$ by $$Lambda(f)=sum_{q geq 0}(-1)^qmbox{Tr}(f_q),$$ where $mbox{Tr}(f)=mbox{tr}( ilde{f})$ is the generalized trace of $f$, ``tr'' is the ordinar…
Recensione: MR2817284 Dhompongsa, S.; Nanan, N. Fixed point theorems by ways of ultra-asymptotic centers. Abstr. Appl. Anal. 2011, Art. ID 826851, 21…
2012
Paper review
Recensione: MR2739903 Haddadi, Mohammad Reza; Mazaheri, Hamid; Labbaf Ghasemi, Mohammad Hussein Relation between fixed point and asymptotical center …
2011
Paper review
MR2524371 (2010g:47114) Domínguez Benavides, T.; García Falset, J.; Llorens-Fuster, E.; Lorenzo Ramírez, P. Fixed point properties and proximinality …
2010
In the paper under review the authors mainly investigate the existence of a fixed point for nonexpansive mappings in the general setting of strictly $L(\tau)$ Banach spaces. They consider a linear topology $\tau$ on a Banach space $(X, \|\cdot \|)$, weaker than the norm topology, then the Banach space $X$ is a strictly $L(\tau)$ space if there exists a continuous function $\delta:[0, \infty[ \times [0, \infty[ \to [0, \infty[$ such that $\delta(\cdot,s)$ and $\delta(r, \cdot)$ are strictly increasing; $\delta(0,s)=s$, for every $s \in [0, \infty[$; and $\phi_{(x_n)}(y)= \delta (\phi_{(x_n)}(0), \|y\|)$, for every $y \in X$ and for every bounded and $\tau$-null sequence $(x_n)$, where $\phi_…
MR2449047 (2009j:47108) Chermisi, Milena; Martellotti, Anna Fixed point theorems for middle point linear operators in $L^1$. Fixed Point Theory Appl.…
2009
In the paper under review the notion of middle point operator is introduced. The authors prove that for a given nonempty, bounded, $\rho$-closed, convex subset K of L1(μ), where $\rho$ is the metric of the convergence locally in measure, if T from (K, $\rho$) to(K, $\rho$) is a continuous, $\rho$-nonexpansive, middle point linear operator, then T has at least one fixed point in K. To prove the theorem they use results of A. V. Bukhvalov [in Operator theory in function spaces and Banach lattices, 95–112, Birkh¨auser, Basel, 1995; MR1322501 (95m:46123)] and M. Furi and A. Vignoli [Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 48 (1970), 195–198; MR0279792 (43 #5513)]. Then they …
Fixed point results for weak contractive mappings in ordered K-metric spaces
2012
In this paper, we derive new coincidence and common fixed point theorems for self-maps satisfying a weak contractive condition in an ordered K-metric space. As application, the obtained results are used to prove an existence theorem of solutions of a nonlinear integral equation.
PPF dependent fixed point results for triangular $alpha_c$-admissible mappings
2014
We introduce the concept of triangular $alpha_c$-admissible mappings (pair of mappings) with respect to $η_c$ nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular $alpha_c$-admissible mappings (pair of mappings) with respect to $η_c$ nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given.
Fixed points for weak $\varphi$-contractions on partial metric spaces
2011
In this paper, following [W.A. Kirk, P.S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003) 79-89], we give a fixed point result for cyclic weak $\varphi$-contractions on partial metric space. A Maia type fixed point theorem for cyclic weak $\varphi$-contractions is also given.
ZBL MS 63/6 Satco, Bianca-Renata; Turcu, Corneliu-Octavian Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on t…
2013
The authors prove an existence result for a nonlinear integral equation on time scales under weak topology assumption in the target Banach space. In the setting of vector valued functions on time scales they consider the Henstock-Kurzweil-Pettis $\Delta$-integral which is a kind of Henstock integral recently introduced by Cichon, M. [Commun. Math. Anal. 11 (2011), no. 1, 94�110]. In this framework they show the existence of weakly continuous solutions for an integral equation x(t)= f(t, x(t))+ (HKP)\int_0^t g(t,s,x(s)) \Delta s governed by the sum of two operators: a continuous operator and an integral one. The main tool to get the solutions is a generalization of Krasnosel'skii fixed point…