ABSTRACT. In this paper, we present some stability results which are implies some fixed point theorem. We study two types of stability.

ABSTRACT. We obtain an extension of some coupled fixed point results.

ABSTRACT. The concept of local contraction was presented by Martins da Rocha and Filipe Vailakis in [Martins-da-Rocha,Filipe, Vailakis, Yiannis, Exis- tence and uniqueness of a xed point for local contractions, Econometrica, vol.78, No.3 (May, 2010) 1127-1141], meanwhile the almost contractive mappings was introduced by V. Berinde in [Berinde, V., Approximat- ing xed points of weak contractions using the Picard iteration Nonlinear Analysis Forum 9(2004) No.1, 43-53]. In this paper we want to unify these two concepts, so we dene the almost local contractions. Then we are going to study the xed points of almost local contractions. The main result of this paper state an existence theorem and also an exis- tence and uniqueness theorem for almost local contractions with constant coecient of contraction. The most general case of variable coecient of contraction is presented at the end of this work, in the existence theorem for xed points of almost local contractions.

ABSTRACT. We merge the concepts of convex contraction, due to Istratescu [Some fixed point theorems for convex contraction mappings and convex nonexpansive mappings. I. Libertas Math. 1 (1981), 151--163] and almost contraction, introduced in [Berinde, Vasile, Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9 (2004), no. 1, 43--53] and thus obtain a larger class of contractive type mappings for which we state and prove some basic fixed point theorems.

ABSTRACT. We consider some recent iterative schemes due to Kadioglu and Yildirim (2014), Thakur et al. (2014) and Phuengrattana and Suantai (2011) for further investigations. In this paper, we compare rate of convergence among the mentioned iterative schemes when applied to well-known contraction mappings. Also, we show that all these iterative schemes are equivalent as all converge to the same fixed point of a contraction mapping. Finally we obtain some data dependence results for the mentioned iterative schemes. Mathematics Subject Classification: 47H09; 4710 Keywords: Iterative schemes; contraction mappings; strong convergence; rate of convergence; data dependence

References [1] N. Kadioglu and I. Yildirim, “Approximating fixed points of nonexpansive mappings by a faster iteration process,” http://arxiv.org/abs/1402, 2014. [2] W. Phuengrattana and S. Suantai, “On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval,” Journal of Computational and Applied Mathematics, vol. 235, no. 9, pp. 3006–3014, 2011. [3] D. Thakur, B. S. Thakur and M. Postolache, New iteration scheme for numerical reckoning fixed points of nonexpansive mappings, J. Inequal. Appl. 328 (2014), 15 pages.

ABSTRACT. Some new additional conditions are proposed to estimate a posteriori error and to guarantee the strong convergence of Picard and Mann iterations in the case of a strongly demicontractive mapping. The simple formulas for a posteriori error estimation are given in both cases. Results on the convergence properties state that the sequence given by each of the two considered methods converges strongly to a fixed point provided that the considered mapping is strongly demicontractive and satisfies some expansive type conditions (orbital expansive or quasi expansive).

ABSTRACT. We prove some common fixed point results in fuzzy metric spaces and derive corresponding coupled coincidence point results in this setting.

References:

J-X Fang, Common coupled fixed point theorems for hybrid $\varphi$-contractions in probabilistic and fuzzy metric spaces, to appear

V. Lakshmikantam V, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal 70 (2009), 4341-4349.

A. Harandi-Amini, D. Mihet, Common fixed points and coupled coincidence points in preordered fuzzy metric spaces, submitted

ABSTRACT. The purpose of this paper is to transpose some of the results regarding the coupled fixed point theory, developed by T. Gnana Bhaskar and V. Lakshmikantham, using the approaches of Hichem Ben-El-Mechaiekh and M. S. Asgari, B. Mousavi. The first approach replaces the partial ordered relation from the Ran-Reurings fixed point theorem with a transitive one, whereas the second one uses a reflexive-only relation. Our aim is to obtain some generalized theorems, containing a more simple symmetrical condition, based on these results.

ABSTRACT. This paper presents some interesting informations about the fixed point theorems for non-self multi-valued almost contractions. It starts from presenting the strict contractions and then we extend this notion to weak contractions single-valued mappings and multi-valued mappings. This helps us to introduce the non-self operators which will show us the next result: Let X be a Banach space, K a non-empty closed subset of X and let T:K→X be a non-self almost contraction. If T has the so called property (M) and satisfies Rothe’s boundary condition, the T has fixed point in K. This theorem links us to what we are going to study, i.e. non-self multi-valued almost contractions.

ABSTRACT. In recent years the study of the convergence of iterative methods has been widely investigated. In this talk, we want to show how the asymptotic behavior of the ratio of the coefficients involved in an iterative method influences the convergence of the algorithm itself.

ABSTRACT. By using geometric conditions on a function and its domain, we introduce an iterative sequence and prove that it converges to a fixed point of the map. Applications are also discussed.

ABSTRACT. Following Maia's fixed point theorem and Presic fixed point theorem, which are the extensions of Banach fixed point theorem, we present a Presic-Maia fixed point theorem which is a unification of these two theorems. Some new research directions are also presented.

ABSTRACT. The article approaches the issue of convergence accuracy of standard genetic algorithms using fixed point theory operates on a simplicial triangulation of searching space and then generates the integer labels at the vertices. The algorithm uses a new operator of increase the dimension used at the actualization of the population which acts on non-labeled individuals, turning them into fully labeled individuals and convergence condition of the population is reached when all simplex are fully labeled. Global optimum point was obtained by applying the Hessian matrix on fully labeled simplex. Genetic algorithm was built in C Sharp, appealing through MapleEngine.cs function in Maple program for solving mathematical equations and for easier and faster in demonstrating the efficiency and stability of the algorithm was created a friendly interface for the user. The optained results demonstrate a global optimization capability greater than the classical genetic algorithms that ensure due triangulation combined with the random local research, thus eliminating the possibility that the algorithm to stop in a local extreme point.