Common fixed point theorems for a weaker Meir–Keeler type function in cone metric spaces

AbstractIn this work, we define a weaker Meir–Keeler type function ψ:intP∪{0}→intP∪{0} in a cone metric space, and under this weaker Meir–Keeler type function, we show the common fixed point theorems of four single-valued functions in cone metric spaces

Best proximity points for asymptotic proximal pointwise weaker Meir–Keeler-type ψ-contraction mappings

AbstractIn this paper, we study the new class of an asymptotic proximal pointwise weaker Meir–Keeler-type ψ-contraction and prove the existence of solutions for the minimization problem in a uniformly convex Banach space. Also, we give some an example for support our main result

Nonlinear generalized cyclic contractions in complete G-metric spaces and applications to integral equations

In this paper we introduce generalized cyclic contractions in G-metric spaces and establish some fixed point theorems. The presented theorems extend and unify various known fixed point results. Examples are given in the support of these results. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is given

On fixed points and convergence results of sequences generated by uniformly convergent and point-wisely convergent sequences of operators in Menger probabilistic metric spaces

Altres ajuts: The authors thank the reviewers for their useful comments and to University Jorge Tadeo Lozano by its support through Grant 644-11-14.In the framework of complete probabilistic Menger metric spaces, this paper investigates some relevant properties of convergence of sequences built through sequences of operators which are either uniformly convergent to a strict k -contractive operator, for some real constant k ∈ (0, 1), or which are strictly k -contractive and point-wisely convergent to a limit operator. Those properties are also reformulated for the case when either the sequence of operators or its limit are strict -contractions. The definitions of strict (k and ) contractions are given in the context of probabilistic metric spaces, namely in particular, for the considered probability density function. A numerical illustrative example is discussed

Fixed points of single-valued and multi-valued mappings with applications

The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space

F-closed sets and coupled fixed point theorems without the mixed monotone property

In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case

Some Coincidence Point Theorems and an Application to Integral Equation in Partially Ordered Metric Spaces

In ordered metric space, the results on coincidence point of the mappings satisfying generalized rational contractions are investigated. Also discussed the integral contractions of the mappings in the same context to obtain the coincidence points. Two numerical examples are presented to justify the results obtained. Apart from in view of an application, the existence and the unique solution of an integral equation is discussed