Search

Boyd and Wong in their celebrated paper 'On nonlinear contractions' assumed the comparison function to be upper semicontinuous from the right. Our requirement presented in this paper is much more general and it extends also the well-known Matkowski condition. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce some basic definitions about fixed point and best proximity point in two classes of probabilistic metric spaces and to prove contraction mapping principle and relevant best proximity point theorems. The first class is the so-called S-probabilistic metric spaces. In S-probabilistic metric spaces, the generalized contraction mapping principle and generalized best proximity point theorems have been proved by authors. These results improve and extend the recent results of Su and Zhang (Fixed Point Theory Appl. 2014:170, 2014). The second class is the so-called Menger probabilistic metric spaces. In Menger probabilistic metric spaces, the contraction mapping principle and relevant best proximity point theorems have been proved by authors. These results also improve and extend the results of many authors. In order to get the results of this paper, some new methods have been used. Meanwhile some error estimate inequalities have been established. [ABSTRACT FROM AUTHOR]

In this paper the fixed point of multivalued mapping is considered. A generalization of the well-known Nadler contraction principle, the Khan contraction theorem and the fixed point theorem in complete metric space with a convex structure is proved. The main result of the paper is formulated by three theorems where the mappings, defined over the complete metric space, are assumed to satisfy some integral type of contraction. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new class of probabilistic normed spaces and to study fixed point problems in this class of probabilistic normed spaces. This paper includes the following two contents: (1) The definition of a new class of probabilistic normed spaces, the so-called S-probabilistic normed spaces, is given. In order to study the fixed point problems, some relevant properties of S-probabilistic normed spaces are discussed and some basic useful results are obtained; (2) The notion of probabilistic weak convergence is firstly presented in this paper. Therefore the probabilistic weak and strong convergence theorems of fixed points for nonexpansive mappings, asymptotically nonexpansive mappings and strongly pseudocontractive mappings are also proved by using the new methods and techniques. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and consider a new hybrid shrinking projection algorithm for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of a system of variational inequality problems, the set of solutions of a system of optimization problems, the common fixed point set of a uniformly closed family of countable quasi-Bregman strictly pseudocontractive mappings in reflexive Banach spaces. Strong convergence theorems have been proved under the appropriate conditions. The main innovative points in this paper are as follows: (1) the notion of the uniformly closed family of countable quasi-Bregman strictly pseudocontractive mappings is presented and the useful conclusions are given; (2) the relative examples of the uniformly closed family of countable quasi-Bregman strictly pseudocontractive mappings are given in classical Banach spaces $l^{2}$ and $L^{2}$; (3) the hybrid shrinking projection method presented in this paper modified some mistakes in the recent result of Ugwunnadi et al. (Fixed Point Theory Appl. 2014:231, 2014). These new results improve and extend the previously known ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups. [ABSTRACT FROM AUTHOR]

In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric's quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained without imposing a continuity condition on the mapping, thereby further generalizing some other related work in the literature. An example is given to show the validity of results obtained. [ABSTRACT FROM AUTHOR]

Set-valued contractions of Leader type in quasi-triangular spaces are constructed, conditions guaranteeing the existence of nonempty sets of periodic points, fixed points and endpoints of such contractions are established, convergence of dynamic processes of these contractions are studied, uniqueness properties are derived, and single-valued cases are considered. Investigated dynamic systems are not necessarily continuous and spaces are not necessarily sequentially complete or Hausdorff. Obtained results suggest, in particular, strategies to new studies of functional Bellman equations and variable discounted Bellman equations in metric spaces and integral Volterra equations in locally convex spaces. Results in this direction are also presented in this paper. More precisely, without continuity of Bellman and Volterra appropriate operators, the sets of solutions of these equations (which are periodic points of these operators) are studied and new and general convergence, existence and uniqueness theorems concerning such equations are proved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized nonexpansive mappings. Some new fixed point theorems for these mappings are obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the notions of Θ-type contractions and Θ-type Suzuki contractions and to establish some new fixed point theorems for these two kinds of mappings in the setting of complete metric spaces. The results presented in the paper are an extension of the Banach contraction principle, the Suzuki contraction theorem, and the Jleli and Samet fixed point theorem. As an application, we utilize our results to study the existence problem of solutions of nonlinear Hammerstein integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate two new iterative algorithms for solving the split equality variational inclusion problem in Hilbert spaces. We also prove that the sequences generated by the proposed algorithms converge strongly to a common solution of the split equality variational inclusion problem and fixed points of a family of nonexpansive mappings, which is also an unique solution of a variational inequality as an optimality condition for a minimization problem. The results presented in this paper extend and generalize a variety of existing results in this area. [ABSTRACT FROM AUTHOR]

In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems of the proposed iteration for an asymptotically nonexpansive nonself-mapping with the condition (BP). Finally, we give two examples to illustrate the main result in this paper. Our results improve and extend the corresponding results given by some authors. [ABSTRACT FROM AUTHOR]

In this paper, based on the viscosity approximation method and the regularized gradient-projection algorithm, we find a common element of the solution set of a constrained convex minimization problem and the set of zero points of the maximal monotone operator problem. In particular, the set of zero points of the maximal monotone operator problem can be transformed into the equilibrium problem. Under suitable conditions, new strong convergence theorems are obtained, which are useful in nonlinear analysis and optimization. As an application, we apply our algorithm to solving the split feasibility problem and the constrained convex minimization problem in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, a new type of G-contraction multivalued mappings in a metric space endowed with a directed graph is introduced and studied. This type of mappings is more general than that of Mizoguchi and Takahashi (J. Math. Anal. Appl. 141:177-188, 1989), Berinde and Berinde (J. Math. Anal. Appl. 326:772-782, 2007), Du (Topol. Appl. 159:49-56, 2012), and Sultana and Vetrivel (J. Math. Anal. Appl. 417:336-344, 2014). A fixed point and coincidence point theorem for this type of mappings is established. Some examples illustrating our main results are also given. The main results obtained in this paper extend and generalize those in (Tiammee and Suantai in Fixed Point Theory Appl. 2014:70, 2014) and many well-known results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove a more generalized contraction mapping principle. By using this more generalized contraction mapping principle, a further generalized best proximity theorem was established. Some concrete results have been derived by using the above two theorems. The results of this paper improve many important results published recently in the literature. [ABSTRACT FROM AUTHOR]

In this work, we introduce the $(\mathit{CLR})$-property for the hybrid pairs of single-valued and multi-valued mappings and give some coincidence and common fixed point theorems for the hybrid pairs of some contractive conditions. Also, we will give some examples to illustrate the main results in this paper. Our results extend and improve some results given by some authors. [ABSTRACT FROM AUTHOR]

In this paper, a semi-local convergence analysis of the Gauss-Newton method for convex composite optimization is presented using the concept of quasi-regularity in order to approximate fixed points in optimization. Our convergence analysis is presented first under the L-average Lipschitz and then under generalized convex majorant conditions. The results extend the applicability of the Gauss-Newton method under the same computational cost as in earlier studies such as Li and Ng (SIAM J. Optim. 18:613-642, 2007), Moldovan and Pellegrini (J. Optim. Theory Appl. 142:147-163, 2009), Moldovan and Pellegrini (J. Optim. Theory Appl. 142:165-183, 2009), Wang (Math. Comput. 68:169-186, 1999) and Wang (IMA J. Numer. Anal. 20:123-134, 2000). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of $(\alpha,\psi)$-rational type contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point for such class of generalized nonlinear contractive mappings in the setting of generalized metric spaces. We also deduce several interesting corollaries. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new iterative scheme for finding a common solution to a variational inclusion problem with a finite family of accretive operators and a modified system of variational inequalities in infinite-dimensional Banach spaces. Under mild conditions, a strong convergence theorem for approximating this common solution is proved. The methods in the paper are novel and different from those in the early and recent literature. [ABSTRACT FROM AUTHOR]

We study self-mappings on complete metric spaces, which we refer to as higher-order Lipschitz mappings. These mappings generalise Lipschitz mappings, the latter which are equivalent to first-order Lipschitz mappings studied in this paper. The main result of this paper is to extend the Banach fixed point theorem (and an often-cited generalisation) to higher-order contraction mappings. We also present results on the problem of local Lipschitzity of these higher-order Lipschitz mappings. [ABSTRACT FROM AUTHOR]

Let the set $C \subset L_{1}([0,1])$ be nonempty, convex and compact for the convergence almost everywhere and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, we study the behavior of the Krasnoselskii-Ishikawa iteration sequence $\{f_{n}\}$ defined by $f_{n+1} = \lambda f_{n} + (1-\lambda)T(f_{n})$, $n = 1, 2, \ldots$ , $\lambda\in(0,1)$. Then we prove a fixed point theorem for these mappings. Our result is new and was never investigated. [ABSTRACT FROM AUTHOR]

In this paper, motivated by Kikkawa-Suzuki's fixed point theorem, we establish some new generalizations of Mizoguchi-Takahashi's fixed point theorem with new local constraints on discussion maps. [ABSTRACT FROM AUTHOR]

In this paper, we show that some examples in (Mursaleen et al. in Fixed Point Theory Appl. 2012:124, 2012) are not correct. Then, we extend, improve and generalize their results. Finally, we state some examples to illustrate our obtained results. MSC: 47H10, 54H25. [ABSTRACT FROM AUTHOR]

Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them. MSC: 46N40, 47H10, 54H25, 46T99. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Our results generalize and extend the results of Joseph et al. (SpringerPlus 5:Article ID 217, 2016). We also give examples to support our results, and applications relating the results to a fixed point for multivalued mappings and fuzzy mappings are studied. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of $\alpha_{qs^{p}}$ -admissible mappings and provide some fixed point theorems involving this class of mappings satisfying some new conditions of contractivity in the setting of b-metric-like spaces. Our results extend, unify, and generalize classical and recent fixed point results for contractive mappings. [ABSTRACT FROM AUTHOR]

The first purpose of this paper is to define a homotopy for fuzzy spaces. We continue our work by showing that the property of having a fixed point is invariant by this homotopy. These theorems generalize and improve well-known results. [ABSTRACT FROM AUTHOR]

In this paper, we establish several fixed point theorems for Meir-Keeler type contractions in partially ordered G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some fixed point theorems for fuzzy mappings in a left K-sequentially complete quasi-pseudo-metric space and in a right K-sequentially complete quasi-pseudo-metric space, respectively. Our analysis is based on the fact that fuzzy fixed point results can be obtained from the fixed point theorem of multivalued mappings with closed values. It is observed that there are many situations in which the mappings are not contractive on the whole space but they may be contractive on its subsets. We feel that this feature of finding the fuzzy fixed points via closed balls was overlooked, and our paper will re-open the research activity into this area. [ABSTRACT FROM AUTHOR]

Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space. [ABSTRACT FROM AUTHOR]

The paper deals with the achievement of introducing the notion of F-cone metric spaces over Banach algebra as a generalization of $N_{p}$ -cone metric space over Banach algebra and $N_{b}$ -cone metric space over Banach algebra and studying some of its topological properties. Also, here we define generalized Lipschitz and expansive maps for such spaces. Moreover, we investigate some fixed points for mappings satisfying such conditions in the new framework. Subsequently, as an application of our results, we provide an example. Our results generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

Meir and Keeler formulated their fixed point theorem for contractive mappings with purely metric condition. This idea was extended by numerous mathematicians. In this paper, we present a simple method of proving such theorems and give new results. [ABSTRACT FROM AUTHOR]

In the paper general theorems on common fixed point for four mappings are presented. The results are compact and they extend and unify the respective part of the fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral equations are given. We also present some research directions. [ABSTRACT FROM AUTHOR]

Let f be an holomorphic function which maps the unit disk into itself. In this paper, consider the zero of order k ( i.e., $f(z)-f(0)$ (or $f(z)$ ) has a zero of order k at $z=0$ ), we obtain the sharp estimates of the classical boundary Schwarz lemma involving the boundary fixed point. The results presented here would generalize the corresponding result obtained by Frolova et al. (Complex Anal. Oper. Theory 8:1129-1149, 2004). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some fixed point and common fixed point theorems for almost generalized $\mathcal{C}$-contractive mappings in an ordered complete metric space. Finally, two examples are given to support our results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish some fixed point results for cyclic contractions in the setting of dislocated quasi- b-metric spaces. We verify that some previous cyclic contraction results in dislocated quasi- b-metric spaces are just equivalent to the non-cyclic ones in the same spaces. Moreover, by using two examples, we highlight the superiority of the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we prove some existence theorems of fixed points of a monotone nonexpansive mapping T in a Banach space E with the partial order '≤', where a such mapping may be discontinuous. In particular, in finite dimensional spaces, such a mapping T has a fixed point in E if and only if the sequence $\{T^{n}0\}$ is bounded in E. In order to find a fixed point of such a mapping T, we prove the weak convergence of the Mann iteration scheme under the condition $\sum_{n=1}^{\infty}\beta_{n}(1-\beta_{n})=\infty$, which entails $\beta _{n}=\frac{1}{n+1}$ as a special case. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new notion of generalized α- ϕ-Geraghty proximal contraction mappings and investigate the existence of the best proximity point for such mappings in complete metric spaces. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. [ABSTRACT FROM AUTHOR]

Based on the concept of a $C^{*}$-algebra-valued b-metric space, this paper establishes some coupled fixed point theorems for mapping satisfying different contractive conditions on such space. As applications, we obtain the existence and uniqueness of a solution for an integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a fixed point theorem for mappings satisfying cyclic φ-contractive conditions in complete metric spaces, which gives a positive answer to the question raised by Radenović (Fixed Point Theory Appl. 2015:189, ). We also find that this result and the fixed point result satisfying cyclic weak ϕ-contractions given by Karapınar (Appl. Math. Lett. 24:822-825, ) are independent of each other. Furthermore, when the number of cyclic sets is odd, we obtain fixed point theorems satisfying cyclic weak ϕ-contractions and cyclic φ-contractions in the setting of generalized metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of cyclic R-contraction mapping and then study the existence of fixed points for such mappings in the framework of metric spaces. Examples and application are presented to support the main result. Our result unify, complement, and generalize various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, the notion of generalized probabilistic G-contractions in Menger probabilistic metric spaces endowed with a directed graph G is introduced and some new fixed point theorems for such mappings are established. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, and Piri and Kumam in Fixed Point Theory Appl. 2014:210, , etc.). Examples are provided to support the usability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized Meir-Keeler contraction mappings in the setup of b-metric-like spaces. Then we establish some fixed point results for this class of contractions. We also provide some examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

Let X be a Banach space or a complete hyperbolic metric space. Let C be a nonempty, bounded, closed, and convex subset of X and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, we show that if X is a Banach space which is uniformly convex in every direction or a uniformly convex hyperbolic metric space, then T has a fixed point. This is the analog to Browder and Göhde's fixed point theorem for monotone nonexpansive mappings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new classes of Hardy-Rogers type cyclic contractions and prove pertinent fixed point theorems for these Hardy-Rogers type contractions in the generating space of a b-dislocated metric family. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point results for α- λ-contractions in the class of quasi b-metric spaces. To illustrate the obtained results, we provide some examples and an application on a solution of an integral equation. We also study the stability of Ulam-Hyers and well-posedness of a fixed point problem. Our obtained results give an answer to an open problem of Kutbi and Sintunavarat (Abstr. Appl. Anal. 2014:268230, ). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the two new concepts of an α-type almost- F-contraction and an α-type F Suzuki contraction and prove some fixed point theorems for such mappings in a complete metric space. Some examples and an application to a nonlinear fractional differential equation are given to illustrate the usability of the new theory. [ABSTRACT FROM AUTHOR]

The aim of this paper to present fixed point results for single-valued operators in b-metric spaces. The case of scalar metric and the case of vector-valued metric approaches are considered. As an application, a system of integral equations is studied. [ABSTRACT FROM AUTHOR]