Search

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

A very impressive research work has been devoted in the last two decades to obtaining fixed point theorems in quasimetric spaces (also called b-metric spaces). Some incorrect and incomplete references with respect to the early developments on fixed point theory in b-metric spaces are though perpetually taking over from the existing publications to the new ones. Starting from this fact, our main aim in this note is threefold: (1) to briefly survey the early developments in the fixed point theory on quasimetric spaces (b-metric spaces); (2) to collect some relevant bibliography related to this topic; (3) to discuss some other aspects of current interest in the fixed point theory on quasimetric spaces (b-metric spaces). [ABSTRACT FROM AUTHOR]

In this paper, we propose a strongly convergent simultaneous cutter method for finding the minimal norm solution over the intersection of fixed point sets of cutters. The proposed method is the combination of the simultaneous cutter method and the strongly variance of Krasnosel'skiĭ-Mann method. We show a strong convergence result of the sequence generated by the proposed method to the unique minimal norm solution. We finally present the numerical experiments on the minimal norm solution over a finite number of linear feasibility problem. [ABSTRACT FROM AUTHOR]

In this paper we provide a new approach in the study of a variational-hemivariational inequality in Hilbert space, based on the theory of maximal monotone operators and the Banach fixed point theorem. First, we introduce the inequality problem we are interested in, list the assumptions on the data and show that it is governed by a multivalued maximal monotone operator. Then, we prove that solving the variational-hemivariational inequality is equivalent to finding a fixed point for the resolvent of this operator. Based on this equivalence result, we use the Banach contraction principle to prove the unique solvability of the problem. Moreover, we construct the corresponding Picard, Krasnoselski and Mann iterations and deduce their convergence to the unique solution of the variational-hemivariational inequality. [ABSTRACT FROM AUTHOR]

In this paper some existence and stability results for cyclic graphical contractions in complete metric spaces are given. An application to a coupled fixed point problem is also derived. [ABSTRACT FROM AUTHOR]

We prove that the convergence theorems for Mann iteration used for approximation of the fixed points of demicontractive mappings in Hilbert spaces can be derived from the corresponding convergence theorems in the class of quasi-nonexpansive mappings. Our derivation is based on an important auxiliary lemma (Lemma 3.2), which shows that if T is k-demicontractive, then for any λ ∈ (0, 1 − k), Tλ is quasi-nonexpansive. In this way we obtain a unifying technique of proof for various well known results in the fixed point theory of demicontractive mappings. We illustrate this reduction technique for the case of two classical convergence results in the class of demicontractive mappings: [Măruşter, Şt. The solution by iteration of nonlinear equations in Hilbert spaces. Proc. [ABSTRACT FROM AUTHOR]

Let (M,d) be a metric space, X⊂ M be a nonempty closed subset and K⊂ M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F:X→ P(X) is said to be a strong Frum-Ketkov type operator if there exists α ∈ ]0,1[ such that ed(F(x),K)\≤ α Dd(x,K), for every x→ X, where ed is the excess functional generated by d and Dd is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators. [ABSTRACT FROM AUTHOR]

Themain aimof this paper is to establish some fixed point theorems for enriched Ćiriū-Reich-Rus contractions in Banach spaces and convex metric spaces, respectively. [ABSTRACT FROM AUTHOR]

In this paper we give some fixed point theorems for nonself generalized contractions on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. S¸erban (I.A. Rus, M.-A. S¸erban, Some fixed point theorems for nonself generalized contractions, Miskolc Math. Notes, 17(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A.J. Zaslavski, A note on Rakotch contractions, Fixed Point Theory, 9(2008), no.1, 267-273) in complete metric spaces. We prove our results without using the completeness of the metric structure. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a common fixed point theory for a pair of multivalued operators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new Stackelberg-population competition model which captures the desired features of both population games and Stackelberg competition model within the same framework. We obtain some characterization results for the Stackelberg-population equilibrium response set and the Stackelberg-population equilibrium leader set by using the variational inequality technique and Brouwer's fixed point theorem. We also show an existence theorem of Nash equilibrium for Stackelbergpopulation competition model under some mild conditions. Finally, we give an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove convergence theorems for a fixed point iterative algorithm of Krasnoselskij- Mann type associated to the class of enriched nonexpansive mappings in Banach spaces. The results are direct generalizations of the corresponding ones in [Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293-304.], from the setting of Hilbert spaces to Banach spaces, and also of some results in [Senter, H. F. and Dotson, Jr., W. G., Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 44 (1974), No. 2, 375-380.], [Browder, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197-228.], by considering enriched nonexpansive mappings instead of nonexpansive mappings. Many other related results in literature can be obtained as particular instances of our results. [ABSTRACT FROM AUTHOR]

In this paper, we present a Tseng-type self-adaptive algorithm for solving a variational inequality and a fixed point problem involving pseudomonotone and pseudocontractive operators in Hilbert spaces. A weak convergent result for such algorithm is proved under a weaker assumption than sequentially weakly continuous imposed on the pseudomonotone operator. Some corollaries are also included. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and Δ-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we discuss similar problems posed by I. A. Rus in Fixed point theory in partial metric spaces (Analele Univ. de Vest TimiŞoara, Mat.-Inform., 46 (2008), 149-160) and in Kasahara spaces (Sci. Math. Jpn., 72 (2010), No. 1, 101-110). We start our considerations with an overview of generalized metric spaces with R+-valued distance and of generalized contractions on such spaces. After that we give some examples of conversions between generalized metric spaces and standard metric spaces with applications in fixed point theory. Some possible applications to theoretical informatics are also considered. [ABSTRACT FROM AUTHOR]

Let K:= R or C, 0 < κ < 1 and f ∈ C([0, b] × K³, K). In this paper we use the weakly Picard operator theory technique to study the following functional-differential equation y0(x) = f(x; y(x); y0(x); y(κx)); x ∈ [0, b]. [ABSTRACT FROM AUTHOR]

The theory of finitely supported algebraic structures is a reformulation of Zermelo-Fraenkel set theory in which every set-based construction is finitely supported according to a canonical action of a group of permutations of some basic elements named atoms. In this paper we study the properties of finitely supported sets that contain infinite uniformly supported subsets, as well as the properties of finitely supported sets that do not contain infinite uniformly supported subsets. Particularly, we focus on fixed points properties. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized weakly contractive mapping of quadratic type and we prove fixed point results for this type of mapping. We justify our result by suitable examples and show that this mapping satisfies properties P and Q. Among other things, as corollaries we recover Banach and Kannan fixed point theorems. [ABSTRACT FROM AUTHOR]

Let (M, d) be a metric space, .... In this paper, we will give sufficient conditions ensuring that a Frum-Ketkov operator is weakly Picard. Some generalized Frum-Ketkov operators are also studied. [ABSTRACT FROM AUTHOR]

In this paper, by considering the concept of set-valued nonlinear P-contraction which is newly introduced, we present some new fixed point theorems for set-valued mappings on complete metric space. Then by considering a single-valued case we provide an existence and uniqueness result for a kind of second order two point boundary value problem. [ABSTRACT FROM AUTHOR]

In this paper, we use Száz maximum principle to prove generalizations of Caristi fixed point theorem in a preordered K-complete quasi metric space. Examples are given to support our results. [ABSTRACT FROM AUTHOR]

Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, presented here for the first time, we introduce and study the class of enriched nonexpansive mappings in Hilbert spaces. In order to approximate the fixed points of enriched nonexpansive mappings we use the Krasnoselskij iteration for which we prove strong and weak convergence theorems. Examples to illustrate the richness of the new class of contractive mappings are also given. Our results in this paper extend some classical convergence theorems established by Browder and Petryshyn in [Browder, F. E., Petryshyn, W. V., Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197-228] from the case of nonexpansive mappings to that of enriched nonexpansive mappings, thus including many other important related results from literature as particular cases. [ABSTRACT FROM AUTHOR]

In this paper we emphasize a split type problem of some integrating ideas of the split feasibility problem and the hierarchical optimization problem. Working on real Hilbert spaces, we propose a subgradient algorithm for approximating a solution of the introduced problem. We discuss its convergence results and present a numerical example. [ABSTRACT FROM AUTHOR]

In this paper we have introduced a new type of contraction condition using a class of simulation functions, in the sequel using the new contraction definition, involving measure of noncompactness; we establish few results on existence of fixed points of continuous functions defined on a subset of Banach space. This result also generalizes other related results obtained in Arab [Arab, R., Some generalizations of Darbo fixed point theorem and its application, Miskolc Math. Notes, 18 (2017), No. 2, 595-610], Bana's [Bana's, J. and Goebel, K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, Dekker, New York, 60 (1980)]. The obtained results are used in establishing existence theorems for a class of nonlinear quadratic equation (which generalizes several types of fractional-quadratic integral equations such as Abel's integral equation) defined on a closed and bounded subset of R. The existence of solution is established with the aid of a measure of noncompactness defined on function space C(I) introduced in [Bana's, J. and Olszowy, L., Measures of Noncompactness related to monotonicity, Comment. Math., 41 (2001), 13-23]. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37-53]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified inertial subgradient extragradient algorithm in a 2-uniformly convex and uniformly smooth real Banach space and prove a strong convergence theorem for approximating a common solution of fixed point equation with a demigeneralized mapping and a variational inequality problem of a monotone and Lipschitz mapping. We present an example to validate our new findings. This work substantially improves and generalizes some well-known results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317] and Secelean, N. A. & Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415-431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point. [ABSTRACT FROM AUTHOR]

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536-545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

In this work, two inertial algorithms for approximating common elements of the sets of solutions of three important problems are constructed. The first problem is a generalized mixed equilibrium one involving relaxed monotone mapping, the second is a zero problem of inverse strongly monotone mappings, while the third one is a fixed point problem of a family of relatively nonexpansive mappings. The first algorithm is a shrinking projection type for a common solution of all the three problems. The second is a generalized Alber projection free method for the second and the third problems. Each of the devised algorithms uses the conjugate gradient-like direction, which allows it to accelerate its iterates toward a solution of the problems. The strong convergence theorem for each of the algorithms is formulated and proved in a real 2 - uniformly convex and uniformly smooth Banach space. Additionally, the applications of our algorithms to convex optimization problems and image recovery problems are studied. The advantages and computational efficiency of our methods are analyzed based on their numerical performance in comparison to some of the existing and recently proposed methods using numerical example. [ABSTRACT FROM AUTHOR]

Let K be a non-empty closed subset of a Banach space X endowed with a graph G. The main result of this paper is a fixed point theorem for nonself Kannan G-contractions T : K → X that satisfy Rothe's boundary condition, i.e., T maps ∂K (the boundary of K) into K. Our new results are extensions of recent fixed point theorems for self mappings on metric spaces endowed with a partial order and also of various fixed point theorems for self and nonself mappings on Banach spaces or convex metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems for non-self G-almost contractive mappings in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein. [ABSTRACT FROM AUTHOR]

Let (X, d) be a metric space, f, fn : X → X, with Ff = ..., n ∈ N. For the fixed point equation (1) x = f(x) we consider the following iterative algorithm, (2) x ∈ X; x0 = x; xn+1(x) = fn(xn(x)); n ∈ N. By definition, the algorithm (2) is convergent if, xn(x) → x*(x) ∈ Ff as n → ∞, ∀ x ∈ X. In this paper we give some conditions on fn and f which imply the convergence of algorithm (2). In this way we improve some results given in [Rus, I. A., An abstract point of view on iterative approximation of fixed points. impact on the theory of fixed point equations, Fixed Point Theory, 13 (2012), No. 1, 179-192]. In our results, in general we do not suppose that, Ff ≠ ∅. Some research directions are formulated. [ABSTRACT FROM AUTHOR]

In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued Fd-contraction on quasi metric space (X; d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative process to approximate fixed points of nonexpansive maps in real Banach spaces having weakly continuous duality map and establish strong convergence theorems for the proposed iterative process. There is no compactness assumption on K or on T. Our results improve important recent results. [ABSTRACT FROM AUTHOR]

Let Ω ⊂ ℝp, p ∈ ℕ* be a nonempty subset and B(Ω) be the Banach lattice of all bounded real functions on Ω, equipped with sup norm. Let X ⊂ B(Ω) be a linear sublattice of B(Ω) and A: X → X be a positive linear operator with constant functions as the fixed point set. In this paper, using the weakly Picard operators techniques, we study the iterates of the operator A: Some relevant examples are also given. [ABSTRACT FROM AUTHOR]

In the present paper, taking into account the recent developments on the theory of fixed point, we give some fixed point results for multivalued nonself mappings on complete metrically convex metric spaces. Our main result properly includes the famous Assad-Kirk fixed point theorem for nonself mappings. Also, we provide a nontrivial example which shows the motivation for such investigations of multivalued nonself contraction mappings. [ABSTRACT FROM AUTHOR]

In this paper, some existence results for a system of operator inclusions are presented. Qualitative properties of the solution set are also discussed. The method is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. The approach is new even for the case of the metric spaces. As an application, an existence result for a mixed boundary and initial value problem for a system of second order differential inclusions is given. [ABSTRACT FROM AUTHOR]

Several iterative processes have been defined by researchers to approximate the fixed points of various classes operators. In this paper we present, by using the basins of attraction for the roots of some complex polynomials, an empirical comparison of some iteration procedures for fixed points approximation of Newton's iteration operator. Some numerical results are presented. The Matlab m-files for generating the basins of attraction are presented, too. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a class of nonsmooth Stackelberg equilibrium problems with differential revenue functions and nonsmooth cost functions. First, we describe the best response set of the follower and the best strategy set of the leader for the considered nonsmooth Stackelberg equilibrium problem via mixed variational inequalities. Then, by using the resolvent operator method and the Banach fixed point theorem, we show the existence and uniqueness of its solution. [ABSTRACT FROM AUTHOR]

In this paper, we study the M-iteration process in hyperbolic spaces and prove some strong and Δ-convergence theorems of this iteration process for generalized nonexpansive mappings. Moreover, we establish the weak w²-stability and data dependence theorems for a class of contractive-type mappings by using M-iteration process. The results presented here extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, using the concepts of f-closed set and inverse f-closed set, we will prove some fixed point theorems for graphic contractions in complete quasimetric space. Then, as applications, coupled fixed point theorems in quasimetric spaces without the mixed monotonicity property are obtained. [ABSTRACT FROM AUTHOR]

Let (X, //⋅//) be a Banach space and T : A → X a contraction mapping, where A ⊂ X is a closed set. Consider a sequence {xn} ⊂ A and define the sequence {yn} ⊂ X, by yn = xn +T xσ(n), where {σ(n)} is a sequence of natural numbers. We highlight some general conditions so that the two sequences {xn} and {yn} are simultaneously convergent. Both cases: 1) σ(n) < n, for all n, and 2) σ(n) ≥ n, for all n, are discussed. In the first case, a general Picard iteration procedure is inferred. The results are then extended to sequences of mappings and some appropriate applications are also proposed. [ABSTRACT FROM AUTHOR]

We show that the choice of stepsize in Korpelevich’s extragradient algorithm is sharp, while the choice of stepsize in Popov’s extragradient algorithm can be relaxed. We also extend Korpelevich’s extragradient algorithm and Popov’s extragradient algorithm (with larger stepsize) to the infinite-dimensional Hilbert space framework, with weak convergence. [ABSTRACT FROM AUTHOR]

We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish ∆ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems. [ABSTRACT FROM AUTHOR]

We study the space of all continuous and increasing self-mappings of the real interval [0, 1] equipped with the topology of uniform convergence. In particular, we show that most such functions have at least two different fixed points. [ABSTRACT FROM AUTHOR]

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (κ) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces. [ABSTRACT FROM AUTHOR]

Starting from the results, established in [Albu, M., A fixed point theorem of Maia-Perov type. Studia Univ. Babeş - Bolyai Math., 23 (1978), No. 1, 76-79] and [Mureşan, V., Basic problem for Maia-Perov's fixed point theorem, Seminar on Fixed Point Theory, Babeş Bolyai Univ., Cluj-Napoca, (1988), Preprint Nr. 3, pp. 43-48] where fixed point theorems of Maia-Perov type are proved, the main aim of this paper is to extend this results to product metric spaces, using Prešić type operators. An existence, uniqueness and data dependence theorem related to the solution of the system of integral equations of Fredholm type in product metric spaces, is also presented. [ABSTRACT FROM AUTHOR]

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165-167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w-distance in fixed point theory. In this paper, we generalize Fisher's result for pair of mappings on metric space to complete metric space with w-distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea. [ABSTRACT FROM AUTHOR]

We give some extensions of the beautiful 1968 fixed point theorem of Maia [Maia, M. G. Un'osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139-143] to three classes of enriched contractive mappings in Banach spaces: enriched contractions, Kannan enriched contractions and Ć irić-Reich-Rus contractions. [ABSTRACT FROM AUTHOR]