Fixed Point Research Articles

ON THE WEIGHTED PSEUDO ALMOST PERIODIC SOLUTIONS FOR LIÉNARD -TYPE SYSTEMS WITH VARIABLE DELAYS

This study deals with Liénard-type differential equation systems with time-varying delays. Some sufficient conditions have been obtained for the existence and uniqueness of the weighted pseudo almost periodic solutions of the considered system by using some differential inequalities, the main features of the weighted pseudo almost periodic and Banach Fixed Point Theorem. Since the weighted pseudo almost periodic functions space is more general than the almost and pseudo almost pseudo periodic functions space, this work is a new and complementary. In addition, an example is given to show the correctness of the created conditions.

COINCIDENCE AND COMMON FIXED POINT THEOREMS IN Ƒ-METRIC SPACES

Recently, the concept of Ƒ metric space has been introduced and have been defined a natural topology in this spaces by Jleli and Samet[6]. Furthermore, a new style of Banach contraction principle has been given in the Ƒ metric spaces. In this paper, we prove some coincidence and common fixed point theorems in Ƒ metric spaces.

On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Many authors used the concept of F−contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

Existencia de soluciones limitadas para ecuaciones retardadas con retardo infinito, impulsos y condición no local

En este trabajo, estudiamos la existencia de soluciones acotadas para una ecuación retardada semilineal con retardo infinito, impulso y condiciones no locales. También mostramos que bajo algunas condiciones esta solución acotada es única, periódica o casi periódica dependiendo de las condiciones impuestas a los términos que involucran la ecuación. A través de este trabajo, asumiremos que la ecuación lineal asociada tiene una dicotomía exponencial, lo que nos permite encontrar una fórmula para las soluciones acotadas, y a partir de esta fórmula, podemos aplicar el Teorema del punto fijo de Banach para demostrar la existencia de tales soluciones acotadas.

The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations

The collocation method based on Chebyshev basis functions, coupled Picard iterative process, is proposed to solve a functional Volterra integral equation of the second kind. Using the Banach Fixed Point Theorem, we prove theorems on the existence and uniqueness solutions in the L2-norm. We also provide the convergence and stability analysis of the proposed method, which indicates that the numerical errors in the L2-norm decay exponentially, provided that the kernel function is sufficiently smooth. Numerical results are presented and they confirm the theoretical prediction of the exponential rate of convergence.

A proximal point algorithm for finding minimizers and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces

The purpose of this article is twofold. One is to establish a proximal point algorithm for finding a minimizer of a proper convex and lower semi-continuous function and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces. The other is to point out and correct a basic and conceptual error in a paper of Ugwunnadi et al. [Theorem 3.1, J. Fixed Point Theory Appl. (2018) 20: 82].

Expression of Concern on “On A New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces”

Expression of Concern on “On A New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces”

Phases of unitary matrix models and lattice QCD2

We investigate the different large $N$ phases of a generalized Gross-Witten-Wadia $U(N)$ matrix model. The deformation mimics the one-loop determinant of fermion matter with a particular coupling to gauge fields. In one version of the model, the GWW phase transition is smoothed out and it becomes a crossover. In another version, the phase transition occurs along a critical line in the two-dimensional parameter space spanned by the 't~Hooft coupling $\lambda$ and the Veneziano parameter $\tau$. We compute the expectation value of Wilson loops in both phases, showing that the transition is third-order. A calculation of the $\beta $ function shows the existence of an IR stable fixed point.

A note on $${\mathcal {F}}$$-metric spaces

A new generalization of the metric space notion, named $${\mathcal {F}}$$ -metric space, was given in [M. Jleli, B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), no. 3, Art. 128, 20 pp.]. In this paper, we investigate some properties of $${\mathcal {F}}$$ -metric spaces. A simple proof is given to show that the natural topology induced by an $${\mathcal {F}}$$ -metric is metrizable. We present a method to construct s- $$\hbox {relaxed}_{{p}}$$ spaces and, therefore, $${\mathcal {F}}$$ -metric spaces from bounded metric spaces. We give some results that reveal differences between metric and $${\mathcal {F}}$$ -metric spaces. In particular, we show that the ordinary open and closed balls in $${\mathcal {F}}$$ -metric spaces are not necessarily topological open and closed, respectively. This answers a question posed implicitly in the quoted paper. We also show that $${\mathcal {F}}$$ -metrics are not necessarily jointly continuous functions. Despite some topological differences between metrics and $${\mathcal {F}}$$ -metrics, we show that the Nadler fixed point theorem and, therefore, the Banach contraction principle in the frame of $${\mathcal {F}}$$ -metric spaces can be reduced to their original metric versions. This reduction even happens when the Schauder fixed point theorem is investigated in $${\mathcal {F}}$$ -normed spaces structure. By applying the given technique in this paper, it turns out that some nonlinear $${\mathcal {F}}$$ -metric contractions and, therefore, the related $${\mathcal {F}}$$ -metric fixed point results can naturally be reduced to their metric versions. In addition, the same happens for some topological fixed point results.

On Fuzzy Fixed Points and an Application to Ordinary Fuzzy Differential Equations

The aim of this paper is to obtain the common fuzz fixed points ofα-fuzzy mappings satisfying generalized almostY,Λ-contraction in complete metric spaces. Our results are extensions and improvements of the several well-known recent and classical results in literature. We give an example for supporting these results. As an application, we apply our obtained results to study the existence of a solution for a second order nonlinear boundary value problem.

Suzuki type multivalued contractions in <i>C</i><sup>*</sup>-algebra valued metric spaces with an application

In the present paper, we established multivalued fixed point results on C*-algebra valued metric spaces and utilized the same to prove fixed point results via Suzuki type contraction. An example is also given to exhibit the utility of our main result. We also provided a system of Fredholm integral equations to examine the existence and uniqueness of solutions supporting our main result.

Common Fixed Point Results for a Pair of Multivalued Mappings in Complex-Valuedb-Metric Spaces

Several fixed point results for the existence of common fixed points of multivalued contractive mappings have been established in complex-valued metric space. In this paper, we study the existence of common fixed points for a pair of multivalued contractive mappings satisfying some rational inequalities in the framework of complex-valuedb-metric spaces. The contractive condition used in this paper generalizes many contractive conditions used by other authors in the literature. Employing our results, we check the existence solution to the Riemann-Liouville equation.

An Algorithm for a Class of Bilevel Variational Inequalities with Split Variational Inequality and Fixed Point Problem Constraints

In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of a split variational inequality and fixed point problem. Strong convergence of the iterative process is proved. In particular, the problem of finding a common solution to a variational inequality with pseudomonotone mapping and a fixed point problem involving demicontractive mapping is also studied. Besides, we get a strongly convergent algorithm for finding the minimum-norm solution to the split feasibility problem, which requires only two projections at each step. A simple numerical example is given to illustrate the proposed algorithm.

Corrigendum: On analytic model for two-choice behavior of the paradise fish based on the fixed point method, J. Fixed Point Theory Appl. 2019, 21:56

The purpose of this short note is to present some corrections and clarifications concerning the proof of the main result given in the paper “On analytic model for two-choice behavior of the paradise fish based on the fixed point method, J. Fixed Point Theory Appl. 2019, 21:56”.

Neutrosophic Soft Fixed Points

In a wide spectrum of mathematical issues, the presence of a fixed point (FP) is equal to the presence of a appropriate map solution. Thus in several fields of math and science, the presence of a fixed point is important. Furthermore, an interesting field of mathematics has been the study of the existence and uniqueness of common fixed point (CFP) and coincidence points of mappings fulfilling the contractive conditions. Therefore, the existence of a FP is of significant importance in several fields of mathematics and science. Results of the FP, coincidence point (CP) contribute conditions under which maps have solutions. The aim of this paper is to explore these conditions (mappings) used to obtain the FP, CP and CFP of a neutrosophic soft set. We study some of these mappings (conditions) such as contraction map, L-lipschitz map, non-expansive map, compatible map, commuting map, weakly commuting map, increasing map, dominating map, dominated map of a neutrosophic soft set. Moreover we introduce some new points like a coincidence point, common fixed point and periodic point of neutrosophic soft mapping. We establish some basic results, particular examples on these mappings and points. In these results we show the link between FP and CP. Moreover we show the importance of mappings for obtaining the FP, CP and CFP of neutrosophic soft mapping.

On the UV completion of the O(N) model in 6 \u2212 \u03f5 dimensions: a stable large-charge sector

We study large charge sectors in the O(N) model in 6 − ϵ dimensions. For 4 < d < 6, in perturbation theory, the quartic O(N) theory has a UV stable fixed point at large N . It was recently argued that this fixed point can be described in terms of an IR fixed point of a cubic O(N) model. By considering a double scaling limit of large charge and weak couplings, we compute two-point and all “extremal” higher-point correlation functions for large charge operators and find a precise equivalence between both pictures. Instanton instabilities are found to be exponentially suppressed at large charge. We also consider correlation function of U(1)-invariant meson operators in the O(2N) ⊃ U(1) × SU(N) theory, as a first step towards tests of (higher spin) AdS/CFT.

Arbitrary Binary Relations, Contraction Mappings, and b-Metric Spaces

We prove some results on the existence and uniqueness of fixed points defined on a b-metric space endowed with an arbitrary binary relation. As applications, we obtain some statements on the coincidence of points involving a pair of mappings. Our results generalize, extend, modify and unify several well-known results and, especially, the results obtained by Alam and Imdad [J. Fixed Point Theory Appl., 17, 693–702 (2015); Fixed Point Theory, 18, 415–432 (2017), and Filomat, 31, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory Appl., 12, 221–238 (2012)]. In addition, we provide an example to illustrate the suitability of the obtained results.

Speed and Area Efficient FXP Adders and Multipliers: A Comparative Analysis for LNS System

In this paper, a variety of adder and multiplier are compared to be implemented in a new logarithmic number system (LNS). Both adder and multiplier are designed with a generic very high-speed integrated circuit hardware description language (Verilog) program. This makes it possible to achieve the optimum performance in latency and area of 0.18µm CMOS technologies LNS chip. Consequently, the optimal configurations vary with speed and area of the schemes and in some cases can be compact area, O(n), fast in latency O(log2 n) or optimized. The program was scripted based on fixed-point (FXP) adders and multipliers that yet will be implemented in LNS system. The functionality of the scheme was tested before synthesized. Outcomes show that Ladner Fisher (LF) adder and modified Baugh Wooley multiplier contribute to fast in latency and consume minimal area.

Generalizations of Kannan and Reich Fixed Point Theorems, Using Sequentially Convergent Mappings and Subadditive Altering Distance Functions

In this paper, first, using interpolative Kannan type contractions, a new fixed point theorem has been proved. Then, by applying sequentially convergent mappings and using subadditive altering distance functions, we generalize contractions in complete metric spaces. Finally, we investigate some fixed point theorems which are generalizations of Kannan and Reich fixed points.