Points Of Mappings Research Articles

On the domain of generalized mean in Nakano sequence space, and its prequasi ideal with some applications

Some topological and geometric behavior of the space of all sequences whose generalized mean transforms are in Nakano sequence space, the multiplication mappings acting on it, and the eigenvalue distribution of mappings ideal generated by this space and s-numbers are discussed. We construct the existence of a fixed point of Kannan contraction mapping on these spaces. Several numerical experiments are presented to illustrate our results. Moreover, some successful applications to the existence of solutions of nonlinear difference equations are explained. The strength here is that the current results are constructed under flexible setups given by controlling the weight and power of these spaces.

Quadruple Best Proximity Points with Applications to Functional and Integral Equations

This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.

Ordered Uniform Convexity in Ordered Convex Metric Spaces with an Application to Fixed Point Theory

In this paper, we introduce the concept of ordered uniform convexity in ordered convex metric spaces and study some properties of order uniform convexity. Finally, as application, we connect our results with existence of fixed points for monotone non-expansive mappings defined on these spaces.

Existence of entire radial solutions to Hessian type system

AbstractIn this paper, the Dirichlet problem of Hessian type system is studied. After converting the existence of an entire solution to the existence of a fixed point of a continuous mapping, the existence of entire radial solutions is established by Schaefer fixed point theorem.

Observation points classifier ensemble for high‐dimensional imbalanced classification

AbstractIn this paper, an Observation Points Classifier Ensemble (OPCE) algorithm is proposed to deal with High‐Dimensional Imbalanced Classification (HDIC) problems based on data processed using the Multi‐Dimensional Scaling (MDS) feature extraction technique. First, dimensionality of the original imbalanced data is reduced using MDS so that distances between any two different samples are preserved as well as possible. Second, a novel OPCE algorithm is applied to classify imbalanced samples by placing optimised observation points in a low‐dimensional data space. Third, optimization of the observation point mappings is carried out to obtain a reliable assessment of the unknown samples. Exhaustive experiments have been conducted to evaluate the feasibility, rationality, and effectiveness of the proposed OPCE algorithm using seven benchmark HDIC data sets. Experimental results show that (1) the OPCE algorithm can be trained faster on low‐dimensional imbalanced data than on high‐dimensional data; (2) the OPCE algorithm can correctly identify samples as the number of optimised observation points is increased; and (3) statistical analysis reveals that OPCE yields better HDIC performances on the selected data sets in comparison with eight other HDIC algorithms. This demonstrates that OPCE is a viable algorithm to deal with HDIC problems.

Bifurcations analysis in implicit maps through the dynamics of cumulated surface errors in milling

In this contribution, we examine the evolution of surface errors during consecutive milling operations. Its description is based on a nonlinear implicit map, which is suitable to investigate the surface quality. It describes the series of consecutive Surface Location Errors (SLE) in roughing operations. As one of the principal results of the paper, bifurcations related to the fixed point of the implicit map are analyzed via normal form theorem. We determined a formula for the criticality of the bifurcation, which allows the approximate computation of the arising period-two solution. The method is demonstrated for the surface error model of milling, and the results are verified by numerical computations. Although the amplitude of the SLE would be negligible, its derivatives has a great influence in the model, which can cause stability problems.

On Certain Quadruple Fixed Points of Integral Type Contraction Mappings in G-Metric Spaces and its Applications

In this paper, the existence of common quadruple fixed point results for integral type contraction of two mappings in G-metric spaces is established. Some interesting consequences of our results are achieved. Moreover, we give an illustration that presents the applicability of the achieved results.

Convergence Theorems of Three-Step Iteration Algorithm in CAT (0) Spaces

In this paper, a modified three-step iteration algorithm for approximating a joint fixed point of non-expansive and contraction mapping is studied. Under appropriate conditions, several strong convergence theorems and Δ-convergence theorems are established in a complete CAT (0) space. a numerical example is introduced to show that this modified iteration algorithm is faster than other iteration algorithms. Finally, we prove that the modified iteration algorithm is stable. Therefore these results are extended and improved to a novel results that are stated by other researchers. Our results are also complement to many well-known theorems in the literature. This type of research can be played a vital role in computer programming, game theory and computational analysis.

Geometry of transit orbits in the periodically-perturbed restricted three-body problem

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are considered, such as perturbation due to the sun (i.e., the bicircular problem) or orbital eccentricity of the primaries. For the case of a time-periodic perturbation, the Lagrange point is replaced by a periodic orbit, equivalently viewed as a hyperbolic-elliptic fixed point of a symplectic map (the stroboscopic Poincaré map). Transit and non-transit orbits can be identified in the discrete map about the fixed point, in analogy with the geometric construction of Conley and McGehee about the index-1 saddle equilibrium point in the continuous dynamical system. Furthermore, though the continuous time system does not conserve the Hamiltonian energy (which is time-varying), the linearized map locally conserves a time-independent effective Hamiltonian function. We demonstrate that the phase space geometry of transit and non-transit orbits is preserved in going from the unperturbed to a periodically-perturbed situation, which carries over to the full nonlinear equations.

Ishikawa type mean convergence theorems for finding common fixed points of nonlinear mappings in Hilbert spaces

Ishikawa type mean convergence theorems for finding common fixed points of nonlinear mappings in Hilbert spaces

New Fixed Point Theorems for Admissible Hybrid Maps

The aim of this work is to investigate the concept of a new hybrid Suzuki contractive by using the Rus-Reich-Ćirić-type interpolative mappings in b -metric spaces. We seek the presence and uniqueness of a fixed point of such new contraction type mappings and prove some related results. We further give an application of Ulam-Hyers-type stability to show the well-posedness of our results.

Fixed point results with respect to a wt-distance in partially ordered b-metric spaces and its application to nonlinear fourth-order differential equation

In this paper we study the existence of the fixed points for Hardy-Rogers type mappings with respect to a wt-distance in partially ordered metric spaces. Our results provide a more general statement, since we replace a w-distance with a wt-distance and ordered metric spaces with ordered b-metric spaces. Some examples are presented to validate our obtained results and an application to nonlinear fourth-order differential equation are given to support the main results.

Some fixed point results for enriched nonexpansive type mappings in Banach spaces

In this paper, we introduce two new classes of nonlinear mappings and present some new existence and convergence theorems for these mappings in Banach spaces. More precisely, we employ the Krasnosel'skii iterative method to obtain fixed points of Suzuki-enriched nonexpansive mappings under different conditions. Moreover, we approximate the fixed point of enriched-quasinonexpansive mappings via Ishikawa iterative method.

A New Iterative Algorithm for General Variational Inequality Problem with Applications

This study aims at investigation of a generalized variational inequality problem. We initiate a new iterative algorithm and examine its convergence analysis. Using this newly proposed iterative method, we estimate the common solution of generalized variational inequality problem and fixed points of a nonexpansive mapping. A numerical example is illustrated to verify our existence result. Further, we demonstrate that the considered iterative algorithm converges with faster rate than normal S -iterative scheme. Furthermore, we apply our proposed iterative algorithm to estimate the solution of a convex minimization problem and a split feasibility problem.

An Accelerated Fixed-Point Algorithm with an Inertial Technique for a Countable Family of G-Nonexpansive Mappings Applied to Image Recovery

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated fixed-point methods have been introduced. The main aim of this paper is to use a coordinate affine structure to create an accelerated fixed-point algorithm with an inertial technique for a countable family of G-nonexpansive mappings in a Hilbert space with a symmetric directed graph G and prove the weak convergence theorem of the proposed algorithm. As an application, we apply our proposed algorithm to solve image restoration and convex minimization problems. The numerical experiments show that our algorithm is more efficient than FBA, FISTA, Ishikawa iteration, S-iteration, Noor iteration and SP-iteration.

General Variational Inclusions and Nonexpansive Mappings

In this paper, we introduce a new class of variational inclusions involving three operators. We suggest and analyze three-step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique. We also study the convergence criteria of three-step iterative method under some mild conditions. Inertial type methods are suggested and investigated for general variational inclusions. Our results include the previous results as special cases and may be considered as an improvement and refinement of the previously known results.

Common Fixed Points of Single-Valued and Multi-Valued Mappings in S-Metric Spaces

In this paper, the notion of limit property (-Tayyab kamran, 2004-) and common limit property (-Yicheng Liu & Jun Wu & Zhixiang Li, 2005-) for singlevalued and multi-valued mappings on metric spaces are generalized to S-metric spaces. This idea is used to make some common fixed point theorems for singlevalued and multi-valued mappings by using a generalization of coincidence point in S-metric spaces. We give an example of an S-metric which is not continuous.

Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces

Let E be a strictly convex real Banach space and let Dsubseteq E be a nonempty closed convex subset of E. Let T_{i}: {D}longrightarrow mathcal{P}({D}), i=1,2,3,ldots be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, mathcal{P}(D) is the family of proximinal and bounded subsets of D. Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps.

Weak and Strong Convergence Theorems of Modified Projection-Type Ishikawa Iteration Scheme for Lipschitz α-Hemicontractive Mappings

In this paper, we establish weak and strong convergence theorems of a two-step modified projection-type Ishikawa iterative scheme to the fixed point of α-hemicontractive mappings without any compactness assumption on the operator or the space. Our results extend, improve and generalize several previously known results of the existing literature.

A new iterative approximation scheme for Reich–Suzuki-type nonexpansive operators with an application

In this article, we propose a faster iterative scheme, called the AH iterative scheme, for approximating fixed points of contractive-like mappings and Reich–Suzuki-type nonexpansive mappings. We show that the AH iterative scheme converges faster than a number of existing iterative schemes for contractive-like mappings. The w^{2}-stability result of the new iterative scheme is established and a supportive example is provided to illustrate the notion of w^{2}-stability. Then, we prove weak and several strong convergence results of our new iterative scheme for fixed points of Reich–Suzuki-type nonexpansive mappings. Further, we carry out a numerical experiment to illustrate the efficiency of our new iterative scheme. As an application, we use our main result to prove the existence of a solution of a mixed-type nonlinear integral equation. An illustrative example to validate the result in our application is also given. Our results extend and generalize several related results in the existing literature.