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In this paper we present some theorems on the multiplicity of fixed points of some operators on a special wedge and using these results we consider x ″ + f (t , x , x ′) = 0 , t ∈ (0 , 1) x (0) = 0 , x (1) = 0 and establish the existence of multiple solutions. [ABSTRACT FROM AUTHOR]

In this paper, it is considered the existence of a solution for a nonlocal equation involving the p-Laplacian operator which is related to several applications such as vibration problems, flow of fluids through a homogeneous isotropic rigid porous medium, nuclear reactor's dynamics and in population dynamics. The approach is based on sub-supersolution arguments and Schauder's fixed point theorem. An important fact is that our result is valid for nonlocal terms which may exhibit a growth higher than p. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a hybrid D-iteration process with inertial extrapolation method for two asymptotically nonexpansive mappings and equilibrium problems in a real Hilbert space. Strong convergence of the proposed scheme is establised. Our results extend and improve some recently announced results in the literature. With numerical example, it is shown that the proposed iterative scheme has faster rate of convergence than inertial hybrid algorithm studied by Harbau and Ahmad [12]. [ABSTRACT FROM AUTHOR]

Lipschitz mapping appears inevitably in many branches of mathematics, especially in functional analysis, and leads to the study of new results in metric fixed point theory. Goebel and Sims (resp. Goebel and Japon-Pineda) introduced a class of the Lipschitz mappings termed as (α , p) -Liptschitz mappings and studied not only the modified form of the Lipschitz condition, but also the behavior of a finite number of their iterates. The purpose of this paper is to discuss the various types of (α , p) -contractions with cyclic representation that extend the results due to Banach, Kannan, and Chatterjea. Moreover, based on such types of contractions and the property of symmetry, we obtain some related fixed-point results in the setting of metric spaces. Some examples are studied to illustrate the validity of our obtained results. As an application of our results, we establish the existence of the solution to a class of Fredholm integral equations. [ABSTRACT FROM AUTHOR]

In order to study Maia type fixed point results for several well-known contractions, we suggest two novel contractions called A-contraction and A'-contraction. The majority of the Maia type fixed point results for various contractions can now be unified through these, which eliminate the need to manage various contractions individually. The advantage of including such contractions in the study of Maia type fixed point results has been demonstrated in suitable examples. We present an application of one of our established results towards the conclusion of the paper. [ABSTRACT FROM AUTHOR]

The main motivation for this paper is to investigate the fixed point property for nonexpansive mappings defined on b-fuzzy metric spaces. First, following the idea of S. Jesi'c's result from 2009, we introduce convex, strictly convex and normal structures for sets in b-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on b-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided. [ABSTRACT FROM AUTHOR]

This paper aims to establish some results on the structure of fixed point sets for mappings in 2-inner product spaces. To this end, we employ some well-known techniques of 2-inner product spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of at least one solution and at least two nonnegative solutions of impulsive differential equations with the two-point integral boundary conditions. We employ the recent fixed point theorems for the sum of two operators on Banach spaces. The applicability of the results is illustrated through an example. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solutions for a fractional integro-differential equation with mixed nonlinearities subject to a new class of nonlocal closed integral boundary conditions. The proposed problem contains a right Liouville–Caputo fractional derivative operator and mixed Riemann-Liouville integral operators. The standard fixed point theorems are applied to derive the desired results, which are well-illustrated with examples. Some interesting observations are presented. [ABSTRACT FROM AUTHOR]

In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by Zµ- contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results. [ABSTRACT FROM AUTHOR]

The Banach contraction principle is the most celebrated fixed point theorem, it has been generalized in various directions. In this paper, inspired by the concept of (ϕ , F) -contraction in metric spaces, introduced by Wardowski. We present the notion of (ϕ , F) -contraction in b-rectangular metric spaces to study the existence and uniqueness of fixed point for the mappings in this spaces. Our results improve many existing results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the notion of MR-Kannan type contractions using the generalized averaged operator. Several examples are provided to illustrate the concept presented herein. We provide a characterisation of normed spaces using MR-Kannan type contractions with a fixed point. We investigate the Ulam–Hyers stability and well-posedness result for the mappings presented here. [ABSTRACT FROM AUTHOR]

In this paper, we extend some fixed point results for various classes of mappings to approximating fixed points, using Mann iterative process in the context of convex G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, a new type of contraction mapping is introduced, called generalized quasi like contractive mapping, and three types of new iterative schemes are presented as multi_L_explicit four step iteration, multi_ L_ explicit Noor iteration and multi_ L_Picard s-iteration. We study the rate of convergence and stability with generalized quasi like contractive mapping [ABSTRACT FROM AUTHOR]

In this paper, we propose sufficient conditions on existence, uniqueness and Ulam-Hyers stability of solutions for coupled systems of fractional nabla difference equations with anti-periodic boundary conditions, by using fixed point theorems. We also support these results through a couple of examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of extended S-metric space of type (α , β) . This extension is a generalization of S-metric space, defined by employing two functions instead of considering a constant in the second condition of the S-metric space definition. Accordingly, we prove some fixed-point results and give some examples to illustrate the validity of our work, along with giving an application of the Fredholm integral equation. [ABSTRACT FROM AUTHOR]

In 2007, in our joint work with D. Butnariu and S. Reich, we proved that if for a self-mapping of a complete metric that is uniformly continuous on bounded sets all its iterates converge uniformly on bounded sets, then this convergence is stable under the presence of small errors. In the present paper, we obtain an extension of this result for self-mappings of a metric space with a graph. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain the common fixed point theorems for two mappings in b--metric space. In this paper we prove that a unique common fixed point exists for two mappings in b--metric space. Moreover an example is discussed to verify the main result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove a common fixed point theorem for a pair of mappings satisfying an implicit relation, generalizing the main results from [6], [10], [11], [13] and other papers. [ABSTRACT FROM AUTHOR]

In this paper, we prove some weak and strong convergence results for mappings satisfying condition (CC) using Ishikawa iteration process in uniformly convex Banach spaces. The results obtained in the paper extend and improve many well-known results in the iterations theory. [ABSTRACT FROM AUTHOR]

The hyperbolic Möbius transformations, which have been defined and proved to be hyperbolic conformal in Golberg and Luna-Elizarrarás (Math Methods Appl Sci 2020, ), are generalizations of Möbius transformations in complex space C (i) and hyperbolic space D to multidimensional hyperbolic space D n . In this paper, we study the hyperbolic Möbius transformation in bicomplex space B C isomorphic to D 2 in detail, present a conjugacy classification according to the number of fixed points in S L (2 , B C) , and detailedly prove that the cross-ratio is invariant under hyperbolic Möbius transformations. Furthermore, the present paper generalizes the classical results, which have closed relation with fixed points and cross-ratios, to B C and may give new energy for the development of hyperbolic Möbius groups. [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]

Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown. [ABSTRACT FROM AUTHOR]

In this paper, based on the extrapolated Landweber‐type operators, we present new strongly convergent block‐iterative schemes for solving the split common fixed point problem (SCFPP) with demiclosed strongly quasi‐nonexpansive operators on Hilbert spaces. The strong convergence is proved without the additional assumptions such as the boundedly regular condition and the closedness property of the range of the transformation operator, assumed recently in the literature for the problem. A necessary and sufficient condition that ensures that a k$$ k $$th iterate is a solution is given. An application of our results to solve the multiple‐sets split convex feasibility problem (MSSCFP) is showed with computational experiments for illustration. [ABSTRACT FROM AUTHOR]

Dynamical systems are one of the interesting concepts where iteration algorithms and chaos can be considered together. In iteration algorithms, one of the basic concepts of fixed point theory, it is well known that the behavior of the iteration mechanism is chaotic if the original transformation is taken as chaotic. One of the natural ways to transform a chaotic system into a dynamical system is through control mechanisms. In this paper, we first consider an iteration class defined on Banach spaces, which is prominent in the literature in terms of both speed and convergence rate. Then, we consider the transformation constituting the iteration class as chaotic and obtain the stability and unstability behaviors of the iterations according to the operator norm by using Gâteaux and Fréchet derivatives representing the direction‐dependent derivative. In this way, we aimed to obtain the chaos control intervals obtained with functions in real space with the help of operators in Banach spaces. Using the operator norm obtained with the Fréchet derivative, we derive interesting dynamical system intervals from a chaotic system with parameter variables of iteration algorithms. It is noteworthy that the parameter variables of the studied iteration classes are the same in some transformation classes. In addition, analytical proofs are followed by computer simulations of parameter‐dependent control intervals considering the logistic operator with a chaotic structure. At the same time, the periodic behavior of the iteration algorithms used in our study is illustrated by the Lyapunov exponent with parameter‐dependent control intervals according to operator norm. Finally, as a real‐life problem, it has been shown that the chaos of the logistic population growth model with dynamic features can be controlled by chaos control mechanisms established by fixed point iteration methods. [ABSTRACT FROM AUTHOR]

Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems. [ABSTRACT FROM AUTHOR]

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This manuscript is devoted to proving some results concerning the existence of solutions for a class of initial value problem for nonlinear implicit fractional Hybrid differential equations and improved conformable fractional derivative. The result is based on a fixed point theorem due to Dhage. Further, an example is provided for the justification of our main result. [ABSTRACT FROM AUTHOR]

The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings established by the authors and their collaborators by using this technique; and third, to survey some related developments in the very recent literature which were authored by other researchers. [ABSTRACT FROM AUTHOR]

In this paper, we establish strong and weak convergence theorems for Suzuki's generalized nonexpansive mapping in uniformly convex Banach spaces using the iterative scheme introduced by Panigrahy et al [9]. Next, we see an example of Suzuki's generalized nonexpansive mapping, which is not a nonexpansive mapping. Using this example and some numerical tests, we infer empirically that the Panigrahy iteration process converges faster than the Krasnoselskij, Thakur, and M-iteration processes. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a new class of noncyclic $\varphi$-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp\'{i}nola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic $\varphi$-contractions as a consequence of our main theorems.

The purpose of this paper is to introduce iterative method for solving generalized split inverse problem given as a task of finding a point which belongs to the intersection of finite family of fixed point sets of demimetric mappings such that its image under a finite number of linear transformations belongs to the intersection of another finite family of fixed point sets of demimetric mappings in the image space. The proposed algorithm is formulated in low-cost sequential computing method with step size selection technique. The strong convergence theorem of the proposed algorithm is derived under the appropriate assumptions. The result presented in the paper generalized several results in the literature. Numerical example is given to illustrate the efficiency and performance of the proposed iterative method. [ABSTRACT FROM AUTHOR]

Recently, fixed point results via E -contractions (also called P- contractions in some papers) for self-mappings in metric spaces have been investigated. Some results generalize the well - known Edelstein's theorem. In this paper, we provide some new fixed point theorems for mappings satisfying conditions of Edelstein - Suzuki type involving E -contractions. We also present several illustrative examples to compare our finding with some know results in the literature. [ABSTRACT FROM AUTHOR]

This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets, such as the intersection of many closed convex sets, the set of all minimizers of a nonsmooth convex function, and the intersection of sublevel sets of nonsmooth convex functions. We focus on adaptive learning rate optimization algorithms, which adapt step-sizes (referred to as learning rates in the machine learning field) to find optimal solutions quickly. We then propose a Riemannian stochastic fixed point optimization algorithm, which combines fixed point approximation methods on Riemannian manifolds with the adaptive learning rate optimization algorithms. We also give convergence analyses of the proposed algorithm for nonsmooth convex and smooth nonconvex optimization. The analysis results indicate that, with small constant step-sizes, the proposed algorithm approximates a solution to the problem. Consideration of the case in which step-size sequences are diminishing demonstrates that the proposed algorithm solves the problem with a guaranteed convergence rate. This paper also provides numerical comparisons that demonstrate the effectiveness of the proposed algorithms with formulas based on the adaptive learning rate optimization algorithms, such as Adam and AMSGrad. [ABSTRACT FROM AUTHOR]

Z-soft rough covering models are important generalizations of classical rough set theory to deal with uncertain, inexact and more complex real world problems. So far, the existing study describes various forms of approximation operators and their properties by means of soft neighborhoods. In this paper, we propose the notion of Z-soft rough covering fixed point set 􀀀 briefly, Z-SRCF P-set induced by covering soft set. We study the conditions that the family of Z-SRCF P-sets become lattice structure. For any covering soft set, the Z-SRCF P-set is a complete and distributive lattice, and at the same time, it is also a double p-algebra. Furthermore, when soft neighborhood forms a partition of the universe, then Z-SRCF P-set is both a boolean lattice and a double stone algebra. Some main theoretical results are obtained and investigated with the help of examples. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding the resolvent of the sum of two maximal monotone operators. Such a problem arises frequently in practice, but it seems that computation of the solution of the problem is not necessarily easy. It is assumed that both the resolvents of two maximal monotone operators can be easily computed. This enables us to consider the case in which a solution to the problem cannot be computed easily. This paper introduces a new mapping, which satisfies the nonexpansivity property, from the individual resolvents of two maximal monotone operators and investigates some of its properties. In particular, we show that the mapping has a fixed point if and only if the problem has a solution. Then, using this mapping, we propose a splitting method for solving the problem in a real Hilbert space. In particular, we show that the sequences generated by the method converge strongly to the solution to the problem under certain assumptions. Convergence rate analysis of the methods is also provided to illustrate the method's efficiency. Finally, we apply the results to a class of optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Bipolar R-metric space that in a way enriches the present literature. Here, on associating a binary relation R with bipolar metric space, we obtain a fixed point result which is well supported with an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a new concept of Z-Z-B spaces, which is a generalization of Z-C-X spaces. Meanwhile, the new concept of the superior cone is introduced. Secondly, we study some new problems for semi-closed 1-set-contractive operators in the Z-Z-B space and obtain some new results. These new theorems are proven by combining partial order theory with fixed point index theory. Regarding these theorems, in the latter part of the paper, the proofs are omitted since the methods of proving these theorems are similar. Moreover, two important inequality lemmas are proven. [ABSTRACT FROM AUTHOR]

The physical implementation of the continuous-time memristor makes it widely used in chaotic circuits, whereas the discrete-time memristor has not received much attention. In this paper, the backward-Euler method is used to discretize the T i O 2 memristor model, and the discretized model also meets the three fingerprints characteristics of the generalized memristor. The short period phenomenon and uneven output distribution of one-dimensional chaotic systems affect their applications in some fields, so it is necessary to improve the dynamic characteristics of one-dimensional chaotic systems. In this paper, a two-dimensional discrete-time memristor model is obtained by linear coupling of the proposed T i O 2 memristor model and one-dimensional chaotic systems. Since the two-dimensional model has infinite fixed points, the stability of these fixed points depends on the coupling parameters and the initial state of the discrete T i O 2 memristor model. Furthermore, the dynamic characteristics of one-dimensional chaotic systems can be enhanced by the proposed method. Finally, we apply the generated chaotic sequence to secure communication. [ABSTRACT FROM AUTHOR]

In their recent papers, A.V. Arutyunov and A.V. Greshnov introduced (q1; q2)-quasimetric spaces and studied their properties: investigated covering mappings between (q1; q2)- quasimetric spaces, established sufficient conditions for the existence of a coincidence point for two mappings acting between (q1; q2)-quasimetric spaces such that one is a covering mapping and the other is Lipschitz continuous, proved Banach's fixed point theorem, obtained generalizations for multivalued mappings. The class of (q1; q2)-quasimetric spaces is sufficiently wide; it includes quasimetric spaces, b-metric spaces, Carnot-Caratheodory spaces with Box-quasimetics, Lp-spaces with p 2 (0; 1), etc. The development of the theory of coincidence points of mappings on (q1; q2)- quasimetric spaces initiated interest in the study of more general f-quasimetric spaces and in generalizing Banach's fixed point theorem to such spaces. The present paper is a review of these results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of initial boundary value problems for a class of the Kawahara equation. We prove existence of at least one solution and existence of at least one nonnegative solution. The arguments are based upon of recent theoretical results. [ABSTRACT FROM AUTHOR]