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In the paper, we introduce a new class of noncyclic φ-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp'ınola, 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 φ-contractions as a consequence of our main theorems. [ABSTRACT FROM AUTHOR]

This paper reports a modified F-iterative process for finding the fixed points of three generalized ff-nonexpansive mappings. We assume certain assumptions to establish the weak and strong convergence of the scheme in the context of a Banach space. We suggest a numerical example of generalized ff-nonexpansive mappings which exceeds, properly, the category of functions furnished with a condition (C). After that, we show that our modified F-iterative scheme of this example converges to a common fixed point of three generalized ff-nonexpansive mappings. As an application of our main findings, we suggest a new projection-type iterative scheme to solve variational inequality problems in the setting of generalized ff-nonexpansive mappings. The main finding of the paper is new and extends many known results of the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also prove some weak and strong theorems for Suzuki nonexpansive type mappings. Numerical example is given to show the efficiency of new iteration process. The results obtained in this paper improve the recent ones announced by Thakur et al. [17], Ullah and Arschad. [ABSTRACT FROM AUTHOR]

This paper proposes a modified D-iteration to approximate the solutions of three quasinonexpansive multivalued mappings in a real Hilbert space. Due to the incorporation of an inertial step in the iteration, the sequence generated by the modified method converges faster to the common fixed point of the mappings. Furthermore, the generated sequence strongly converges to the required solution using a shrinking technique. Numerical results obtained indicate that the proposed iteration is computationally effcient and outperforms the standard forward-backward with inertial step. [ABSTRACT FROM AUTHOR]

In this paper, we take advantage of implicit relationships to come up with a new concept called "Aϑ-α-contraction mapping". We utilized our new notion to formulate and prove some common fixed point theorems for two and four self-mappings over complete extended quasi b-metric spaces under a set of conditions. Our main results widen and improve many existing results in the literature. To support our research, we present some examples as applications to our main findings. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with n vertices, m edges and having diameter d. The distance Laplacian matrix DL is defined as DL = Diag(T r) − D, where Diag(T r) is the diagonal matrix of vertex transmissions and D is the distance matrix of G. The distance Laplacian eigenvalues of G are the eigenvalues of DL and are denoted by δ1, δ1, . . ., δn. In this paper, we obtain (a) the upper bounds for the sum of k largest and (b) the lower bounds for the sum of k smallest non-zero, distance Laplacian eigenvalues of G in terms of order n, diameter d and Wiener index W of G. We characterize the extremal cases of these bounds. Also, we obtain the bounds for the sum of the powers of the distance Laplacian eigenvalues of G. Finally, we obtain a sharp lower bound for the sum of the βth powers of the distance Laplacian eigenvalues, where β ̸= 0, 1. [ABSTRACT FROM AUTHOR]

This paper studies the drive-response synchronization for quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with mixed delays. First, QVSICNN is decomposed into an equivalent real-valued system in order to avoid the non-commutativity of the multiplicity. Then, the existence of almost periodic solutions is obtained based on the Banach fixed point theorem. An novel state-feedback controller is designed to ensure the global exponential almost periodic synchronization. At the end of the paper, an example is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we have generalized F-contraction to MF-contraction, a new of notation in metric space and we have proved some results with examples and corollaries. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the following boundary value problems of fractional discontinuous differential equations with impulses:... ...By using Krasnosel skii's fixed point theorem for discontinuous operators on cones, some sufficient conditions for the existence of single or multiple positive solutions for the above discontinuous differential system are established. An example is given to confirm the main results in the end. [ABSTRACT FROM AUTHOR]

By processing the problem through fixed point theory and propagator theory, we investigate the periodicity of solutions to a class of impulsive evolution equations in Hilbert spaces and establish some existence theorems for periodic solutions. Moreover, the asymptotic stability of periodic solutions is obtained under suitable conditions. As one will see, the concept of an impulsive propagator is introduced for the first time in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51–60] and Benavides et al. [Math. Nachr. 248(2003), 62–71]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of a positive solution to the singular third-order boundary value problem {-u"' (t) + k²u'(t) = f(t; u(t); u'(t)); a.e. t > 0 u(0) = u'(0) = u'(+∞) = 0; where k is a positive constant and the function f : (0,+ ∞)³ ! ℝ is continuous and may be singular at t = 0; u = 0 and at u' = 0: The main existence result is proved by means of Guo-Krasnoselskii's version of expansion and compression of a cone principal in a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the additive (α, β)-functional equation ... for all complex numbers α with [α] D 1 and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α, β)-functional equation (0.1) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

Let (X, d) be a complete metric space and T: X→X a mapping of X. In 1975 Dass and Gupta introduced the following rational type contractive condition to prove a generalization of Banach's Fixed Point Theorem: For α, β∈ [0, 1), such that α + β < 1, we have ∀x, y ∈ X, d(Tx, Ty) ≤ α d(y, Ty)(1 +d(x, Tx)) / 1 + d(x, y) + βd(x, y), where T is continuous. There are several generalization and extension of Dass and Gupta’s result under the hypothesis that T is continuous and α + β < 1. In this paper, we prove some fixed point theorems in a complete metric space setting by employing more general rational type contractive conditions than the above one. We show in our results that the continuity of the above operator T is unnecessary and the restrictive condition that α + β < 1 is also removed. Our results generalize and extend those of Das and Gupta and several known results in the literature. [ABSTRACT FROM AUTHOR]

This article is devoted to the multiplicative perturbation analysis of the generalized Cholesky block downdating problem. The strong rigorous multiplicative perturbation bounds are first presented by bringing together the modified matrix-vector equation approach with the technique of Lyapunov majorant function and the Banach fixed point theorem. Then, the weak rigorous multiplicative bounds are developed by using the matrix-equation approach. Numerical results demonstrate that these bounds are constantly tighter than the additive perturbation bounds. [ABSTRACT FROM AUTHOR]

The subject of this work is the existence and Mittag-Leffler-Ulam (MLU) stability of solutions for fractional pantograph equations with three sequential fractional derivatives. Suffcient conditions for the existence and uniqueness of solutions are constructed by utilizing well-known classical fixed point theorems such as the Banach contraction principle, and Leray-Schauder nonlinear alternative. The generalized singular Gronwall's inequality is used to show the MLU stability results. An illustrated example is provided to support the main findings. [ABSTRACT FROM AUTHOR]

We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle, Ćirić's fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodríguez-López. This new concept of generalized metric spaces recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces. [ABSTRACT FROM AUTHOR]