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The aim of this work is to introduce the concept of an (F , γ) R -contraction which is a weak idea of an F-contraction in metric spaces endowed with a binary relation. Fixed point results for such new contractions are investigated, and its benefit is showing from an example. As applications, we apply theoretical results together with the Thompson metric for solving nonlinear matrix equations. Finally, we give a numerical example showing the usage of the proposed algorithm to solve nonlinear matrix equations. [ABSTRACT FROM AUTHOR]

Nowadays, the usage of the existence and convergence results of a common fixed point for nonlinear semigroups of various kinds of self-mappings is applied to several problems in mathematics and another branches. Surprisingly, nobody considered the study on the nonlinear semigroups of weak contraction self-mappings in the sense of Berinde. The purpose of this paper is to attempt to complete this direction and so we investigate the existence of the common fixed point for nonlinear semigroups of weak contraction self-mappings in the sense of Berinde on a bounded closed convex subset of a real Banach space with uniformly normal structure. More precisely, we prove the convergence theorem for the common fixed point of a weak contraction semigroups. An illustrative example is presented. [ABSTRACT FROM AUTHOR]

In this paper, we are dealing with a particular type of predator–prey model in which a predator has two choices of preys with probabilities x and 1 - x , respectively. Our aims are to analyze the behavior of predator animals in such situation and to construct a general functional equation for it, which covers all the aspects of such type of relationship. The Banach fixed point theorem is being used to investigate the existence and uniqueness results of the proposed predator–prey model; Hyers–Ulam and Hyers–Ulam–Rassias type stability of the functional equation has also been discussed in it. [ABSTRACT FROM AUTHOR]

This paper deals with a specific type of traumatic avoidance for the learning process of normal dogs enclosed into a small compartment with a steel grid floor. Our aim is to analyze the behavior of the dogs in such situations and to construct a suitable mathematical model for it. The existence and uniqueness results of the proposed traumatic avoidance learning model are being investigated by the use of the Banach fixed point theorem. [ABSTRACT FROM AUTHOR]

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". [ABSTRACT FROM AUTHOR]

In this work, we introduce the concept of an s-simulation function, where s is a given real number with $$s \ge 1$$ , and use this concept for proving many results in b-metric spaces. One of these results is the existence and uniqueness of a fixed point for nonlinear mappings involving s-simulation functions. Also, we give some examples to illustrate the main results with some numerical results. Our results generalize and improve many results in b-metric spaces and also in metric spaces. [ABSTRACT FROM AUTHOR]

In (Fixed Point Theory Appl 94:6, 2012), the author introduced a new kind of contractions, called F- contractions, that extended the Banach contractions in a newfangled way. In this work, we introduce the notion of $$F_\mathfrak {R}$$ - contraction where $$\mathfrak {R}$$ is a binary relation on its domain that has not to be neither transitive nor a partial order. Consequently, we establish some fixed point results for such contractions in complete metric spaces that improve the Wardowski's original idea and we also give illustrative examples. Furthermore, we show some results to guarantee existence and uniqueness of fixed point of N-order. As an application, we apply our main result to study a class of nonlinear matrix equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of generalized cyclic contraction pairs in b-metric spaces. We establish some fixed point results on b-metric spaces and also give some examples to illustrate the main results. As applications, we show the existence of a common solution for the following system of integral equations: where $$a, b \in \mathbb {R}$$ with $$a

In this paper, the notion of α-ψ-contractive mappings in the setting of w-distance is introduced and some new fixed point theorems for such mappings are established. Presented fixed point theorems generalize recent results of Samet et al. [Nonlinear Anal. 75 (2012), 2154-2165] and others. Moreover, some examples and an application to nonlinear fractional differential equations are given to illustrate the usability of the new theory. [ABSTRACT FROM AUTHOR]

In this paper, we aim to introduce new types of α-admissibility in the framework of b-metric spaces. Some examples to show the independently of each type of α-admissibility are given. Using these concepts, fixed point theorems satisfying generalized weak contractive condition in the setting of b-metric spaces are established. We furnish an illustrative example to demonstrate the validity of the hypotheses and the degree of utility of our results. As an application, we discuss the existence of a solution for the following nonlinear integral equation: where $${a, b \in {\mathbb{R}}}$$ such that $${a < b, x \in C[a, b]}$$ (the set of all continuous functions from [ a, b] into $${{\mathbb{R}}}$$ ), $${\phi : [a, b] \rightarrow {\mathbb{R}}}$$ and $${K : [a, b] \times [a, b] \times {\mathbb{R}} \rightarrow {\mathbb{R}}}$$ are given mappings. [ABSTRACT FROM AUTHOR]

In this work we present a new type of stability results for generalized Cauchy functional equation of the form where $${a, b \in \mathbb{N}}$$ and $${f}$$ is a mapping from a commutative semigroup ( $${G_1, \ast}$$ ) to a commutative group ( $${G_2, \diamond}$$ ). Using this form we generalize, extend and complement some earlier classical results concerning the stability of additive Cauchy functional equations. Our results are improvement and generalization of main results of Brzdȩk [Fixed Point Theory Appl. 2013 (), doi::285] and many results in literature. Some of the stability results for many types of functional equations are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this work, we improve the concept of the Banach contractive condition in the setting of D -generalized metric spaces and obtain φ -fixed point results in such spaces. Our φ -fixed point results improve and extend some recently obtained results in several abstract metric spaces. Moreover, some example and numerical results are also presented. [ABSTRACT FROM AUTHOR]

The choice behavior model is the model which describes the spiritual process of thinking which is concerned with the process of judging the merits of the numerous options and making the decision to determine one of them for action. The aim of this paper is to analyze the one specific type of choice behavior model for the learning process of the paradise fish. The existence and uniqueness results of the solution of the proposed choice behavior model are investigated via the fixed point tool. [ABSTRACT FROM AUTHOR]

The purpose of this work is to establish new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces by using the concept of a weak altering distance function. Two illustrative examples are provided to advocate the usability of our results. Also, we present a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear Fredholm integral equations. [ABSTRACT FROM AUTHOR]

In this work, we introduce the notion of a Z R -contraction mapping, where R is an binary relation on its domain, which improves upon the idea of Khojasteh et al. (Filomat 29:1189–1194, 2015). We establish some fixed point results for Z R -contraction mappings in complete metric spaces endowed with a transitive relation and also give two illustrative examples. Moreover, we show that N-th order fixed point theorems are derived from our main results. As an application, we apply our main result to study a class of nonlinear matrix equation. Finally, as numerical experiments, we approximate the definite solution of a nonlinear matrix equation using MATLAB. [ABSTRACT FROM AUTHOR]