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In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x)−f(y))=f(x+y)+f(x−y)−f(x)−f(y),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y), where ff maps from a (β,p)\left(\beta ,p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite ss-functional inequality is discussed via our results.

In this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x−3y)+f(x+2y)+f(x−2y)+22f(x)+24f(y)=13[f(x+y)+f(x−y)]+12f(2y),f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

The aim of this work is to introduce the notion of weak altering distance functions and prove new fixed point theorems in metric spaces endowed with a transitive binary relation by using weak altering distance functions. We give some examples which support our main results where previous results in literature are not applicable. Then the main results of the paper are applied to the multidimensional fixed point results. As an application, we apply our main results to study a nonlinear matrix equation. Finally, as numerical experiments, we approximate the definite solution of a nonlinear matrix equation using MATLAB.

The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.

In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations: x (t) = ∫abK1 (t,r,x(r)) dr,x (t) = ∫abK2 (t,r,x(r)) dr, $$\matrix {x (t) = \int \limits_a^b {{K_1}} (t, r, x(r))dr, & & x(t) = \int \limits_a^b {{K_2}}(t, r, x(r))dr,} $$

In 2014, Asadi et al. introduced the concept of an M -metric space which is a generalization of a partial metric space and established Banach and Kannan fixed point theorems on M -metric spaces. In this work, we prove two fixed point theorems for Chatterjea contraction mappings in the framework of M -metric spaces. These provide partial answers to a question posed by Asadi et al. concerning a fixed point for Chatterjea contraction mappings. We also give some examples and numerical results which can be obtained from our results. [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]

Let $X$ and $Y$ be two normed spaces over fields $\mathbb{F}$ and $\mathbb{K}$, respectively. We prove new generalised hyperstability results for the general linear equation of the form $g(ax+by)=Ag(x)+Bg(y)$, where $g:X\rightarrow Y$ is a mapping and $a,b\in \mathbb{F}$, $A,B\in \mathbb{K}\backslash \{0\}$, using a modification of the method of Brzdęk [‘Stability of additivity and fixed point methods’, Fixed Point Theory Appl.2013 (2013), Art. ID 285, 9 pages]. The hyperstability results of Piszczek [‘Hyperstability of the general linear functional equation’, Bull. Korean Math. Soc.52 (2015), 1827–1838] can be derived from our main result. [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]

Let $X$ be a nonempty subset of a normed space such that $0\notin X$ and $X$ is symmetric with respect to $0$ and let $Y$ be a Banach space. We study the generalised hyperstability of the Drygas functional equation $$\begin{eqnarray}f(x+y)+f(x-y)=2f(x)+f(y)+f(-y),\end{eqnarray}$$ where $f$ maps $X$ into $Y$ and $x,y\in X$ with $x+y,x-y\in X$. Our first main result improves the results of Piszczek and Szczawińska [‘Hyperstability of the Drygas functional equation’, J. Funct. Space Appl.2013 (2013), Article ID 912718, 4 pages]. Hyperstability results for the inhomogeneous Drygas functional equation can be derived from our results. [ABSTRACT FROM PUBLISHER]

In this work, we introduce the new concept of a generalization of ( F , φ ) -contraction mapping and establish some existence results of φ -fixed point for such mappings. We also state some illustrative examples to support our results and give numerical experiment for approximating the φ -fixed point in this example. As an application, the obtained results are used to deduce some fixed point theorems in partial metric spaces and the application to nonlinear integral equations is given in order to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $$\alpha $$ -integral type G-contraction mappings to generalize the notions of Banach G-contraction and integral G-contraction mappings. We also prove some fixed point theorems for $$\alpha $$ -integral type G-contraction mappings. By providing some example, we show that our results are real generalization of several results in literature. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce some new notions of generalized convex contraction mappings and establish some approximate fixed point theorems for such mappings in the setting of complete metric spaces. Examples and application to approximate fixed point results for cyclic mappings are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $(\alpha,\theta,k)$-contraction multi-valued mappings and establish some fixed point results for such mappings by using some control functions due to Jleli et al. (J. Inequal. Appl. 2014:439, 2014) in metric spaces and furnish some interesting examples to illustrate our main results. Also, we give some fixed point results in metric spaces endowed with a graph. Our results generalize and extend recent results given by some authors. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish a new fixed point theorem for generalized contraction mappings with respect to w-distances in complete metric spaces. An illustrative example is provided to advocate the usability of our results. Also, we give 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 integral equations and nonlinear fractional differential equations of Caputo type. [ABSTRACT FROM AUTHOR]