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The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work. [ABSTRACT FROM AUTHOR]

In this article, we define a new space named the modular-like space with its related concepts to prove the existence of a fixed point and a point of coincidence for mappings on this space. Also, we defined Ćirić-Reich-Rus type weakly contractive mappings on modular-like spaces and discussed some conditions that guarantee the existence of the fixed points for these kind of mappings. Some examples are also provided to elaborate the usability of our main results. It is worth mentioning that a modular-like space is a generalization of a modular space, thus our theorems are more general and applicable than the fixed point theorems on modular spaces. [ABSTRACT FROM AUTHOR]

In this paper by taking into account three trends, prevalent in metric fixed point theory, namely, use of control functions instead of contraction constants, consideration of relational structure in the metric space and fixed point studies of discontinuous functions, we formulate and solve a new problem in relational metric fixed point theory. Our result extends the well known result of Kannan. The theorems are illustrated with examples. Further the problem is shown to have Hyers-Ulam-Rassias stability property. We make an application of our main result to a problem of a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

A new concept of set-valued Mizoguchi-Takahashi G-contractions is introduced in this paper and some fixed point theorems for such mappings in b-metric spaces endowed with directed graphs are established under some suffcient conditions. Our results improve and extend those of [20] and [24]. We also give some examples supporting our main results. As an applications, we prove the existence of fixed points for multivalued mappings satisfying generalized MT-contractive condition in ϵ-chainable b-metric spaces and the existence of a solution for some integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for three self-mappings satisfying various new contractive conditions in complete G-metric spaces. We also discuss that these mappings are G-continuous on such a common fixed point. And a non-trivial example is provided to support our new result in the framework of nonsymmetric G-metric spaces. At the end of the results, we give an existence theorem for common solution of three integral equations. The results obtained in this paper differ from the recent relative results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of periodic and positive periodic solutions of the nonlinear neutral integro-differential equation x'(t) = - ∫t-τ(t)t a(t,s)x(s)ds + d/dt Q(t,x(t-τ(t))) + G(t,x(t), x(t-τ(t))). We invert this equation to obtain an integral equation. By using Krasnoselski's fixed point Theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness, an example is included to show the feasibility of our results. The positive solutions are studied. [ABSTRACT FROM AUTHOR]

In this paper we use the contraction mapping theorem to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some previous results due to T. A. Burton [6], B. Zhang [20], Y. M. Dib, M. R. Maroun, Y. N. Raffoul [14]. Two examples are also given to illustrate our work. [ABSTRACT FROM AUTHOR]

We study the existence and uniqueness of periodic solutions and the stability of the zero solution of the nonlinear neutral differential equation d/dt x(t) = -a(t)x(t) + d/dt Q(t, x(t - g(t))) + G(t, x(t), x(t - g(t))). In the process we use integrating factors and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution and the asymptotic stability of the zero solution provided that Q(0, 0) = G(t, 0, 0) = 0. [ABSTRACT FROM AUTHOR]

We use Krasnoselskii's fixed point theorem to show that the non-linear neutral differential equation with functional delay x'(t) = -a(t)x(t) + c(t)x'(t - g(t)) + q(t,x(t), x(t - g(t)) has a periodic solution. Also, by transforming the problem to an integral equation we are able, using the contraction mapping principle, to show that the periodic solution is unique. [ABSTRACT FROM AUTHOR]