Search Results (22)

In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of ($\alpha$-$\psi$)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors. Full article

This article describes a fractal-based MIMO antenna for 5G mm-wave mobile applications with micro-strip feeding. The proposed structure is a fractal-based spherical configuration that incorporates spherical slots of different iterations on the patch, as well as rectangular slots on the ground plane. These additions are meant to reduce patch isolation. The two-element MIMO antenna has closely spaced antenna elements that resonate at multiple frequencies, 9.5 GHz, 11.1 GHz, 13.4 GHz, 15.8 GHz, 21.1 GHz, and 26.6 GHz, in the frequency range of 8 to 28 GHz. The antenna’s broadest operational frequency range spans from 17.7 GHz to 28 GHz, encompassing a bandwidth of 10,300 MHz. Consequently, it is well-suited for utilization within the millimeter wave (mm wave) application, specifically for the 5G new radio frequency band n258, and partially covers some other bands X (8.9–9.9 GHz, 10.4–11.4 GHz), and Ku (13.1–13.7 GHz, 15.4–16.2 GHz). All the resonating bands have isolation levels below the acceptable range of (|S12| > −16 dB). The proposed antenna utilizes a FR4 material with dimension of 28.22 mm $\times$ 44 mm. An investigation is conducted to analyze the effectiveness of parameters of the antenna, including radiation pattern, surface current distributions and S parameters. Furthermore, an examination and assessment are conducted on the efficacy of the diversity system inside the multiple input multiple output (MIMO) framework. This evaluation encompasses the analysis of key performance metrics such as the envelope correlation coefficient (ECC), diversity gain (DG), and mean effective gain (MEG). All antenna characteristics are determined to be within a suitable range for this suggested MIMO arrangement. The antenna design underwent experimental validation and the simulated outcomes were subsequently verified. Full article

We define the class of extended $b_v\left(s\right)$-metric spaces by replacing the real number $s\ge 1$ with a strictly increasing continuous function $\varphi$ in the definition of a $b_v\left(s\right)$-metric space. Also, we presented an example for this newly introduced space and exhibited that in a particular situation, the class of extended $b_v\left(s\right)$-metric spaces reduces to the class of $b_v\left(s\right)$-metric spaces. Afterwards, we establish a fixed point theorem which ensured the existence of a fixed point for the self-map satisfying the Banach contractive condition in the context of this newly defined space. Moreover, we compared the proved result with the existing fixed point theorems in the literature. Full article

In this article, we introduce the concept of a fuzzy triple controlled metric like space in the sense that the self distance may not be equal to one. We have used three functions in our space that generalize fuzzy controlled rectangular, extended fuzzy rectangular, fuzzy $b–$rectangular and fuzzy rectangular metric like spaces. Various examples are given to justify our definitions and results. As for the topological aspect, we prove a fuzzy triple controlled metric like space is not Hausdorff. We also apply our main result to solve the uniqueness of the solution of a fractional differential equation. Full article

This work introduces the concepts of rectangular Menger probabilistic metric ($RMPM$) space and rectangular Menger probabilistic b-metric ($RMPbM$) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic b-metric space, respectively. Some nonunique fixed-point and coupled-fixed-point results for contractive mappings are provided. The findings extend and improve outcomes presented in the existing literature. The main results are illustrated with examples, and validated by means of an application to a system of integral equations. The importance of spaces with non-Hausdorff topology is high, as is the case of computer science, with the Tarskian approach to programming language semantics. Full article

As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using $\alpha -\psi$-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique. Full article

The objective of this paper is to obtain new relation-theoretic coincidence and common fixed point results for some mappings F and g via hybrid contractions and auxiliary functions in extended rectangular b-metric spaces, which improve the existing results and give some relevant results. Finally, some nontrivial examples and applications to justify the main results. Full article

In this article, we present an extension of the controlled rectangular b-metric spaces, so-called controlled rectangular metric-like spaces, where we keep the symmetry condition and we only change the condition $\left[D\right(s,r)=0\iff s=r]\mathrm{to}\left[D\right(s,r)=0\Rightarrow s=r]$, which means we may have a non-zero self distance; also, $D(s,s)$ is not necessarily less than $D(s,r).$ This new type of metric space is a generalization of controlled rectangular b-metric spaces and partial rectangular metric spaces. Full article

In this paper, we first introduce the concept of rectangular $G_b$-metric space which generalizes the notion of rectangular metric space and $G_b$-metric space. Then, some fixed point results connected with certain contractions are obtained in the setting of rectangular $G_b$-metric spaces. Additionally, we also introduce the concept of convex rectangular $G_b$-metric space by means of the convex structure and study the fixed points of enriched type contractions in this space. Full article

In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of $\rho$-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces. Full article

In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides a complete solution to an open problem raised by Zoran D. Mitrović (A note on a Banach’s fixed point theorem in b-rectangular metric space and b-metric space). The result presented in the paper generalizes and unifies some results in fixed point theory. Full article

The focus of this research article is to investigate the notion of fuzzy extended hexagonal b-metric spaces as a technique of broadening the fuzzy rectangular b-metric spaces and extended fuzzy rectangular b-metric spaces as well as to derive the Banach fixed point theorem and several novel fixed point theorems with certain contraction mappings. The analog of hexagonal inequality in fuzzy extended hexagonal b-metric spaces is specified as follows utilizing the function $b(c,d)$: ${\mathfrak{m}}_{\mathsf{h}}\left(c,d,t+s+u+v+w\right)\ge {\mathfrak{m}}_{\mathsf{h}}\left(c,e,\frac{t}{b(c,d)}\right)\ast {\mathfrak{m}}_{\mathsf{h}}\left(e,f,\frac{s}{b(c,d)}\right)\ast {\mathfrak{m}}_{\mathsf{h}}\left(f,g,\frac{u}{b(c,d)}\right)\ast {\mathfrak{m}}_{\mathsf{h}}\left(g,k,\frac{v}{b(c,d)}\right)\ast {\mathfrak{m}}_{\mathsf{h}}\left(k,d,\frac{w}{b(c,d)}\right)$ for all $t,s,u,v,w>0$ and $c\ne e,e\ne f,f\ne g,g\ne k,k\ne d$. Further to that, this research attempts to provide a feasible solution for the Caputo type nonlinear fractional differential equations through effective applications of our results obtained. Full article

In this article, the concept of extended fuzzy rectangular b-metric space (EFR_bMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFR_bMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed. Full article

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result. Full article