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The objective of this research is to propose some new fixed point theorems for fuzzy-dominated operators that satisfy a nonlinear contraction on a closed ball in a complete b-multiplicative metric space. Our strategy involves the use of a combination of two distinct kinds of mappings: one belongs to a weaker class of strictly increasing mappings, and the other is a class of dominated mappings. In order to demonstrate the validity of our new findings, we provide instances that are both illustrative and substantial. Finally, in order to illustrate the novelty of our findings, we provide applications that allow us to derive the common solution to integral and fractional differential equations. Our findings have a significant impact on the interpretation of a large number of previously published studies, both present and historical. [ABSTRACT FROM AUTHOR]

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.

This article exhibits the thermoelastic interactions because of a consistent heat source in an isotropic, homogeneous, unbounded elastic solid with regards to the modified theory of thermoelasticity without energy dissipation. A novel modification for the three-phase-lag Green–Naghdi (TPL G–N) heat conduction equation is proposed for this purpose. A new potential function is employed to help in solving the present problem together with Laplace and Hankel transforms. After inverting Laplace transforms, the small-time approximated solutions are used to obtain expository expressions for the field variables inside the medium. The trend of variations in all quantities past the elastic wavefront to the heat wavefront is investigated. The quantities suddenly bounce to a high worth just previously the situation of the heat wavefront and from that point hop again to zero qualities. [ABSTRACT FROM AUTHOR]

This article has been devoted to investigating the thermoelastic diffusion problem of an infinite medium. The simple and refined single/dual-phase-lag Green–Naghdi models with and without energy dissipation are proposed. The exact solution of thermodiffusion coupling equations has been obtained considering the regularity conditions. The distributions of the non-dimensional temperature, dilatation, displacement, stresses, concentration and chemical potential are obtained and illustrated graphically. The validity of results is acceptable by comparing all outcomes. Benchmark results are reported to help other investigators in their future comparisons. [ABSTRACT FROM AUTHOR]

Fuzzy set is a modern tool for depicting uncertainty. This paper introduces the concept of fuzzy sub e-group as an extension of fuzzy subgroup. The concepts of identity and inverse are generalized in fuzzy sub e-groups. Every fuzzy subgroup is proven to be a fuzzy sub e-group, but the converse is not true. Various properties of fuzzy sub e-groups are established. Moreover, the concepts of proper fuzzy sub e-group and super fuzzy sub e-group are discussed. Further, the concepts of fuzzy e-coset and normal fuzzy sub e-group are presented. Finally, we describe the effect of e-group homomorphism on normal fuzzy sub e-groups. [ABSTRACT FROM AUTHOR]

In this article, we familiarize a subclass of Kamali-type starlike functions connected with limacon domain of bean shape. We examine certain initial coefficient bounds and Fekete-Szegö inequalities for the functions in this class. Analogous results have been acquired for the functions f − 1 and ξ / f ξ and also found the upper bound for the second Hankel determinant a 2 a 4 − a 3 2 . [ABSTRACT FROM AUTHOR]

The MnO2-based heterogeneous catalyst has been considered as one of the most efficient catalysts for enzyme-like catalysis, however, it usually suffers from low stability and difficulty in recycling and reuse. Herein, MnO2 nanosheets supported on nickel foam (NF@MnO2) have been fabricated, via a facile one-step hydrothermal process, as an artificial oxidase for the detection and quantification of ascorbic acid (AA). NF, as a magnetic support, possesses a three-dimensional (3D) skeleton and excellent conductivity, which greatly facilitate the utilization of active sites, electron transfer, as well as separation from the solution with an external magnet. Owing to this unique architecture and the synergistic effect between NF and MnO2, the designed NF@MnO2 composites show enhanced enzyme-like activity toward the oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) as compared to NF or MnO2 alone. By virtue of the reducing ability of ascorbic acid (AA), the AA selectively inhibited this reaction with a detection limit of 0.1 μM. More importantly, this kind of NF-based design can be easily extended to the synthesis of other functional materials for enzyme-like catalytic applications. [ABSTRACT FROM AUTHOR]

Supported nonprecious metal nanoparticles (NPs) have attracted considerable interest for their low cost and excellent properties. However, immobilizing them with good dispersion on supports is still a great challenge. Herein, we report a one-pot Stöber method to prepare a high coverage of nickel (Ni) NPs anchored to a resorcinol–formaldehyde (RF)-derived graphic carbon layer on silica. By simple removal of the Ni NPs and silica cores, highly desired hollow graphitic carbon spheres with distinctive properties can be fabricated. Notably, nickel ions not only boost the polymerization of RF-Ni2+ but also control nickel-induced carbon graphitization when Ni NPs are generated from the nickel ions. Meanwhile, the RF-Ni2+ polymer can be finely covered on various supports, including MnO2 nanowires, graphene oxide, and carbon nanofibers, and can easily result in well-dispersed Ni NPs on these supports. Moreover, resorcinol can be replaced by similar chemicals like 3-aminophenol, melamine, and 2,4-dihydroxybenzoic acid to synthesize various polymers, greatly expanding the versatility of this method. Additionally, by a change of the molar ratio of resorcinol to nickel ion or control of the annealing temperature, the coverage and size of Ni NPs could be finely adjusted. Because of the high coverage of Ni NPs with good dispersion, the resultant SiO2@C-Ni hybrids display excellent performance in both the reduction of 4-nitrophenol and adsorption on histidine-rich proteins. [ABSTRACT FROM AUTHOR]

Conversion‐type transition metal oxide MoO3 has attracted considerable interest as a promising anode material for lithium ion batteries (LIBs), but it suffers from the low electronic conductivity and the large volume changes upon lithiation/delithiation. To overcome these drawbacks, we herein report the full encapsulation of core‐shelled MoO3‐TiO2 into the carbon nanofibers (CNFs) via a facile coaxial electrospinning followed by a two‐step annealing process. TiO2 shells and MoO3 cores were coaxially integrated into the porous CNFs (denote the composite as TiO2/MoO3@CNFs). The two‐step annealing strategy (carbonization in Ar and then oxidization in air) allows the readily encapsulation of MoO3 into CNFs. When applied as anode materials for LIBs, the coaxial TiO2/MoO3@CNFs demonstrate superior lithium storage performance, delivering a high reversible capacity of 561 mAh/g after 300 cycles at 1000 mA/g with a much higher capacity retention of 70.8% than that of the MoO3@CNFs without TiO2 layers (only 42.3%). The results clearly demonstrate that the CNFs matrices and the TiO2 shells together efficiently enhance the electrode conductivity and buffer the volume changes of MoO3 upon cycling. [ABSTRACT FROM AUTHOR]

The encapsulation of small non-noble metal nanoparticles (NPs) within an inorganic layer has received considerable attention owing to their enhanced stability and high catalytic activity. Using a combination of emulsion-free polymerization, inner RF-Ni2+ and outer SiO2 coating, and subsequent carbonization treatment, herein, we have fabricated worm-like structured Ni-based composites in which a high density of nickel NPs are embedded in a carbon layer and also entrapped by SiO2 nanocages. We find that the carbonization temperature plays a vital role in adjusting the size of the Ni NPs. A detailed examination of the encapsulated nickel particles synthesized at 700 °C exhibited the best performance on the catalysis of the reduction of 4-NPs. Moreover, owing to the good alloying ability of the Ni NPs with noble metal NPs, the Ni–Pd alloy NPs are also entrapped in the SiO2 nanocages, which exhibit better performance on the catalysis than the Ni-based composites. The encapsulation of Ni–Pd alloys within SiO2 nanocages also improves stability against agglomeration and metal separation during catalytic operation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce spherical fuzzy sets (SFSs) which is an advanced tool of the fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets. We investigate the basic properties of SFSs and compare the idea SFSs with picture fuzzy sets. The spaces of spherical membership grades and picture membership grades are examined by graphically. Some useful operation such as spherical fuzzy t'-norms and spherical fuzzy t'-conorms are introduced. Also introduced spherical fuzzy negator and some classifications of spherical fuzzy t'-norms and spherical fuzzy t′-conorms which are useful for development the aggregation operator to aggregate the spherical fuzzy information. Finally, a food circulation center evaluation problem is given as a practical application to demonstrate the usage and applicability of the proposed ranking approach. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce α-generalized multi-valued contractions in cone metric spaces over Banach Algebras with solid cones and show the existence of fixed points of these contractions in this context. Our results generalize and extend several known results in metric and cone metric spaces given by some authors. Also, we give one example to illustrate significance of the main result in this paper. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the cone b-metric spaces over Banach Algebra with solid cones and establish some fixed points of multivalued mappings in this setting. Our results generalize and extend several known results of metric, cone metric and cone b-metric spaces. An example and certain consequences are presented to illustrate significance of established results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to generalize common fixed point theorems under contractive condition involving rational expressions on a complete complex-valued metric space. Obtained results in this article extend, generalize, and improve wellknown comparable results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results for generalized contractive multimaps with respect to generalized distance. Consequently, several known fixed point results either generalized or improved including the corresponding recent fixed point results of Ciric, BinDehaish-Latif, Latif-Albar, Klim-Wardowski, Feng-Liu. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some new fixed point results for Ćirić type α-η-GF-contraction in a complete metric space. We extend the con-cept of F-contraction and introduce the notion Ćirić type α-η-GF-contraction. An example is given to demonstrate the novelty of our work. [ABSTRACT FROM AUTHOR]

Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi G-contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in ε-chainable metric space are also discussed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some new fixed point results for Ćirić type α-η-GF-contraction in a complete metric space. We extend the concept of F-contraction and introduce the notion Ćirić type α-η-GF-contraction. An example is given to demonstrate the novelty of our work. [ABSTRACT FROM AUTHOR]

Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the Pecaric work on Montgomery's identity via an arbitrary weight function, which no longer needs to be a probability density function, and apply it to derive some generalized Chebyshev type inequalities for any absolutely continuous function. [ABSTRACT FROM AUTHOR]

We first introduce a new class of contractivemappings in the setting of metric spaces and then we present certain Greguš type fixed point theorems for such mappings. As an application, we derive certain Greguš type common fixed theorems. Our results extend Greguš fixed point theoreminmetric spaces and generalize and unify some related results in the literature. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]

Let (X, d) be a complex valued metric space and let S, T bemappings from X to a set of all fuzzy subsets of X .We present sufficient conditions for the existence of a common α-fuzzy fixed point of S and T. Our results improve and extend certain recent results in literature. Moreover, we discuss an illustrative example to highlight the realized improvements. [ABSTRACT FROM AUTHOR]