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There has been a long-lasting impact of the lockdown imposed due to COVID-19 on several fronts. One such front is climate which has seen several implications. The consequences of climate change owing to this lockdown need to be explored taking into consideration various climatic indicators. Further impact on a local and global level would help the policymakers in drafting effective rules for handling challenges of climate change. For in-depth understanding, a temporal study is being conducted in a phased manner in the New Delhi region taking NO2 concentration and utilizing statistical methods to elaborate the quality of air during the lockdown and compared with a pre-lockdown period. In situ mean values of the NO2 concentration were taken for four different dates, viz. 4th February, 4th March, 4th April, and 25th April 2020. These concentrations were then compared with the Sentinel (5p) data across 36 locations in New Delhi which are found to be promising. The results indicated that the air quality has been improved maximum in Eastern Delhi and the NO2 concentrations were reduced by one-fourth than the pre-lockdown period, and thus, reduced activities due to lockdown have had a significant impact. The result also indicates the preciseness of Sentinel (5p) for NO2 concentrations. [ABSTRACT FROM AUTHOR]

In this study, we examine the plant–herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the extended weak-predator response to Holling type-II response. We explore the dynamical and qualitative analysis of this model and investigate the conditions for stability and bifurcation. Our study demonstrates the presence of the Neimark–Sacker bifurcation at the interior equilibrium and the transcritical bifurcation at the trivial equilibrium, both of which have biological feasibility. To avoid unpredictable outcomes due to bifurcation, we employ chaos control methods. Furthermore, to support our theoretical and mathematical findings, we develop numerical simulation techniques with examples. In summary, our research enhances the comprehension of the dynamics pertaining to interactions between plants and herbivores in the context of discrete-time population models. [ABSTRACT FROM AUTHOR]

In this manuscript, a novel general class of contractions, called Jaggi–Suzuki-type hybrid (G-α-ϕ)-contraction, is introduced and some fixed point theorems that cannot be deduced from their akin in metric spaces are proved. The dominance of this family of contractions is that its contractive inequality can be specialized in various manners, depending on multiple parameters. Nontrivial comparative examples are constructed to validate the assumptions of our obtained theorems. Consequently, a number of corollaries that reduce our result to some prominent results in the literature are highlighted and analyzed. Additionally, we examine Ulam-type stability and well-posedness for the new contraction proposed herein. Finally, one of our obtained corollaries is applied to set up unprecedented existence conditions for solution to a class of integral equations. For future aspects of our results, an open problem is noted concerning the discretized population balance model, whose solution may be analyzed using the techniques established herein. [ABSTRACT FROM AUTHOR]

In theoretical ecology, recent field experiments on terrestrial vertebrates observe that the predator–prey interaction can not only be curtailed by direct consumption but also governed by some indirect effects such as the fear of predator which may reduce the reproduction rate of prey individuals. Based on this fact, we have developed and explored the predator–prey interaction with the influence of both cost and benefit of fear effect (felt by prey). A Holling type III functional response with the effect of habitat complexity has been taken to consume the prey biomass. Positivity and boundedness of the studied system prove that the model is well-behaved. The uniform persistence of the studied system is derived analytically under some parametric restrictions. The feasibility conditions and stability criteria of each equilibrium points have been discussed. Next, we have exhibited the existence of Hopf-bifurcation around the interior equilibrium point. Our mathematical analyses show that habitat complexity and fear effect both have a great impact on the persistence of the predator biomass. Furthermore, we have investigated the effect of breeding delay parameter such that the system loses its stability behaviour and enters into a limit cycle oscillations through Hopf-bifurcation. Numerical simulations are illustrated to verify our analytical outcomes. Numerically, we have perturbed the death rates of prey and predator species with Gaussian white noise terms due to the effects of environmental fluctuations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some new fixed point results for a pair of multivalued dominated locally contractive mappings in b-multiplicative metric space. Further, fixed point theorems for multigraph-dominated mappings are also established. Some new fixed point results on a closed ball are obtained for a pair of multigraph-dominated mappings endowed with graphic structure in b-multiplicative metric space. An illustrative example is given to show the validity of the hypothesis of our obtained result. Moreover, applications for a coupled system of nonlinear Volterra-type integral equations and functional equations in dynamic programming are presented to show the novelty of our results. [ABSTRACT FROM AUTHOR]

The performance and thermal properties of convective–radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by 30 % approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation. [ABSTRACT FROM AUTHOR]

The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton–zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark–Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark–Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper. [ABSTRACT FROM AUTHOR]

We propose a new class of implicit relations and an implicit type contractive condition based on it in the relational metric spaces under w-distance functional. Further we derive fixed points results based on them. Useful examples illustrate the applicability and effectiveness of the presented results. We apply these results to discuss sufficient conditions ensuring the existence of a unique positive definite solution of the nonlinear matrix equation (NME) of the form U = Q + ∑ i = 1 k A i ∗ G (U) A i , where Q is an n × n Hermitian positive definite matrix, A 1 , A 2 , ..., A m are n × n matrices and G is a nonlinear self-mapping of the set of all Hermitian matrices which are continuous in the trace norm. In order to demonstrate the obtained conditions, we consider an example together with convergence and error analysis and visualisation of solutions in a surface plot. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to present some fixed-point results for a pair of fuzzy dominated mappings which are generalized V-contractions in modular-like metric spaces. Some theorems using a partial order are discussed and also some useful results to graphic contractions for fuzzy-graph dominated mappings are developed. To explain the validity of our results, 2D and 3D graphs have been constructed. Also, applications are provided to show the novelty of our obtained results and their usage in engineering and computer science. [ABSTRACT FROM AUTHOR]

In this work, we solve the system of integro-differential equations (in terms of Caputo–Fabrizio calculus) using the concepts of the best proximity pair (point) and measure of noncompactness. We first introduce the concept of cyclic (noncyclic) Θ-condensing operator for a pair of sets using the measure of noncompactness and then establish results on the best proximity pair (point) on Banach spaces and strictly Banach spaces. In addition, we have illustrated the considered system of integro-differential equations by three examples and discussed the stability, efficiency, and accuracy of solutions. [ABSTRACT FROM AUTHOR]

In this paper, we study the behavior of L (ω , C) -contraction mappings and establish some results on common fixed circles and discs. We explain the significance of our main theorems through examples and applications. [ABSTRACT FROM AUTHOR]

This research aims to investigate a novel coincidence point (cp) of generalized multivalued contraction (gmc) mapping involved a directed graph in b-metric spaces (b-ms). An example and some corollaries are derived to strengthen our main theoretical results. We end the manuscript with two important applications, one of them is interested in finding a solution to the system of nonlinear integral equations (nie) and the other one relies on the existence of a solution to fractional integral equations (fie). [ABSTRACT FROM AUTHOR]

In this manuscript, the existence theorem for a unique solution to a coupled system of impulsive fractional differential equations in complex-valued fuzzy metric spaces is studied and the fuzzy version of some fixed point results by using the definition and properties of a complex-valued fuzzy metric space is presented. Ultimately, some appropriate examples are constructed to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The new COVID-19 coronavirus disease has emerged as a global threat and not just to human health but also the global economy. Due to the pandemic, most countries affected have therefore imposed periods of full or partial lockdowns to restrict community transmission. This has had the welcome but unexpected side effect that existing levels of atmospheric pollutants, particularly in cities, have temporarily declined. As found by several authors, air quality can inherently exacerbate the risks linked to respiratory diseases, including COVID-19. In this study, we explore patterns of air pollution for ten of the most affected countries in the world, in the context of the 2020 development of the COVID-19 pandemic. We find that the concentrations of some of the principal atmospheric pollutants were temporarily reduced during the extensive lockdowns in the spring. Secondly, we show that the seasonality of the atmospheric pollutants is not significantly affected by these temporary changes, indicating that observed variations in COVID-19 conditions are likely to be linked to air quality. On this background, we confirm that air pollution may be a good predictor for the local and national severity of COVID-19 infections. [ABSTRACT FROM AUTHOR]

Chua's circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua's circuit is obtained by transforming the classical model of Chua's circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua's circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operators. [ABSTRACT FROM AUTHOR]

Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo inequality. As an application, we study the existence of solutions for a system of functional integral equations in C [ 0 , T ] . Finally, we expose a genuine example to support the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of α L ψ -rational contractive and cyclic α L ψ - rational contractive mappings and establish the existence and uniqueness of fixed points for such mappings in complete metric-like spaces (dislocated metric spaces). The results presented here substantially generalize and extend several comparable results in the existing literature. As an application, we prove new fixed point results for ψ L -graphic and cyclic ψ L -graphic rational contractive mappings. Moreover, some examples and an application to integral equation are presented here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

For the classical Jensen inequality of convex functions, i.e., an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given. [ABSTRACT FROM AUTHOR]

In the present study, we work on the problem of the existence of positive solutions of fractional integral equations by means of measures of noncompactness in association with Darbo's fixed point theorem. To achieve the goal, we first establish new fixed point theorems using a new contractive condition of the measure of noncompactness in Banach spaces. By doing this we generalize Darbo's fixed point theorem along with some recent results of (Aghajani et al. (J. Comput. Appl. Math. 260:67-77, 2014)), (Aghajani et al. (Bull. Belg. Math. Soc. Simon Stevin 20(2):345-358, 2013)), (Arab (Mediterr. J. Math. 13(2):759-773, 2016)), (Banaś et al. (Dyn. Syst. Appl. 18:251-264, 2009)), and (Samadi et al. (Abstr. Appl. Anal. 2014:852324, 2014)). We also derive corresponding coupled fixed point results. Finally, we give an illustrative example to verify the effectiveness and applicability of our results. [ABSTRACT FROM AUTHOR]

We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order ⪯. This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann iteration. Some useful examples are presented to illustrate the facts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce best proximal contractions in complete ordered non-Archimedean fuzzy metric space and obtain some proximal results. The obtained results unify, extend, and generalize some comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this manuscript we extend very recent fixed point theorems in the setting of Menger spaces in three senses: on the one hand, we introduce the notion of Menger probabilistic metric-like space by avoiding a non-necessary constraint (at least, for our purposes) in the properties that define a Menger space; on the other hand, we consider a more general class of auxiliary functions in the contractivity condition; finally, we show that the function $t\rightarrow1/t-1$ (which appears in many fixed point theorems in the fuzzy context) can be replaced by more appropriate and general functions. We illustrate our main statements with an example in which previous results cannot be applied. [ABSTRACT FROM AUTHOR]

This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given. [ABSTRACT FROM AUTHOR]

This paper investigates the existence and potential uniqueness of equilibrium points and some stability, instability and oscillatory properties of a discrete nonlinear epidemic model, which generalises previous Stevic’s model, whose solutions possess memory from a finite chain of preceding samples. An application example is provided where the proposed model is ‘ad hoc’ adapted to a class of SIS models widely used in epidemiology. [ABSTRACT FROM AUTHOR]

The correct affiliations of the author Hassen Aydi are as follows: 2Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, 4000, H. Sousse, Tunisia. References 1 Khan M.S. Qualitative analysis of a discrete-time phytoplankton-zooplankton model with Holling type-II response and toxicity. The original article can be found online at https://doi.org/10.1186/s13662-021-03599-z Correction Following publication of the original article [[1]], two affiliations were missed for the author Hassen Aydi. [Extracted from the article]

Using the fixed point method, we prove the Hyers–Ulam stability of a cubic and quartic functional equation and of an additive and quartic functional equation in matrix Banach algebras. [ABSTRACT FROM AUTHOR]

We prove the existence of tripled fixed points (TFPs) of a new generalized nonlinear contraction mapping in complete cone b-metric spaces (CCbMSs). Also, we present some exciting consequences as corollaries and three nontrivial examples. Finally, we find a solution for a tripled-system of integral equations (TSIE) and discussed a unique stationary distribution for the Markov process (SDMP). [ABSTRACT FROM AUTHOR]

In this paper, we present a new notion of metric called dislocated Hausdorff A-quasi-metric spaces. We highlight some of its properties, and establish the existence of fixed point of multivalued mappings in the setting of several comparable existing generalized metric spaces. These results unify, improve and generalize various recent related results in the existing literature. [ABSTRACT FROM AUTHOR]