We present a number of fixed point results for general classes of maps defined on a variety of extension type and admissible type spaces.
{"title":"A note on set valued maps on admissible extension type spaces","authors":"D. O'Regan","doi":"10.22436/jnsa.016.04.04","DOIUrl":"https://doi.org/10.22436/jnsa.016.04.04","url":null,"abstract":"We present a number of fixed point results for general classes of maps defined on a variety of extension type and admissible type spaces.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"36 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135038350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Y. Hamayun, N. Ullah, R. Khan, Kh. Ahmad, M. Gh. Khan, B. Khan
By making use of the concept of basic (or q -) calculus, a subclass of q -starlike functions with reference to symmetric points, which is associated with the q -exponential function, is introduced in the open unit disc. Further, we derived upper bounds for the third-order Hankel determinant for the defined class. For the validity of our results, relevant connections with those in earlier works are also pointed out
{"title":"Third Hankel determinant for q -analogue of symmetric starlike connected to q -exponential function","authors":"Y. Hamayun, N. Ullah, R. Khan, Kh. Ahmad, M. Gh. Khan, B. Khan","doi":"10.22436/jnsa.016.04.01","DOIUrl":"https://doi.org/10.22436/jnsa.016.04.01","url":null,"abstract":"By making use of the concept of basic (or q -) calculus, a subclass of q -starlike functions with reference to symmetric points, which is associated with the q -exponential function, is introduced in the open unit disc. Further, we derived upper bounds for the third-order Hankel determinant for the defined class. For the validity of our results, relevant connections with those in earlier works are also pointed out","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134971596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Viscosity approximation method for a variational problem","authors":"R. May","doi":"10.22436/jnsa.016.04.02","DOIUrl":"https://doi.org/10.22436/jnsa.016.04.02","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"58 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134971599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, reduced order models (ROMs) for the tumor growth model, which is a nonlinear cross-diffusion system are presented. Linear-quadratic ordinary differential equations are obtained by applying the finite difference method to the tumor growth model for spatial discretization. The structure of the ROMs is the same as the structure of the full order model. Proper orthogonal decomposition method with tensorial form is sufficient to compute the reduced solutions efficiently and fast. The results of ROM are presented for one-and two-dimensional cases. Finally, the entropy structure for the reduced solutions, which are in decay form are presented
{"title":"Model order reduction of tumor growth model","authors":"G. Mulayim","doi":"10.22436/jnsa.016.04.03","DOIUrl":"https://doi.org/10.22436/jnsa.016.04.03","url":null,"abstract":"In this paper, reduced order models (ROMs) for the tumor growth model, which is a nonlinear cross-diffusion system are presented. Linear-quadratic ordinary differential equations are obtained by applying the finite difference method to the tumor growth model for spatial discretization. The structure of the ROMs is the same as the structure of the full order model. Proper orthogonal decomposition method with tensorial form is sufficient to compute the reduced solutions efficiently and fast. The results of ROM are presented for one-and two-dimensional cases. Finally, the entropy structure for the reduced solutions, which are in decay form are presented","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134971600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider the following nonlocal integro-differential operator of L´evy-type L α ε , δ given by L αε , δ f ( x ) := (cid:90) R d { 0 } (cid:20) f (cid:16) x + εσ (cid:16) x δ , y (cid:17)(cid:17) − f ( x ) − εσ i (cid:16) x δ , y (cid:17) ∂ i f ( x ) 1 B ( y ) (cid:21) ν αε ( dy ) + (cid:20)(cid:16) ε δ (cid:17) α − 1 b i 0 (cid:16) x δ (cid:17) + b i 1 (cid:16) x δ (cid:17)(cid:21) ∂ i f ( x ) , related to stochastic differential equations driven by multiplicative isotropic α -stable L´evy noise (1 < α < 2). We study by using homogenization theory the behavior of u ε , δ : R d −→ R of double perturbed Kolmogorov, Petrovskii and Piskunov (KPP)-type with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1 /ε , (cid:14)
{"title":"Coupling homogenization and large deviations, with applications to nonlocal parabolic partial differential equations","authors":"A. Coulibaly","doi":"10.22436/jnsa.016.03.03","DOIUrl":"https://doi.org/10.22436/jnsa.016.03.03","url":null,"abstract":"Consider the following nonlocal integro-differential operator of L´evy-type L α ε , δ given by L αε , δ f ( x ) := (cid:90) R d { 0 } (cid:20) f (cid:16) x + εσ (cid:16) x δ , y (cid:17)(cid:17) − f ( x ) − εσ i (cid:16) x δ , y (cid:17) ∂ i f ( x ) 1 B ( y ) (cid:21) ν αε ( dy ) + (cid:20)(cid:16) ε δ (cid:17) α − 1 b i 0 (cid:16) x δ (cid:17) + b i 1 (cid:16) x δ (cid:17)(cid:21) ∂ i f ( x ) , related to stochastic differential equations driven by multiplicative isotropic α -stable L´evy noise (1 < α < 2). We study by using homogenization theory the behavior of u ε , δ : R d −→ R of double perturbed Kolmogorov, Petrovskii and Piskunov (KPP)-type with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1 /ε , (cid:14)","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135252203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution","authors":"B. Khan, M. Ghaffar Khan, T. G. Shaba","doi":"10.22436/jnsa.016.03.04","DOIUrl":"https://doi.org/10.22436/jnsa.016.03.04","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135252208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Taxation policy for fishing received global consent to protect fisheries from drastic harvesting. Still, it should be applied sustainably for a greater ecological and economic benefit because over-taxation may impair fishers’ earnings and reduce the overall societal revenue. The fish disease may alter the system dynamics and reduce the revenue generation from the fishery. This paper proposes a nonlinear bioeconomic harvesting model of a single-species fishery with infection, variable market price, and nonlinear demand to explore taxation’s ecological and economic effects. We provide the stability results of the system’s different ecological and economic equilibrium points. The analytical conditions for the existence of transcritical bifurcation are also established. The computational results show that the system exhibits three dynamical regimes depending on the fishing tax. Taxation might control intensive harvesting but augment disease spreading and price hiking. Higher regulatory tax may even cause a regime shift, where the system enters into a non-harvesting regime from the harvesting one, causing an ecological and economic imbalance. Using Pontryagin’s maximum principle, we decipher that some optimal fishing tax exists for the maximum societal benefit in a disease-induced fishery.
{"title":"Dynamic behaviour of a single-species nonlinear fishery model with infection: the role of fishing tax and time-dependent market price","authors":"B. Sarkar, S. Bhattacharya, N. Bairagi","doi":"10.22436/jnsa.016.03.02","DOIUrl":"https://doi.org/10.22436/jnsa.016.03.02","url":null,"abstract":"Taxation policy for fishing received global consent to protect fisheries from drastic harvesting. Still, it should be applied sustainably for a greater ecological and economic benefit because over-taxation may impair fishers’ earnings and reduce the overall societal revenue. The fish disease may alter the system dynamics and reduce the revenue generation from the fishery. This paper proposes a nonlinear bioeconomic harvesting model of a single-species fishery with infection, variable market price, and nonlinear demand to explore taxation’s ecological and economic effects. We provide the stability results of the system’s different ecological and economic equilibrium points. The analytical conditions for the existence of transcritical bifurcation are also established. The computational results show that the system exhibits three dynamical regimes depending on the fishing tax. Taxation might control intensive harvesting but augment disease spreading and price hiking. Higher regulatory tax may even cause a regime shift, where the system enters into a non-harvesting regime from the harvesting one, causing an ecological and economic imbalance. Using Pontryagin’s maximum principle, we decipher that some optimal fishing tax exists for the maximum societal benefit in a disease-induced fishery.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135252202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a q -parameter","authors":"E. Negiz, M. Acikgoz, U. Duran","doi":"10.22436/jnsa.016.01.02","DOIUrl":"https://doi.org/10.22436/jnsa.016.01.02","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136095413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the resonance response of piezoelectric vibration energy harvester (VEH) driven by bounded noise is discussed through the quasi-conservative stochastic averaging method. A nonlinear transformation based on the total energy is firstly established to transform piezoelectric VEH system from an electromechanical coupled nonlinear system into a single-degree-offreedom (SDOF) system. Then the SDOF system is rewritten as Itô stochastic system about the energy and residual phase under the case of p:q resonance through the quasi-conservative stochastic averaging method. And the joint probability density function (JPDF) of the stationary response is obtained by solving the corresponding two-dimensional Fokker-Planck-Kolmogorov (FPK) equation using the finite difference method. Meanwhile, the mean-square electric voltage and the mean output power are further analytically given through the JPDF. Finally, the resonance response of piezoelectric VEH system is analyzed in detail in case of the primary resonance, and the Monte Carlo (MC) simulation technique is adopted to validate the effectiveness of the finite difference method.
{"title":"Resonance response analysis of nonlinear vibration energy harvesting system under bounded noise excitation","authors":"Di Liu, Qianqian Fu","doi":"10.22436/JNSA.015.01.01","DOIUrl":"https://doi.org/10.22436/JNSA.015.01.01","url":null,"abstract":"In this paper, the resonance response of piezoelectric vibration energy harvester (VEH) driven by bounded noise is discussed through the quasi-conservative stochastic averaging method. A nonlinear transformation based on the total energy is firstly established to transform piezoelectric VEH system from an electromechanical coupled nonlinear system into a single-degree-offreedom (SDOF) system. Then the SDOF system is rewritten as Itô stochastic system about the energy and residual phase under the case of p:q resonance through the quasi-conservative stochastic averaging method. And the joint probability density function (JPDF) of the stationary response is obtained by solving the corresponding two-dimensional Fokker-Planck-Kolmogorov (FPK) equation using the finite difference method. Meanwhile, the mean-square electric voltage and the mean output power are further analytically given through the JPDF. Finally, the resonance response of piezoelectric VEH system is analyzed in detail in case of the primary resonance, and the Monte Carlo (MC) simulation technique is adopted to validate the effectiveness of the finite difference method.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"64 1 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78098385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abel et al. [U. Abel, M. Ivan, R. Păltănea, Appl. Math. Comput., 259 (2015), 116–123] introduced a Durrmeyer type integral variant of the Bernstein type operators based on two parameters defined by Stancu [D. D. Stancu, Calcolo, 35 (1998), 53–62]. Kajla [A. Kajla, Appl. Math. Comput., 316 (2018), 400–408] considered a Kantorovich modification of the Stancu operators wherein he studied some basic convergence theorems and also the rate of A-statistical convergence. In the present paper, we define a bivariate case of the operators proposed in [A. Kajla, Appl. Math. Comput., 316 (2018), 400–408] to study the degree of approximation for functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the complete modulus of continuity, the partial moduli of continuity and the Peetre’s K-functional. Voronovskaya and Grüss Voronovskaya type theorems are also established. We introduce the associated GBS (Generalized Boolean Sum) operators of the bivariate operators and discuss the approximation degree of these operators with the aid of the mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions.
{"title":"Approximation degree of bivariate Kantorovich Stancu operators","authors":"P. Agrawal, N. Bhardwaj, J. Singh","doi":"10.22436/JNSA.014.06.05","DOIUrl":"https://doi.org/10.22436/JNSA.014.06.05","url":null,"abstract":"Abel et al. [U. Abel, M. Ivan, R. Păltănea, Appl. Math. Comput., 259 (2015), 116–123] introduced a Durrmeyer type integral variant of the Bernstein type operators based on two parameters defined by Stancu [D. D. Stancu, Calcolo, 35 (1998), 53–62]. Kajla [A. Kajla, Appl. Math. Comput., 316 (2018), 400–408] considered a Kantorovich modification of the Stancu operators wherein he studied some basic convergence theorems and also the rate of A-statistical convergence. In the present paper, we define a bivariate case of the operators proposed in [A. Kajla, Appl. Math. Comput., 316 (2018), 400–408] to study the degree of approximation for functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the complete modulus of continuity, the partial moduli of continuity and the Peetre’s K-functional. Voronovskaya and Grüss Voronovskaya type theorems are also established. We introduce the associated GBS (Generalized Boolean Sum) operators of the bivariate operators and discuss the approximation degree of these operators with the aid of the mixed modulus of smoothness for Bögel continuous and Bögel differentiable functions.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"74 1","pages":"423-439"},"PeriodicalIF":0.0,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86279272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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