Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0106
J. Ferreira, João Paulo Rodrigues de Andrade, Willian S. Panni, M. Shahrouzi
In this article we study the existence of periodic and strong solutions of Navier-Stokes equations, in two dimensions, with non-local viscosity.
本文研究了具有非局部黏度的二维Navier-Stokes方程周期解和强解的存在性。
{"title":"Strong and periodic solutions of Navier-Stokes equations, in 2D, with non-local viscosity","authors":"J. Ferreira, João Paulo Rodrigues de Andrade, Willian S. Panni, M. Shahrouzi","doi":"10.30538/psrp-oma2022.0106","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0106","url":null,"abstract":"In this article we study the existence of periodic and strong solutions of Navier-Stokes equations, in two dimensions, with non-local viscosity.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47746991","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}
Pub Date : 2022-06-21DOI: 10.30538/psrp-oma2022.0100
Xiaojing Chen, W. Chu
In this paper, the (q)-derivative operator and the principle of subordination were employed to define a subclass (mathcal{B}_q(tau,lambda,phi)) of analytic and bi-univalent functions in the open unit disk (mathcal{U}). For functions (f(z)inmathcal{B}_q(tau,lambda,phi)), we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.
{"title":"On a generalized class of bi-univalent functions defined by subordination and (q)-derivative operator","authors":"Xiaojing Chen, W. Chu","doi":"10.30538/psrp-oma2022.0100","DOIUrl":"https://doi.org/10.30538/psrp-oma2022.0100","url":null,"abstract":"In this paper, the (q)-derivative operator and the principle of subordination were employed to define a subclass (mathcal{B}_q(tau,lambda,phi)) of analytic and bi-univalent functions in the open unit disk (mathcal{U}). For functions (f(z)inmathcal{B}_q(tau,lambda,phi)), we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46925873","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}
Pub Date : 2021-12-24DOI: 10.30538/psrp-oma2021.0098
Kuldeep Kaur Shergill, S. S. Billing
In the present paper, we use the technique of differential subordination and superordination involving meromorphic functions with respect to symmetric points and also derive some sandwich results. As a consequence of main result, we obtain results for meromorphic starlike functions with respect to symmetrical points.
{"title":"Sandwich type results for meromorphic functions with respect to symmetrical points","authors":"Kuldeep Kaur Shergill, S. S. Billing","doi":"10.30538/psrp-oma2021.0098","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0098","url":null,"abstract":"In the present paper, we use the technique of differential subordination and superordination involving meromorphic functions with respect to symmetric points and also derive some sandwich results. As a consequence of main result, we obtain results for meromorphic starlike functions with respect to symmetrical points.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41303497","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}
Pub Date : 2021-12-24DOI: 10.30538/psrp-oma2021.0097
U. Udofia, A. Ofem, D. Igbokwe
In this paper, we introduce a four step iterative algorithm which converges faster than some leading iterative algorithms in the literature. We show that our new iterative scheme is (T)-stable and data dependent. As an application, we use the new iterative algorithm to find the unique solution of a nonlinear integral equation. Our results are generalizations and improvements of several well known results in the existing literature.
{"title":"Convergence analysis for a new faster four steps iterative algorithm with an application","authors":"U. Udofia, A. Ofem, D. Igbokwe","doi":"10.30538/psrp-oma2021.0097","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0097","url":null,"abstract":"In this paper, we introduce a four step iterative algorithm which converges faster than some leading iterative algorithms in the literature. We show that our new iterative scheme is (T)-stable and data dependent. As an application, we use the new iterative algorithm to find the unique solution of a nonlinear integral equation. Our results are generalizations and improvements of several well known results in the existing literature.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46564371","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}
Pub Date : 2021-12-24DOI: 10.30538/psrp-oma2021.0096
Yenny Rangel-Oliveros, E. Nwaeze
The Simpson's inequality cannot be applied to a function that is twice differentiable but not four times differentiable or have a bounded fourth derivative in the interval under consideration. Loads of articles are bound for twice differentiable convex functions but nothing, to the best of our knowledge, is known yet for twice differentiable exponentially convex and quasi-convex functions. In this paper, we aim to do justice to this query. For this, we prove several Simpson's type inequalities for exponentially convex and exponentially quasi-convex functions. Our findings refine, generalize and complement existing results in the literature. We regain previously known results by taking (alpha=0). In addition, we also show the importance of our results by applying them to some special means of positive real numbers and to Simpson's quadrature rule. The obtained results can be extended for different kinds of convex functions.
{"title":"Simpson’s type inequalities for exponentially convex functions with applications","authors":"Yenny Rangel-Oliveros, E. Nwaeze","doi":"10.30538/psrp-oma2021.0096","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0096","url":null,"abstract":"The Simpson's inequality cannot be applied to a function that is twice differentiable but not four times differentiable or have a bounded fourth derivative in the interval under consideration. Loads of articles are bound for twice differentiable convex functions but nothing, to the best of our knowledge, is known yet for twice differentiable exponentially convex and quasi-convex functions. In this paper, we aim to do justice to this query. For this, we prove several Simpson's type inequalities for exponentially convex and exponentially quasi-convex functions. Our findings refine, generalize and complement existing results in the literature. We regain previously known results by taking (alpha=0). In addition, we also show the importance of our results by applying them to some special means of positive real numbers and to Simpson's quadrature rule. The obtained results can be extended for different kinds of convex functions.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43588878","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}
Pub Date : 2021-12-24DOI: 10.30538/psrp-oma2021.0095
Houdeifa Melki, A. Makhlouf
In this article, we consider the limit cycles of a class of planar polynomial differential systems of the form [dot{x}=-y+varepsilon (1+sin ^{n}theta )xP(x,y)] [ dot{y}=x+varepsilon (1+cos ^{m}theta )yQ(x,y), ] where (P(x,y)) and (Q(x,y)) are polynomials of degree (n_{1}) and (n_{2}) respectively and (varepsilon) is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a linear center ( dot{x}=-y, dot{y}=x,) by using the averaging theory of first order.
{"title":"Limit cycles of a planar differential system via averaging theory","authors":"Houdeifa Melki, A. Makhlouf","doi":"10.30538/psrp-oma2021.0095","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0095","url":null,"abstract":"In this article, we consider the limit cycles of a class of planar polynomial differential systems of the form [dot{x}=-y+varepsilon (1+sin ^{n}theta )xP(x,y)] [ dot{y}=x+varepsilon (1+cos ^{m}theta )yQ(x,y), ] where (P(x,y)) and (Q(x,y)) are polynomials of degree (n_{1}) and (n_{2}) respectively and (varepsilon) is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a linear center ( dot{x}=-y, dot{y}=x,) by using the averaging theory of first order.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43385481","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}
Pub Date : 2021-11-01DOI: 10.30538/psrp-oma2021.0094
S. Ege, F. Topal
This work deals with a boundary value problem for a nonlinear semipositone multi-point fractional differential equation. By using the Schauder fixed point theorem, we show the existence of one solution for this problem. Our result extend some recent works in the literature.
{"title":"Existence result for a semipositone fractional boundary value problem","authors":"S. Ege, F. Topal","doi":"10.30538/psrp-oma2021.0094","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0094","url":null,"abstract":"This work deals with a boundary value problem for a nonlinear semipositone multi-point fractional differential equation. By using the Schauder fixed point theorem, we show the existence of one solution for this problem. Our result extend some recent works in the literature.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48243771","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}
Pub Date : 2021-11-01DOI: 10.30538/psrp-oma2021.0093
J. Kwakye, J. Tchuenche
A two-strain model of the transmission dynamics of herpes simplex virus (HSV) with treatment is formulated as a deterministic system of nonlinear ordinary differential equations. The model is then analyzed qualitatively, with numerical simulations provided to support the theoretical results. The basic reproduction number (R_0) is computed with (R_0=text{max}lbrace R_1, R_2 rbrace ) where (R_1) and (R_2) represent respectively the reproduction number for HSV1 and HSV2. We also compute the invasion reproductive numbers (tilde{R}_1) for strain 1 when strain 2 is at endemic equilibrium and (tilde{R}_2) for strain 2 when strain 1 is at endemic equilibrium. To determine the relative importance of model parameters to disease transmission, sensitivity analysis is carried out. The reproduction number is most sensitive respectively to the contact rates (beta_1), (beta_2) and the recruitment rate (pi). Numerical simulations indicate the co-existence of the two strains, with HSV1, dominating but not driving out HSV2 whenever (R_1 > R_2 > 1) and vice versa.
{"title":"A simple two-strain HSV epidemic model with palliative treatment","authors":"J. Kwakye, J. Tchuenche","doi":"10.30538/psrp-oma2021.0093","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0093","url":null,"abstract":"A two-strain model of the transmission dynamics of herpes simplex virus (HSV) with treatment is formulated as a deterministic system of nonlinear ordinary differential equations. The model is then analyzed qualitatively, with numerical simulations provided to support the theoretical results. The basic reproduction number (R_0) is computed with (R_0=text{max}lbrace R_1, R_2 rbrace ) where (R_1) and (R_2) represent respectively the reproduction number for HSV1 and HSV2. We also compute the invasion reproductive numbers (tilde{R}_1) for strain 1 when strain 2 is at endemic equilibrium and (tilde{R}_2) for strain 2 when strain 1 is at endemic equilibrium. To determine the relative importance of model parameters to disease transmission, sensitivity analysis is carried out. The reproduction number is most sensitive respectively to the contact rates (beta_1), (beta_2) and the recruitment rate (pi). Numerical simulations indicate the co-existence of the two strains, with HSV1, dominating but not driving out HSV2 whenever (R_1 > R_2 > 1) and vice versa.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45450205","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}
Pub Date : 2021-09-06DOI: 10.30538/psrp-oma2021.0091
O. Ogola, N. B. Okelo, O. Ongati
In this paper, we give characterizations of separation criteria for bitopological spaces via (ij)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let ((X, tau_{1}, tau_{2})) be a (T_{0}) space then, the property of (T_{0}) is topological and hereditary. Similarly, when ((X, tau_{1}, tau_{2})) is a (T_{1}) space then the property of (T_{1}) is topological and hereditary. Next, we show that separation axiom (T_{0}) implies separation axiom (T_{1}) which also implies separation axiom (T_{2}) and the converse is true.
{"title":"On separability criteria for continuous Bitopological spaces","authors":"O. Ogola, N. B. Okelo, O. Ongati","doi":"10.30538/psrp-oma2021.0091","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0091","url":null,"abstract":"In this paper, we give characterizations of separation criteria for bitopological spaces via (ij)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let ((X, tau_{1}, tau_{2})) be a (T_{0}) space then, the property of (T_{0}) is topological and hereditary. Similarly, when ((X, tau_{1}, tau_{2})) is a (T_{1}) space then the property of (T_{1}) is topological and hereditary. Next, we show that separation axiom (T_{0}) implies separation axiom (T_{1}) which also implies separation axiom (T_{2}) and the converse is true.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45718062","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}
Pub Date : 2021-09-06DOI: 10.30538/psrp-oma2021.0092
A. Lasode, T. Opoola
In this paper, the (q)-derivative operator and the principle of subordination were employed to define a subclass (mathcal{B}_q(tau,lambda,phi)) of analytic and bi-univalent functions in the open unit disk (mathcal{U}). For functions (f(z)inmathcal{B}_q(tau,lambda,phi)), we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.
{"title":"On a generalized class of bi-univalent functions defined by subordination and (q)-derivative operator","authors":"A. Lasode, T. Opoola","doi":"10.30538/psrp-oma2021.0092","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0092","url":null,"abstract":"In this paper, the (q)-derivative operator and the principle of subordination were employed to define a subclass (mathcal{B}_q(tau,lambda,phi)) of analytic and bi-univalent functions in the open unit disk (mathcal{U}). For functions (f(z)inmathcal{B}_q(tau,lambda,phi)), we obtained early coefficient bounds and some Fekete-Szegö estimates for real and complex parameters.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46803950","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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