Pub Date : 2023-01-01DOI: 10.31838/rna/2023.06.01.001
We provide a characterization of Δ -open and Δ -closed sets in topological spaces. Besides, based on the concepts of Δ -open and Δ -closed sets we investigate the notions of Δ -interior, Δ -exterior, Δ -closure, Δ -derived sets, Δ -boundary sets
{"title":"Topological-like notions via Δ-open sets","authors":"","doi":"10.31838/rna/2023.06.01.001","DOIUrl":"https://doi.org/10.31838/rna/2023.06.01.001","url":null,"abstract":"We provide a characterization of Δ -open and Δ -closed sets in topological spaces. Besides, based on the concepts of Δ -open and Δ -closed sets we investigate the notions of Δ -interior, Δ -exterior, Δ -closure, Δ -derived sets, Δ -boundary sets","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44725611","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}
The local convergence analysis of a seventh order algorithm for solving nonlinear equations is presented inthe current discussion by assuming that the ?rst-order Fréchet derivative belongs to the Lipschitz class. Thisapproach yields radii of convergence ball, error bound and uniqueness of the solution. Further, generalizationof the study extended by considering Hölder continuity condition. At last, we estimated the radii of theconvergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.
{"title":"BROADENING THE CONVERGENCE DOMAIN OF SEVENTH-ORDER METHOD SATISFYING LIPSCHITZ AND HOLDER CONDITIONS","authors":"A. Saxena, J. P. Jai̇swal, Kamal Raj Paradasani̇","doi":"10.53006/rna.1146027","DOIUrl":"https://doi.org/10.53006/rna.1146027","url":null,"abstract":"The local convergence analysis of a seventh order algorithm for solving nonlinear equations is presented inthe current discussion by assuming that the ?rst-order Fréchet derivative belongs to the Lipschitz class. Thisapproach yields radii of convergence ball, error bound and uniqueness of the solution. Further, generalizationof the study extended by considering Hölder continuity condition. At last, we estimated the radii of theconvergence balls using a variety of numerical examples, including a nonlinear Hammerstein equation.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43082098","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, we propose a new proximal gradient method for a convex minimization problem in real Hilbert spaces. We suggest a new linesearch which does not require the condition of Lipschitz constant and improve conditions of inertial term which speed up performance of convergence. Moreover, we prove the weak convergence of the proposed method under some suitable conditions. The numerical implementations in data classification are reported to show its efficiency.
{"title":"A double proximal gradient method with new linesearch for solving convex minimization problem with application to data classification","authors":"S. Kesornprom, P. Cholamjiak","doi":"10.53006/rna.1143531","DOIUrl":"https://doi.org/10.53006/rna.1143531","url":null,"abstract":"In this paper, we propose a new proximal gradient method for a convex minimization problem in real Hilbert spaces. We suggest a new linesearch which does not require the condition of Lipschitz constant and improve conditions of inertial term which speed up performance of convergence. Moreover, we prove the weak convergence of the proposed method under some suitable conditions. The numerical implementations in data classification are reported to show its efficiency.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41521157","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}
Ali El Mfadel, Fatima Ezzahra Bourhi̇m, M. Elomari
The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.
{"title":"Existence of mild solutions for semilinear $psi-$Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces","authors":"Ali El Mfadel, Fatima Ezzahra Bourhi̇m, M. Elomari","doi":"10.53006/rna.1121916","DOIUrl":"https://doi.org/10.53006/rna.1121916","url":null,"abstract":"The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45021054","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}
The notion of third order semicanonical dynamic equations on time scales is introduced so that any third order equation is either in canonical, noncanonical, or semicanonical form. Then a technique for transforming each of the two types of semicanonical equations to an equation in canonical form is given. The end result is that oscillation and other asymptotic results for canonical equations can then be applied to obtain analogous results for semicanonical equations.
{"title":"Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales","authors":"J. Graef","doi":"10.53006/rna.1075859","DOIUrl":"https://doi.org/10.53006/rna.1075859","url":null,"abstract":"The notion of third order semicanonical dynamic equations on time scales is introduced so that any third order equation is either in canonical, noncanonical, or semicanonical form. Then a technique for transforming each of the two types of semicanonical equations to an equation in canonical form is given. The end result is that oscillation and other asymptotic results for canonical equations can then be applied to obtain analogous results for semicanonical equations.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41457600","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 article, we study the global behavior of the following higher-order nonautonomous rational difference equation [ y_{n+1}=frac{alpha_n+y_{n-r}}{alpha_n+y_{n-k}},quad n=0,1,..., ] where (left{alpha_nright}_{ngeq0}) is a bounded sequence of positive numbers, (k,r) are nonnegative integers such that (r
{"title":"On the global behavior of the rational difference equation (y_{n+1}=frac{alpha_n+y_{n-r}}{alpha_n+y_{n-k}})","authors":"Sihem Oudi̇na, M. Kerker, Abdelouahab Salmi","doi":"10.53006/rna.974156","DOIUrl":"https://doi.org/10.53006/rna.974156","url":null,"abstract":"In this article, we study the global behavior of the following higher-order nonautonomous rational difference equation \u0000[ \u0000y_{n+1}=frac{alpha_n+y_{n-r}}{alpha_n+y_{n-k}},quad n=0,1,..., \u0000] \u0000where (left{alpha_nright}_{ngeq0}) is a bounded sequence of \u0000positive numbers, (k,r) are nonnegative integers such that (r","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71186084","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 work, we prove the existence of a solution for the initial value problem of nonlinear fractional differential equation with quadratic perturbations involving the Caputo fractional derivative ( cDα0+−ρt cDβ0+)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1<α<2,0<β<α( cD0+α−ρt cD0+β)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1<α<2,0<β<α with conditions x0=x(0)f(0,x(0))x0=x(0)f(0,x(0)) and x1=x(1)f(1,x(1))x1=x(1)f(1,x(1)). Dhage's fixed-point the theorem was used to establish this existence. As an application, we have given example to demonstrate the effectiveness of our main result.
{"title":"Existence of Solution for a Nonlinear Fractional Order Differential Equation with a Quadratic Perturbations","authors":"A. Kajouni, Najat Chefnaj, K. Hilal","doi":"10.53006/rna.1124961","DOIUrl":"https://doi.org/10.53006/rna.1124961","url":null,"abstract":"In this work, we prove the existence of a solution for the initial value problem of nonlinear fractional differential equation with quadratic perturbations involving the Caputo fractional derivative ( cDα0+−ρt cDβ0+)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1<α<2,0<β<α( cD0+α−ρt cD0+β)(x(t)f(t,x(t)))=g(t,x(t)),t∈J=[0,1],1<α<2,0<β<α with conditions x0=x(0)f(0,x(0))x0=x(0)f(0,x(0)) and x1=x(1)f(1,x(1))x1=x(1)f(1,x(1)). Dhage's fixed-point the theorem was used to establish this existence. As an application, we have given example to demonstrate the effectiveness of our main result.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41302890","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 we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; in follow we derive some interesting results as byproducts. Eventually, we apply our results in solving fuzzy Volterra integral equations and Caputo-Hadamard type of fractional differential equations.
{"title":"Solution of Fuzzy Volterra Integral and Fractional Differential Equations via Fixed Point Theorems","authors":"Sushma Basi̇l, S. Antony","doi":"10.53006/rna.1089900","DOIUrl":"https://doi.org/10.53006/rna.1089900","url":null,"abstract":"In this paper we present fuzzy coupled fixed point results in the turf of complete b-metric spaces via nonlinear F-contraction; in follow we derive some interesting results as byproducts. Eventually, we apply our results in solving fuzzy Volterra integral equations and Caputo-Hadamard type of fractional differential equations.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42422336","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}
A. Wiriyapongsanon, W. Inthakon, N. Phudolsitthiphat
OurmainpurposeofthispaperistointroducethemodifiedMannandIshikawaiteratesforfindingacommonattractivepoint of a finite family of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. Weobtain necessary and sufficient conditions to guarantee the strong convergence of the proposed algorithms withoutclosedness of the domain of such mappings. Moreover, we derive some consequences from our main result to fixedpoint result of such mappings. Finally, the numerical results are provided to support our main theorem.
{"title":"Common Attractive Point Theorems for a Finite Family of Multivalued Nonexpansive Mappings in Banach Spaces","authors":"A. Wiriyapongsanon, W. Inthakon, N. Phudolsitthiphat","doi":"10.53006/rna.1128729","DOIUrl":"https://doi.org/10.53006/rna.1128729","url":null,"abstract":"OurmainpurposeofthispaperistointroducethemodifiedMannandIshikawaiteratesforfindingacommonattractivepoint of a finite family of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. Weobtain necessary and sufficient conditions to guarantee the strong convergence of the proposed algorithms withoutclosedness of the domain of such mappings. Moreover, we derive some consequences from our main result to fixedpoint result of such mappings. Finally, the numerical results are provided to support our main theorem.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44123032","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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