Pub Date : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4850
W. Saleh, B. Meftah, A. Lakhdari, A. Kılıçman
This paper investigates the companion of Ostrowski's inequality in the framework of fractal sets. First, a new identity related to local fractional integrals is introduced, serving as the foundation for establishing a set of inequalities applicable to functions with generalized $s$-convex and $s$-concave derivatives. An illustrative example is presented to validate the obtained results, demonstrating their accuracy. Additionally, the paper discusses several practical applications, highlighting the significance of the established inequalities. The research presented in this paper contributes to the growing field of studying functions on fractal sets, which has attracted considerable interest from scientists and engineers.
{"title":"Exploring the Companion of Ostrowski's Inequalities via Local Fractional Integrals","authors":"W. Saleh, B. Meftah, A. Lakhdari, A. Kılıçman","doi":"10.29020/nybg.ejpam.v16i3.4850","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4850","url":null,"abstract":"This paper investigates the companion of Ostrowski's inequality in the framework of fractal sets. First, a new identity related to local fractional integrals is introduced, serving as the foundation for establishing a set of inequalities applicable to functions with generalized $s$-convex and $s$-concave derivatives. An illustrative example is presented to validate the obtained results, demonstrating their accuracy. Additionally, the paper discusses several practical applications, highlighting the significance of the established inequalities. The research presented in this paper contributes to the growing field of studying functions on fractal sets, which has attracted considerable interest from scientists and engineers.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42333119","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4872
S. Ahn, H. Kim, S. Song, Y. Jun
To investigate the filter and deductive system of the Schaefer stroke Hilbert algebra using the Dokdo structure, the concept of Dokdo filter and Dokdo deductive system is defined, examples are given, and various properties are investigated. The Dokdo filter is formed by attaching appropriate conditions to the given Dokdo structure. The characterization of Dokdo filter is studied. Dokdo filters related to filters are constructed. Dokdo filter and Dokdo deductive system turn out to be the same concept.
{"title":"Dokdo Filters and Deductive Systems of Sheffer Stroke Hilbert Algebras","authors":"S. Ahn, H. Kim, S. Song, Y. Jun","doi":"10.29020/nybg.ejpam.v16i3.4872","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4872","url":null,"abstract":"To investigate the filter and deductive system of the Schaefer stroke Hilbert algebra using the Dokdo structure, the concept of Dokdo filter and Dokdo deductive system is defined, examples are given, and various properties are investigated. The Dokdo filter is formed by attaching appropriate conditions to the given Dokdo structure. The characterization of Dokdo filter is studied. Dokdo filters related to filters are constructed. Dokdo filter and Dokdo deductive system turn out to be the same concept.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42882080","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4832
E. Roh, Eunsuk Yang, Y. Jun
In this paper, we apply the concept of an intuitionistic fuzzy set to ordered subalgebras in ordered BCI-algebras in the sense of intuitionistic fuzzy point. We introduce the notion of an intuitionistic fuzzy (ordered) subalgebra in ordered BCI-algebras, and investigate some related properties. We provide relations between an intuitionistic fuzzy ordered subalgebra and an intuitionistic fuzzy subalgebra. We give characterizations of an intuitionistic fuzzy (ordered) subalgebra. Finally, we provide relations between a $q_{(t,s)}$-level set of intuitionistic fuzzy set and an intuitionistic fuzzy ordered subalgebra.
{"title":"Intuitionistic Fuzzy Ordered Subalgebras in Ordered BCI-algebras","authors":"E. Roh, Eunsuk Yang, Y. Jun","doi":"10.29020/nybg.ejpam.v16i3.4832","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4832","url":null,"abstract":"In this paper, we apply the concept of an intuitionistic fuzzy set to ordered subalgebras in ordered BCI-algebras in the sense of intuitionistic fuzzy point. We introduce the notion of an intuitionistic fuzzy (ordered) subalgebra in ordered BCI-algebras, and investigate some related properties. We provide relations between an intuitionistic fuzzy ordered subalgebra and an intuitionistic fuzzy subalgebra. We give characterizations of an intuitionistic fuzzy (ordered) subalgebra. Finally, we provide relations between a $q_{(t,s)}$-level set of intuitionistic fuzzy set and an intuitionistic fuzzy ordered subalgebra.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44408225","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4768
A. Swaminathan, C. Ozel, Ibtesam Alshammari
We define hesitant fuzzy maximal open cover to establish hesitant fuzzy m-compactness and discuss its properties. Further we obtain few more results on hesitant fuzzy minimal c-regular and minimal c-normal spaces. We have proved that a hesitant fuzzy Haussdorff m-compact space is hesitant fuzzy minimal c-normal.
{"title":"Hesitant Fuzzy Compactness and Hesitant Fuzzy Regularity in Hesitant Fuzzy Topological Spaces","authors":"A. Swaminathan, C. Ozel, Ibtesam Alshammari","doi":"10.29020/nybg.ejpam.v16i3.4768","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4768","url":null,"abstract":"We define hesitant fuzzy maximal open cover to establish hesitant fuzzy m-compactness and discuss its properties. Further we obtain few more results on hesitant fuzzy minimal c-regular and minimal c-normal spaces. We have proved that a hesitant fuzzy Haussdorff m-compact space is hesitant fuzzy minimal c-normal.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41913941","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 : 2023-07-30DOI: 10.29020/nybg.ejpam.v16i3.4787
Daouda Kabré, André Conseibo
In this paper we study the class of algebras satisfying a polynomial identity of degree six that are principal train algebras of rank $3$ or $4$, for which we give the explicit form of the train equation. If the rank of $A$ is $ngeq 5$ in general, we provide the form of the train equation in some cases.
{"title":"Algebras Satisfying Polynomial Identity of Degree Six that are Principal Train","authors":"Daouda Kabré, André Conseibo","doi":"10.29020/nybg.ejpam.v16i3.4787","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4787","url":null,"abstract":"In this paper we study the class of algebras satisfying a polynomial identity of degree six that are principal train algebras of rank $3$ or $4$, for which we give the explicit form of the train equation. If the rank of $A$ is $ngeq 5$ in general, we provide the form of the train equation in some cases.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368017","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 : 2023-07-01DOI: 10.29020/nybg.ejpam.v16i3.4843
Vuk Stojiljković
( newcommandnorm[1]{leftlVert#1rightrVert}newcommandnormx[1]{leftVert#1rightVert} )In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities are obtained with variations due to the convexity properties of the mapping $f$$$norm{(1otimes B-Aotimes 1)^{-1}[operatorname{exp}(1otimes B)-operatorname{exp}(Aotimes 1)]- operatorname{exp}left(frac{Aotimes 1+1otimes B}{2}right)}$$$$leqslant norm{1otimes B-Aotimes 1}^{2}frac{norm{f''}_{I,+infty}}{24}.$$
{"title":"Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces","authors":"Vuk Stojiljković","doi":"10.29020/nybg.ejpam.v16i3.4843","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i3.4843","url":null,"abstract":"(\u0000newcommandnorm[1]{leftlVert#1rightrVert}newcommandnormx[1]{leftVert#1rightVert}\u0000)In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities are obtained with variations due to the convexity properties of the mapping $f$$$norm{(1otimes B-Aotimes 1)^{-1}[operatorname{exp}(1otimes B)-operatorname{exp}(Aotimes 1)]- operatorname{exp}left(frac{Aotimes 1+1otimes B}{2}right)}$$$$leqslant norm{1otimes B-Aotimes 1}^{2}frac{norm{f''}_{I,+infty}}{24}.$$","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43274286","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 : 2023-04-30DOI: 10.29020/nybg.ejpam.v16i2.4769
Ahmad Mohammad Qazza, Mohamed A. Abdoon, Rania Saadeh, Mohammed Berir
The subject of this study is the solution of a fractional Bernoulli equation and a chaotic system by using a novel scheme for the fractional derivative and comparison of approximate and exact solutions. It is found that the suggested method produces solutions that are identical to the exact solution. We can therefore generalize the strategy to different systems to get more accurate results. We think that the novel fractional derivative scheme that has been offered and the algorithm that has been suggested will be utilized in the future to construct and simulate a variety of fractional models that can be used to solve more difficult physics and engineering challenges.
{"title":"A New Scheme for Solving a Fractional Differential Equation and a Chaotic System","authors":"Ahmad Mohammad Qazza, Mohamed A. Abdoon, Rania Saadeh, Mohammed Berir","doi":"10.29020/nybg.ejpam.v16i2.4769","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i2.4769","url":null,"abstract":"The subject of this study is the solution of a fractional Bernoulli equation and a chaotic system by using a novel scheme for the fractional derivative and comparison of approximate and exact solutions. It is found that the suggested method produces solutions that are identical to the exact solution. We can therefore generalize the strategy to different systems to get more accurate results. We think that the novel fractional derivative scheme that has been offered and the algorithm that has been suggested will be utilized in the future to construct and simulate a variety of fractional models that can be used to solve more difficult physics and engineering challenges.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46510366","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 : 2023-04-30DOI: 10.29020/nybg.ejpam.v16i2.4693
Rasha F. Ahmed, W. Al-Hayani, A. Al-Bayati
This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.
{"title":"The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions","authors":"Rasha F. Ahmed, W. Al-Hayani, A. Al-Bayati","doi":"10.29020/nybg.ejpam.v16i2.4693","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i2.4693","url":null,"abstract":"This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45949190","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 : 2023-04-30DOI: 10.29020/nybg.ejpam.v16i2.4703
C. Corcino, R. Corcino
Asymptotic approximation formulas for polynomials of the type Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi with integer order and real parameters are obtained via hyperbolic functions. The derivation of the formulas is done using the principle of saddle point and expansion of appropriate hyperbolic function about a saddle point.
{"title":"Asymptotic approximations for Generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials in terms of Hyperbolic Functions","authors":"C. Corcino, R. Corcino","doi":"10.29020/nybg.ejpam.v16i2.4703","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i2.4703","url":null,"abstract":"Asymptotic approximation formulas for polynomials of the type Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi with integer order and real parameters are obtained via hyperbolic functions. The derivation of the formulas is done using the principle of saddle point and expansion of appropriate hyperbolic function about a saddle point.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41726351","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 : 2023-04-30DOI: 10.29020/nybg.ejpam.v16i2.4746
Yoksal A. Laylani, Hisham M. Khudhur, Edrees M. Nori, K. Abbo
The paper in discusses conjugate gradient methods, which are often used for unconstrained optimization and are the subject of this discussion. In the process of studying and implementing conjugate gradient algorithms, it is standard practice to assume that the descent condition is true. Despite the fact that this sort of approach very seldom results in search routes that slope in a downward direction, this assumption is made routinely. As a result of this research, we propose a revised method known as the improved hybrid conjugate gradient technique. This method is a convex combination of the Dai-Yuan and Hestenes-Stiefel methodologies. The descending property and global convergence are both exhibited by the Wolfe line search. The numerical data demonstrates that the strategy that was presented is an efficient one.
{"title":"A hybridization of the Hestenes-Stiefel and Dai-Yuan Conjugate Gradient Methods","authors":"Yoksal A. Laylani, Hisham M. Khudhur, Edrees M. Nori, K. Abbo","doi":"10.29020/nybg.ejpam.v16i2.4746","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v16i2.4746","url":null,"abstract":"The paper in discusses conjugate gradient methods, which are often used for unconstrained optimization and are the subject of this discussion. In the process of studying and implementing conjugate gradient algorithms, it is standard practice to assume that the descent condition is true. Despite the fact that this sort of approach very seldom results in search routes that slope in a downward direction, this assumption is made routinely. As a result of this research, we propose a revised method known as the improved hybrid conjugate gradient technique. This method is a convex combination of the Dai-Yuan and Hestenes-Stiefel methodologies. The descending property and global convergence are both exhibited by the Wolfe line search. The numerical data demonstrates that the strategy that was presented is an efficient one.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41467970","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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