Pub Date : 2023-06-27DOI: 10.9734/arjom/2023/v19i9696
Shalini Tomar
The goal of this paper is to investigate the Generalized Hyers - Ulam - Rassias (HUR) stability of generalquartic functional equation (GQFE) fq(kr1 + (k -1)r2) + fq(kr1 - (k -1)r2) = 2k4fq(r1) + 2(k -1)4fq(r2) +6k2(k -1)2[fq(r1 + r2) + fq(r1 - r2)] - 12k2(k - 1)2[fq(r1) + fq(r2)] in fuzzy normed spaces (F.N. spaces). The stability of the equation is proved by using direct method. The stability in sense of Hyers - Ulam and Ulam- Gavruta - Rassias is also studied.
{"title":"On Direct Fuzzy Stability of General Quartic Functional Equation","authors":"Shalini Tomar","doi":"10.9734/arjom/2023/v19i9696","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9696","url":null,"abstract":"The goal of this paper is to investigate the Generalized Hyers - Ulam - Rassias (HUR) stability of generalquartic functional equation (GQFE) \u0000 fq(kr1 + (k -1)r2) + fq(kr1 - (k -1)r2) = 2k4fq(r1) + 2(k -1)4fq(r2) +6k2(k -1)2[fq(r1 + r2) + fq(r1 - r2)] - 12k2(k - 1)2[fq(r1) + fq(r2)]\u0000in fuzzy normed spaces (F.N. spaces). The stability of the equation is proved by using direct method. The stability in sense of Hyers - Ulam and Ulam- Gavruta - Rassias is also studied.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132321339","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 : 2023-06-27DOI: 10.9734/arjom/2023/v19i9697
Patrick Kwame Babah, Richard Ayamah, Stella Sitsofe Yawa Asase, Adolf Odei
The purpose of the study was to determine the effectiveness of Know-Want-Learn (KWL) strategy in basic five pupils’ achievement in finding perimeter and area of plane figures. The study was conducted using a quasi-experimental design. The whole research was conducted at Sogasco Basic School in the South Tungu District in the Volta Region of Ghana, and it covered about four-week period. The participants of the study were 81 pupils, divided into two groups, ensuring gender balance: one an experimental group (n = 41) and the other a control group (n = 40). Two achievement tests (pre-test and post-test) were used to collect data for the study. The validity and reliability of the test results were established by using Conbrach Alpha method. SPSS was used to analyze the data. The findings revealed that, at five percent significant level, there were statistically significant differences between the mean scores of the pupils in the experimental and the control groups, in favor of the experimental group in terms of higher performances in the post-test; hence the KWL strategy used in the teaching of mathematics was very effective and had a great positive impact on the pupils’ mathematics concept build-up and problem-solving abilities in the basic schools.
{"title":"The Effectiveness of Know-Want-Learn (KWL) Strategy on Ghanaian Basic Five Pupils’ Achievements in Mathematics","authors":"Patrick Kwame Babah, Richard Ayamah, Stella Sitsofe Yawa Asase, Adolf Odei","doi":"10.9734/arjom/2023/v19i9697","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9697","url":null,"abstract":"The purpose of the study was to determine the effectiveness of Know-Want-Learn (KWL) strategy in basic five pupils’ achievement in finding perimeter and area of plane figures. The study was conducted using a quasi-experimental design. The whole research was conducted at Sogasco Basic School in the South Tungu District in the Volta Region of Ghana, and it covered about four-week period. The participants of the study were 81 pupils, divided into two groups, ensuring gender balance: one an experimental group (n = 41) and the other a control group (n = 40). Two achievement tests (pre-test and post-test) were used to collect data for the study. The validity and reliability of the test results were established by using Conbrach Alpha method. SPSS was used to analyze the data. The findings revealed that, at five percent significant level, there were statistically significant differences between the mean scores of the pupils in the experimental and the control groups, in favor of the experimental group in terms of higher performances in the post-test; hence the KWL strategy used in the teaching of mathematics was very effective and had a great positive impact on the pupils’ mathematics concept build-up and problem-solving abilities in the basic schools.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133460104","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 : 2023-06-22DOI: 10.9734/arjom/2023/v19i9695
S. Devi, M. Kumar, S. Devi
We introduce the concept of generalized (beta) - (gamma) - Z contraction mapping with respect to a simulation function ξ and study the existence of fixed points for such mappings in complete -metric spaces. Further, we extend it to partially ordered complete -metric spaces.
{"title":"Some Fixed Point Theorems in S-metric Spaces via Simulation Function","authors":"S. Devi, M. Kumar, S. Devi","doi":"10.9734/arjom/2023/v19i9695","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9695","url":null,"abstract":"We introduce the concept of generalized (beta) - (gamma) - Z contraction mapping with respect to a simulation function ξ and study the existence of fixed points for such mappings in complete -metric spaces. Further, we extend it to partially ordered complete -metric spaces.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130950080","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 : 2023-06-19DOI: 10.9734/arjom/2023/v19i8693
Lao Hussein Mude, O. M. Oduor, O. M. Onyango
Let R be a commutative unital finite rings and Z(R) be its set of zero divisors. The study of automorphisms of algebraic structures via zero divisor graphs is still an active area of research. Perhaps, because of the fact that automorphisms have got real life application in capturing the symmetries of algebraic structures. In this study, the automorphisms zero divisor graphs of such rings in which the product of any four zero divisor is zero has been determined.
{"title":"Automorphisms of Zero Divisor Graphs of Power Four Radical Zero Completely Primary Finite Rings","authors":"Lao Hussein Mude, O. M. Oduor, O. M. Onyango","doi":"10.9734/arjom/2023/v19i8693","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i8693","url":null,"abstract":"Let R be a commutative unital finite rings and Z(R) be its set of zero divisors. The study of automorphisms of algebraic structures via zero divisor graphs is still an active area of research. Perhaps, because of the fact that automorphisms have got real life application in capturing the symmetries of algebraic structures. In this study, the automorphisms zero divisor graphs of such rings in which the product of any four zero divisor is zero has been determined.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"742 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116089379","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 : 2023-06-19DOI: 10.9734/arjom/2023/v19i9694
Yuxuan Wei, Zhinan Gao, X. Lu
In this paper, we focus on calculate the number of spanning trees of the general wheel graphs, which meansthe original wheel graphs adding large amount of vertices and edges. Particularly, we introduce the C-graphand deduce a new equation that computing the spanning trees by removing C-graphs instead of edges.In Addition, we test our results by Kirchhoff’s matrix-tree theorem in some simple cases and provide thetree entropy of the general wheel graphs. Finally, we analyse the relation between the wheel graph anddouble-wheel graphs and propose the idea of calculating the spanning trees of double-wheel graphs.
{"title":"The Complexity of Wheel Graphs with Multiple Edges and Vertices","authors":"Yuxuan Wei, Zhinan Gao, X. Lu","doi":"10.9734/arjom/2023/v19i9694","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i9694","url":null,"abstract":"In this paper, we focus on calculate the number of spanning trees of the general wheel graphs, which meansthe original wheel graphs adding large amount of vertices and edges. Particularly, we introduce the C-graphand deduce a new equation that computing the spanning trees by removing C-graphs instead of edges.In Addition, we test our results by Kirchhoff’s matrix-tree theorem in some simple cases and provide thetree entropy of the general wheel graphs. Finally, we analyse the relation between the wheel graph anddouble-wheel graphs and propose the idea of calculating the spanning trees of double-wheel graphs.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126093298","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 : 2023-06-07DOI: 10.9734/arjom/2023/v19i8692
Koech Vincent, Musundi Sammy, Kinyanjui Jeremiah
Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.
{"title":"Derivation of Fixed-Point Theorem Using Expansive Mapping Approach","authors":"Koech Vincent, Musundi Sammy, Kinyanjui Jeremiah","doi":"10.9734/arjom/2023/v19i8692","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i8692","url":null,"abstract":"Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115259685","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 : 2023-06-03DOI: 10.9734/arjom/2023/v19i8691
M. A. Assabaai, A. Kherd
In this study, we numerically solve the singular linear ordinary differential equations (SLODEs) of higher order using the collocation method based on the NB1 polynomial. An operational matrix form of the given ordinary differential equations (ODEs), the relations of various solutions and the derivatives are obtained from NB1 polynomials. The proposed method reduces the given problem to a linear algebraic equation system, which removes the singularity of ordinary differential equations. The inverse matrix method is used to solve the resulting system to obtain the coefficients of NB1 polynomials. The obtained exact solutions to different problems of high orders show the reliability and accuracy of the presented method.
{"title":"Exact Solutions for Some Singular Linear Ordinary Differential Equations of High Orders via NB1 Polynomials","authors":"M. A. Assabaai, A. Kherd","doi":"10.9734/arjom/2023/v19i8691","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i8691","url":null,"abstract":"In this study, we numerically solve the singular linear ordinary differential equations (SLODEs) of higher order using the collocation method based on the NB1 polynomial. An operational matrix form of the given ordinary differential equations (ODEs), the relations of various solutions and the derivatives are obtained from NB1 polynomials. The proposed method reduces the given problem to a linear algebraic equation system, which removes the singularity of ordinary differential equations. The inverse matrix method is used to solve the resulting system to obtain the coefficients of NB1 polynomials. The obtained exact solutions to different problems of high orders show the reliability and accuracy of the presented method.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121970260","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 : 2023-06-02DOI: 10.9734/arjom/2023/v19i8688
K. Vithyasangaran, S. Sathaananthan, J. Sriranganesan
We discuss about gr -connectedness and different properties of it, such as remarks, examples and theorems.
讨论了广义连通性及其不同性质，如注释、例子和定理。
{"title":"gr-connectedness in Topological Spaces","authors":"K. Vithyasangaran, S. Sathaananthan, J. Sriranganesan","doi":"10.9734/arjom/2023/v19i8688","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i8688","url":null,"abstract":"We discuss about gr -connectedness and different properties of it, such as remarks, examples and theorems.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131278546","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 : 2023-06-02DOI: 10.9734/arjom/2023/v19i8690
Y. Soykan, Inci Okumuş, Nazmiye Gönül Bilgin
It is aimed to describe generalized Bigollo sequences and to examine Bigollo and Bigollo-Lucas sequences in this article. For this purpose, we give Binet’s formulas, Simson formulas, generating functions and we introduce a lot of main features of these sequences. Also, we get some formulas and give special matrices for these generalized sequences. Finally, we have determined some close relationships between Bigollo and Bigollo-Lucas numbers and Mersenne, Mersenne-Lucas numbers.
{"title":"On Generalized Bigollo Numbers","authors":"Y. Soykan, Inci Okumuş, Nazmiye Gönül Bilgin","doi":"10.9734/arjom/2023/v19i8690","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i8690","url":null,"abstract":"It is aimed to describe generalized Bigollo sequences and to examine Bigollo and Bigollo-Lucas sequences in this article. For this purpose, we give Binet’s formulas, Simson formulas, generating functions and we introduce a lot of main features of these sequences. Also, we get some formulas and give special matrices for these generalized sequences. Finally, we have determined some close relationships between Bigollo and Bigollo-Lucas numbers and Mersenne, Mersenne-Lucas numbers.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125046338","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 : 2023-05-24DOI: 10.9734/arjom/2023/v19i8687
T. Fujita
Linear-width is a widely recognized and highly valued graph width parameter. The concepts of linear tangle and linear obstacle are dual concepts of linear-width. In this concise paper, we present an alternative proof of the equivalence between linear tangle and linear obstacle.
{"title":"Alternative Proof of Linear Tangle and Linear Obstacle: An Equivalence Result","authors":"T. Fujita","doi":"10.9734/arjom/2023/v19i8687","DOIUrl":"https://doi.org/10.9734/arjom/2023/v19i8687","url":null,"abstract":"Linear-width is a widely recognized and highly valued graph width parameter. The concepts of linear tangle and linear obstacle are dual concepts of linear-width. In this concise paper, we present an alternative proof of the equivalence between linear tangle and linear obstacle.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128735541","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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