"The main object of this paper is to present some generalizations of fractional integral inequalities involving Euler's beta function of Hermite-Hadamard type which cover the previously published result such as Riemann integral, Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral."
{"title":"\"On the generalized trapezoid and midpoint type inequalities involving Euler's beta function}\"","authors":"","doi":"10.37193/cmi.2023.01.07","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.07","url":null,"abstract":"\"The main object of this paper is to present some generalizations of fractional integral inequalities involving Euler's beta function of Hermite-Hadamard type which cover the previously published result such as Riemann integral, Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125891394","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 finite group $G$ is said to be a POS-group if, for each $xin G$, the cardinality of the set ${yin G,,:,, o(y)=o(x)}$ is a divisor of the order of $G$. A POS-group $G$ is said to be a Hereditary Perfect Order Subset group if all even order subgroups of $G$ are POS-group. In this paper we study the structure of Hereditary perfect order subset groups.
{"title":"Hereditary Perfect Order Subset Groups","authors":"S. Vinod, S. Sajikumar, G. S. Biju","doi":"10.37193/cmi.2023.01.12","DOIUrl":"https://doi.org/10.37193/cmi.2023.01.12","url":null,"abstract":"A finite group $G$ is said to be a POS-group if, for each $xin G$, the cardinality of the set ${yin G,,:,, o(y)=o(x)}$ is a divisor of the order of $G$. A POS-group $G$ is said to be a Hereditary Perfect Order Subset group if all even order subgroups of $G$ are POS-group. In this paper we study the structure of Hereditary perfect order subset groups.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121180038","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}
S. DIVYA MARY DAISE, S. DEEPTHI MARY TRESA, Shery Fernandez
A well known result in fuzzy group theory states that “level subgroups of any fuzzy subgroup of a finite group form a chain”. We check the validity of this statement in the intuitionistic fuzzy perspective. We do this using Dihedral Group $D_3$, which is a non-cyclic group. We prove that $D_3$ has 100 distinct intuitionistic fuzzy subgroups (IFSGs) upto isomorphism. The intuitionistic level subgroups (ILSGs) of exactly 76 among them make chains, and hence it can be concluded that the result is not true in the intuitionistic fuzzy perspective. We also enlist all the 100 distinct intuitionistic fuzzy subgroups of $D_3$ upto isomorphism.
{"title":"Intuitionistic Level Subgroups in the Dihedral Group D3","authors":"S. DIVYA MARY DAISE, S. DEEPTHI MARY TRESA, Shery Fernandez","doi":"10.37193/cmi.2022.02.04","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.04","url":null,"abstract":"A well known result in fuzzy group theory states that “level subgroups of any fuzzy subgroup of a finite group form a chain”. We check the validity of this statement in the intuitionistic fuzzy perspective. We do this using Dihedral Group $D_3$, which is a non-cyclic group. We prove that $D_3$ has 100 distinct intuitionistic fuzzy subgroups (IFSGs) upto isomorphism. The intuitionistic level subgroups (ILSGs) of exactly 76 among them make chains, and hence it can be concluded that the result is not true in the intuitionistic fuzzy perspective. We also enlist all the 100 distinct intuitionistic fuzzy subgroups of $D_3$ upto isomorphism.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127336004","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 research article, we investigate and study the intuitionistic fuzzy structure space of a $Gamma$-ring $M$ set up by the class of intuitionistic fuzzy prime ideals of $M$ called the intuitionistic fuzzy prime spectrum of $Gamma$-ring. Apart from studying basic properties of this structure space, we explore separation axioms, compactness, irreducibility and connectedness in this structure space.
{"title":"On Intuitionistic Fuzzy Structure Space On Γ-Ring","authors":"P. K. Sharma, Hem Lata, Nitin Bharadwa","doi":"10.37193/cmi.2022.02.07","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.07","url":null,"abstract":"In this research article, we investigate and study the intuitionistic fuzzy structure space of a $Gamma$-ring $M$ set up by the class of intuitionistic fuzzy prime ideals of $M$ called the intuitionistic fuzzy prime spectrum of $Gamma$-ring. Apart from studying basic properties of this structure space, we explore separation axioms, compactness, irreducibility and connectedness in this structure space.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"24 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114128404","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 derived some new algebraic results on continued fraction expansion of the ratio of the two consecutive balcobalancing numbers, circulant matrices and spectral norms, Pythagorean triples, characteristic polynomials and eigenvalues of the $n^{text{th}}$ power of the companion matrices, Cassini and Catalan identities, cross-ratios and Heisenberg groups related to balcobalancing numbers, Lucas-balcobalancing numbers and balcobalancers."
{"title":"Balcobalancing Numbers and Balcobalancers II","authors":"A. Tekcan, Meryem Yildiz","doi":"10.37193/cmi.2022.02.10","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.10","url":null,"abstract":"\"In this work, we derived some new algebraic results on continued fraction expansion of the ratio of the two consecutive balcobalancing numbers, circulant matrices and spectral norms, Pythagorean triples, characteristic polynomials and eigenvalues of the $n^{text{th}}$ power of the companion matrices, Cassini and Catalan identities, cross-ratios and Heisenberg groups related to balcobalancing numbers, Lucas-balcobalancing numbers and balcobalancers.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125626538","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 introduce and study the concept of strongly n-polynomial convexity functions and their some algebraic properties. We prove two Hermite-Hadamard type inequalities for the newly intro- duced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respec- tively at least one, is strongly n-polynomial convexity. Also, we compare the obtained results with both Hölder, Hölder- Işcan inequalities and power-mean, improved-power-mean integral inequalities and show that the re- sult obtained with H ̈older- ̇Is ̧can and improved power-mean inequalities give better approach than the others."
{"title":"Strongly n-polynomial convexity and related inequalities","authors":"Canan Ataman, M. Kadakal, İmdat ̇ İşca","doi":"10.37193/cmi.2022.02.02","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.02","url":null,"abstract":"\"In this paper, we introduce and study the concept of strongly n-polynomial convexity functions and their some algebraic properties. We prove two Hermite-Hadamard type inequalities for the newly intro- duced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respec- tively at least one, is strongly n-polynomial convexity. Also, we compare the obtained results with both Hölder, Hölder- Işcan inequalities and power-mean, improved-power-mean integral inequalities and show that the re- sult obtained with H ̈older- ̇Is ̧can and improved power-mean inequalities give better approach than the others.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122442101","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}
This article is to study the notions of hesitant fuzzy minimal clopen and hesitant fuzzy maximal clopen sets. In this article, we have proved hesitant fuzzy maximal and minimal clopen sets are independent to hesitant fuzzy minimal and maximal open sets(resp. closed sets). Using hesitant fuzzy disconnectedness certain properties of both hesitant fuzzy minimal and maximal clopen sets are discussed.
{"title":"Hesitant Fuzzy Maximal and Minimal Clopen Sets","authors":"A. Swaminathan, S. Sivaraja","doi":"10.37193/cmi.2022.02.09","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.09","url":null,"abstract":"This article is to study the notions of hesitant fuzzy minimal clopen and hesitant fuzzy maximal clopen sets. In this article, we have proved hesitant fuzzy maximal and minimal clopen sets are independent to hesitant fuzzy minimal and maximal open sets(resp. closed sets). Using hesitant fuzzy disconnectedness certain properties of both hesitant fuzzy minimal and maximal clopen sets are discussed.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126761638","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 main aim of the paper is to determine the extreme values of the product $P=a_1a_2cdots a_n$ under the constraints $sum_{i=1}^n a_i=S$ and $sum_{i=1}^{n}frac 1{a_i+1}=S_0$ for $nge 3$ nonnegative real numbers $a_1,a_2,ldots, a_n$ and some given constants $S$ and $S_0$. Some interesting applications of our results are provided as well.
{"title":"On a particular extension of the EV-Theorem","authors":"V. Cîrtoaje, L. Giugiuc","doi":"10.37193/cmi.2022.02.03","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.03","url":null,"abstract":"The main aim of the paper is to determine the extreme values of the product $P=a_1a_2cdots a_n$ under the constraints $sum_{i=1}^n a_i=S$ and $sum_{i=1}^{n}frac 1{a_i+1}=S_0$ for $nge 3$ nonnegative real numbers $a_1,a_2,ldots, a_n$ and some given constants $S$ and $S_0$. Some interesting applications of our results are provided as well.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133518512","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}
"n this paper, we consider almost type F -contraction on orthogonal metric space and we estab- lish the existence and uniqueness of fixed point of such mapping. At the end, we give an illustrative example."
{"title":"\"Some fixed point results for almost contraction on orthogonal metric space\"","authors":"Ö. Acar, Eşref Erdoǧan","doi":"10.37193/cmi.2022.02.01","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.01","url":null,"abstract":"\"n this paper, we consider almost type F -contraction on orthogonal metric space and we estab- lish the existence and uniqueness of fixed point of such mapping. At the end, we give an illustrative example.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132662546","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}
" This paper is concerned with the estimation of fourth Hankel determinant for a subclass of analytic functions defined by generalized S~{a}l~{a}gean operator in the open unit disc $E={z: |z|<1}$. The present study sets the stage for other researchers to investigate the fourth Hankel determinant for some other subclasses of analytic functions."
{"title":"\"Fourth Hankel determinant for a subclass of analytic functions defined by generalized Sălăgean operator\"","authors":"Gurmeet Singh, G. Singh, G. Singh","doi":"10.37193/cmi.2022.02.08","DOIUrl":"https://doi.org/10.37193/cmi.2022.02.08","url":null,"abstract":"\" This paper is concerned with the estimation of fourth Hankel determinant for a subclass of analytic functions defined by generalized S~{a}l~{a}gean operator in the open unit disc $E={z: |z|<1}$. The present study sets the stage for other researchers to investigate the fourth Hankel determinant for some other subclasses of analytic functions.\"","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122934733","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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