. In this article, we initiate the study of conformal vector fields in paracontact geometry. First, we establish that if the Reeb vector field ζ is a conformal vector field on N ( k ) -paracontact metric manifold, then the manifold becomes a para-Sasakian manifold. Next, we show that if the conformal vector field V is pointwise collinear with the Reeb vector field ζ , then the manifold recovers a para-Sasakian manifold as well as V is a constant multiple of ζ . Furthermore, we prove that if a 3-dimensional N ( k ) -paracontact metric manifold admits a Killing vector field V , then either it is a space of constant sectional curvature k or, V is an infinitesimal strict paracontact transformation. Besides these, we also investigate conformal vector fields on para-Kenmotsu manifolds.
{"title":"Conformal vector fields on N(k)-paracontact and para-Kenmotsu manifolds","authors":"Arpan Sardar, Uday Chand De","doi":"10.18514/mmn.2023.4098","DOIUrl":"https://doi.org/10.18514/mmn.2023.4098","url":null,"abstract":". In this article, we initiate the study of conformal vector fields in paracontact geometry. First, we establish that if the Reeb vector field ζ is a conformal vector field on N ( k ) -paracontact metric manifold, then the manifold becomes a para-Sasakian manifold. Next, we show that if the conformal vector field V is pointwise collinear with the Reeb vector field ζ , then the manifold recovers a para-Sasakian manifold as well as V is a constant multiple of ζ . Furthermore, we prove that if a 3-dimensional N ( k ) -paracontact metric manifold admits a Killing vector field V , then either it is a space of constant sectional curvature k or, V is an infinitesimal strict paracontact transformation. Besides these, we also investigate conformal vector fields on para-Kenmotsu manifolds.","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135659538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Simon Jaraldpushparaj, Britto Antony Xavier Gnanaprakasam, Sina Etemad, Shahram Rezapour
. In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into (cid:96) -difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results.
{"title":"Mittag-Leffler function for real index and its application in solving difference and differential equations","authors":"Simon Jaraldpushparaj, Britto Antony Xavier Gnanaprakasam, Sina Etemad, Shahram Rezapour","doi":"10.18514/mmn.2023.4117","DOIUrl":"https://doi.org/10.18514/mmn.2023.4117","url":null,"abstract":". In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into (cid:96) -difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results.","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135659809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems.
{"title":"Convergence, optimal points and applications","authors":"Shagun Sharma, Sumit Chandok","doi":"10.18514/mmn.2023.4265","DOIUrl":"https://doi.org/10.18514/mmn.2023.4265","url":null,"abstract":". In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems.","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135660489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anju Panwar, Pinki Lamba, Vladimir Rakočević, Dhananjay Gopal
. Enriched contraction, a class that contains the Picard -Banach contractions and some nonexpansive mappings, are generalized from Banach space framework into a nonlinear context, namely, geodesic metric spaces of nonpositive curvature. We establish general implications that extend the well-known results for enriched mappings formed on Banach spaces. We also look at the results for fixed points involving the contractions i
{"title":"New fixed point results of some enriched contractions in CAT(0) spaces","authors":"Anju Panwar, Pinki Lamba, Vladimir Rakočević, Dhananjay Gopal","doi":"10.18514/mmn.2023.4159","DOIUrl":"https://doi.org/10.18514/mmn.2023.4159","url":null,"abstract":". Enriched contraction, a class that contains the Picard -Banach contractions and some nonexpansive mappings, are generalized from Banach space framework into a nonlinear context, namely, geodesic metric spaces of nonpositive curvature. We establish general implications that extend the well-known results for enriched mappings formed on Banach spaces. We also look at the results for fixed points involving the contractions i","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135660509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We characterize the α -large submodules of α -modules in terms of certain sequences of ordinals, and give some of their interesting properties. Also, we deal with α -large submodules of the closure of an unbounded direct sum of uniserial modules, and the α -large submodules of the smallest α -pure fully invariant submodules of the closure containing a given element.
{"title":"Characterizations of generalized submodules of QTAG-modules","authors":"Ayazul Hasan","doi":"10.18514/mmn.2023.4051","DOIUrl":"https://doi.org/10.18514/mmn.2023.4051","url":null,"abstract":". We characterize the α -large submodules of α -modules in terms of certain sequences of ordinals, and give some of their interesting properties. Also, we deal with α -large submodules of the closure of an unbounded direct sum of uniserial modules, and the α -large submodules of the smallest α -pure fully invariant submodules of the closure containing a given element.","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135659804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. We present new formulas for the g -Drazin inverse of the sum in a Banach algebra. The block representations for the g -Drazin inverse of a 2 × 2 block operator matrix are thereby established. These extend the known results obtained in [3,7].
{"title":"Block representations for the g-Drazin inverse in Banach algebras","authors":"Huanyin Chen, Marjan Sheibani","doi":"10.18514/mmn.2023.3925","DOIUrl":"https://doi.org/10.18514/mmn.2023.3925","url":null,"abstract":". We present new formulas for the g -Drazin inverse of the sum in a Banach algebra. The block representations for the g -Drazin inverse of a 2 × 2 block operator matrix are thereby established. These extend the known results obtained in [3,7].","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135660097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In current study, we establish some new quantum Hermite Hadamard-Jensen-Mercer type integral inequalities by way of recently newly defined integral.Then we investigate the connections between our results and those in earlier works.Furthermore, we present some examples which satisfied our main outcomes. We expect that this innovative way opens many avenues for interested researchers will reconcile discovering further quantum approximations of Hermite-Hadamard type variants for other classes of convex functions, and, additionally, to discover uses in the aforementioned scientific disciplines.
{"title":"On new version of Hermite-Jensen-Mercer inequalities for newly defined quantum integral","authors":"Ghazala Gulshan, Hüseyin Budak, Rashida Hussain, Asad Sadiq, Pınar Kösem","doi":"10.18514/mmn.2023.4220","DOIUrl":"https://doi.org/10.18514/mmn.2023.4220","url":null,"abstract":". In current study, we establish some new quantum Hermite Hadamard-Jensen-Mercer type integral inequalities by way of recently newly defined integral.Then we investigate the connections between our results and those in earlier works.Furthermore, we present some examples which satisfied our main outcomes. We expect that this innovative way opens many avenues for interested researchers will reconcile discovering further quantum approximations of Hermite-Hadamard type variants for other classes of convex functions, and, additionally, to discover uses in the aforementioned scientific disciplines.","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135660319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tauberian theorems for Nörlund-Cesáro mean via statistically convergence in m-Normed spaces","authors":"Naim Braha, Valdete Loku, Ram Mohapatra","doi":"10.18514/mmn.2023.3976","DOIUrl":"https://doi.org/10.18514/mmn.2023.3976","url":null,"abstract":"","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135658925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. In this paper, we introduce three new fractional operators, MRL fractional integral, MRL fractional derivative and MC fractional derivative operators, which including generalized M-series in their kernels and give some of their fundamental properties. Then we apply Laplace, Mellin and beta integral transformations to the new fractional operators and obtain conclusions involving classical gamma and beta and modified gamma and beta functions. As examples, we also obtain similar conclusions by applying new fractional operators to the functions z λ and ( 1 − az ) − λ . Furthermore, we present the relationships of the new fractional operators with other fractional operators in the literature. Finally, we compare the behavior of the function z 2 in classical Riemann-Liouville and Caputo fractional operators and MRL and MC fractional operators for orders ε = 0 . 2 , 0 . 4 , 0 . 6 , 0 . 8.
{"title":"On the new fractional operators generating modified gamma and beta functions","authors":"Enes Ata","doi":"10.18514/mmn.2023.4124","DOIUrl":"https://doi.org/10.18514/mmn.2023.4124","url":null,"abstract":". In this paper, we introduce three new fractional operators, MRL fractional integral, MRL fractional derivative and MC fractional derivative operators, which including generalized M-series in their kernels and give some of their fundamental properties. Then we apply Laplace, Mellin and beta integral transformations to the new fractional operators and obtain conclusions involving classical gamma and beta and modified gamma and beta functions. As examples, we also obtain similar conclusions by applying new fractional operators to the functions z λ and ( 1 − az ) − λ . Furthermore, we present the relationships of the new fractional operators with other fractional operators in the literature. Finally, we compare the behavior of the function z 2 in classical Riemann-Liouville and Caputo fractional operators and MRL and MC fractional operators for orders ε = 0 . 2 , 0 . 4 , 0 . 6 , 0 . 8.","PeriodicalId":51252,"journal":{"name":"Miskolc Mathematical Notes","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":"135659524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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