Pub Date : 2023-06-13DOI: 10.24193/subbmath.2023.2.01
L. Agamalieva, Y. Gasimov, J. E. Napoles-Valdes
"In this paper, we present generalized versions of the Wirtinger inequality, which contains as particular cases many of the well-known versions of this classic isoperimetric inequality. Some applications and open problems are also presented in the work."
{"title":"On a generalization of the Wirtinger inequality and some its applications","authors":"L. Agamalieva, Y. Gasimov, J. E. Napoles-Valdes","doi":"10.24193/subbmath.2023.2.01","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.01","url":null,"abstract":"\"In this paper, we present generalized versions of the Wirtinger inequality, which contains as particular cases many of the well-known versions of this classic isoperimetric inequality. Some applications and open problems are also presented in the work.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76794404","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.06
Nityagopal Biswas, P. Sahoo
"In this paper, we investigate the relations between the growth of entire coefficients and that of solutions of complex homogeneous and non-homogeneous linear difference equations with entire coefficients of $% varphi $-order by using a slow growth scale, the $varphi $-order, where $% varphi $ is a non-decreasing unbounded function. We extend some precedent results due to Zheng and Tu (2011) [15] and others."
{"title":"Growth properties of solutions of linear difference equations with coefficients having $varphi$-order","authors":"Nityagopal Biswas, P. Sahoo","doi":"10.24193/subbmath.2023.2.06","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.06","url":null,"abstract":"\"In this paper, we investigate the relations between the growth of entire coefficients and that of solutions of complex homogeneous and non-homogeneous linear difference equations with entire coefficients of $% varphi $-order by using a slow growth scale, the $varphi $-order, where $% varphi $ is a non-decreasing unbounded function. We extend some precedent results due to Zheng and Tu (2011) [15] and others.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75180580","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.05
Hardeep Kaur, R. Brar, S. S. Billing
To obtain the main result of the present paper we use the technique of differential subordination. As special cases of our main result, we obtain sufficient conditions for $finmathcal A$ to be $phi-$like, starlike and close-to-convex in a parabolic region.
{"title":"Certain sufficient conditions for phi-like functions in a parabolic region","authors":"Hardeep Kaur, R. Brar, S. S. Billing","doi":"10.24193/subbmath.2023.2.05","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.05","url":null,"abstract":"To obtain the main result of the present paper we use the technique of differential subordination. As special cases of our main result, we obtain sufficient conditions for $finmathcal A$ to be $phi-$like, starlike and close-to-convex in a parabolic region.","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90858597","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.07
Andra Manu
"In this paper, we obtain certain generalizations of some results from [13] and [14]. Let $Phi_{n, alpha, beta}$ be the extension operator introduced in cite{GrahamHamadaKohrSuffridge} and let $Phi_{n, Q}$ be the extension operator introduced in [7]. Let $a in C$, $b in R$ be such that $|1-a| < b leq {rm Re} a$. We consider the Janowski classes $S^*(a,b, B)$ and $A S^*(a,b, B)$ with complex coefficients introduced in [16]. In the case $n=1$, we denote $S^*(a,b, mathbb{B}^1)$ by $S^*(a,b)$ and $A S^*(a,b, mathbb{B}^1)$ by $A S^*(a,b)$. We shall prove that the following preservation properties concerning the extension operator $Phi_{n, alpha, beta}$ hold: $Phi_{n, alpha, beta} (S^*(a,b)) subseteq S^*(a,b, B)$, $Phi_{n, alpha, beta} (A S^*(a,b)) subseteq A S^*(a,b, B)$. Also, we prove similar results for the extension operator $Phi_{n, Q}$: $$Phi_{n, Q}(S^*(a,b)) subseteq S^*(a,b, B), Phi_{n, Q}(A S^*(a,b)) subseteq A S^*(a,b, B).$$ "
在本文中，我们对[13]和[14]的一些结果进行了一定的推广。设$Phi_{n, alpha, beta}$为cite{GrahamHamadaKohrSuffridge}中引入的扩展算子，$Phi_{n, Q}$为[7]中引入的扩展算子。让$a in C$, $b in R$这样$|1-a| < b leq {rm Re} a$。我们考虑在[16]中引入的具有复系数的Janowski类$S^*(a,b, B)$和$A S^*(a,b, B)$。对于$n=1$，我们用$S^*(a,b)$表示$S^*(a,b, mathbb{B}^1)$，用$A S^*(a,b)$表示$A S^*(a,b, mathbb{B}^1)$。我们将证明下列关于扩展算子$Phi_{n, alpha, beta}$的保存性质成立:$Phi_{n, alpha, beta} (S^*(a,b)) subseteq S^*(a,b, B)$, $Phi_{n, alpha, beta} (A S^*(a,b)) subseteq A S^*(a,b, B)$。此外，我们还证明了扩展算子$Phi_{n, Q}$: $$Phi_{n, Q}(S^*(a,b)) subseteq S^*(a,b, B), Phi_{n, Q}(A S^*(a,b)) subseteq A S^*(a,b, B).$$的类似结果。
{"title":"Extension operators and Janowski starlikeness with complex coe cients","authors":"Andra Manu","doi":"10.24193/subbmath.2023.2.07","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.07","url":null,"abstract":"\"In this paper, we obtain certain generalizations of some results from [13] and [14]. Let $Phi_{n, alpha, beta}$ be the extension operator introduced in cite{GrahamHamadaKohrSuffridge} and let $Phi_{n, Q}$ be the extension operator introduced in [7]. Let $a in C$, $b in R$ be such that $|1-a| < b leq {rm Re} a$. We consider the Janowski classes $S^*(a,b, B)$ and $A S^*(a,b, B)$ with complex coefficients introduced in [16]. In the case $n=1$, we denote $S^*(a,b, mathbb{B}^1)$ by $S^*(a,b)$ and $A S^*(a,b, mathbb{B}^1)$ by $A S^*(a,b)$. We shall prove that the following preservation properties concerning the extension operator $Phi_{n, alpha, beta}$ hold: $Phi_{n, alpha, beta} (S^*(a,b)) subseteq S^*(a,b, B)$, $Phi_{n, alpha, beta} (A S^*(a,b)) subseteq A S^*(a,b, B)$. Also, we prove similar results for the extension operator $Phi_{n, Q}$: $$Phi_{n, Q}(S^*(a,b)) subseteq S^*(a,b, B), Phi_{n, Q}(A S^*(a,b)) subseteq A S^*(a,b, B).$$ \"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89693751","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.14
Ionut T. Iancu
"In this paper we generalize the result on statistical uniform convergence in the Korovkin theorem for positive and linear operators in C([a; b]), to the more general case of monotone and sublinear operators. Our result is illustrated by concrete examples."
本文推广了C([a];B])，到更一般的单调和次线性算子的情况。我们的结果得到了具体实例的验证。
{"title":"Statistical Korovkin-type theorem for monotone and sublinear operators","authors":"Ionut T. Iancu","doi":"10.24193/subbmath.2023.2.14","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.14","url":null,"abstract":"\"In this paper we generalize the result on statistical uniform convergence in the Korovkin theorem for positive and linear operators in C([a; b]), to the more general case of monotone and sublinear operators. Our result is illustrated by concrete examples.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88175948","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.10
Farah Balaadich, E. Azroul
"Using the theory of Young measures, we prove the existence of solutions to a strongly quasilinear parabolic system [frac{partial u}{partial t}+A(u)=f,] where $A(u)=-text{div},sigma(x,t,u,Du)+sigma_0(x,t,u,Du)$, $sigma(x,t,u,Du)$ and $sigma_0(x,t,u,Du)$ are satisfy some conditions and $fin L^{p'}(0,T;W^{-1,p'}(Omega;R^m))$."
{"title":"Strongly quasilinear parabolic systems","authors":"Farah Balaadich, E. Azroul","doi":"10.24193/subbmath.2023.2.10","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.10","url":null,"abstract":"\"Using the theory of Young measures, we prove the existence of solutions to a strongly quasilinear parabolic system [frac{partial u}{partial t}+A(u)=f,] where $A(u)=-text{div},sigma(x,t,u,Du)+sigma_0(x,t,u,Du)$, $sigma(x,t,u,Du)$ and $sigma_0(x,t,u,Du)$ are satisfy some conditions and $fin L^{p'}(0,T;W^{-1,p'}(Omega;R^m))$.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76549731","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.08
S. Santra
"In this paper, necessary and sufficient conditions are establish of the solutions to second-order delay differential equations of the form begin{equation} Big(r(t)big(x'(t)big)^gammaBig)' +sum_{i=1}^m q_i(t)f_ibig(x(sigma_i(t))big)=0 text{ for } t geq t_0,notag end{equation} We consider two cases when $f_i(u)/u^beta$ is non-increasing for $betagamma$ where $beta$ and $gamma$ are the quotient of two positive odd integers. Our main tool is Lebesgue's Dominated Convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem."
本文建立了形式为begin{equation} Big(r(t)big(x'(t)big)^gammaBig)' +sum_{i=1}^m q_i(t)f_ibig(x(sigma_i(t))big)=0 text{ for } t geq t_0,notag end{equation}的二阶时滞微分方程解的充分必要条件。我们考虑两种情况，即$f_i(u)/u^beta$对$betagamma$不递增，其中$beta$和$gamma$是两个正奇数的商。我们的主要工具是勒贝格主导收敛定理。文中还举例说明了结果的适用性，并说明了一个有待解决的问题。
{"title":"\"Necessary and sufficient conditions for oscillation of second-order differential equation with several delays\"","authors":"S. Santra","doi":"10.24193/subbmath.2023.2.08","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.08","url":null,"abstract":"\"In this paper, necessary and sufficient conditions are establish of the solutions to second-order delay differential equations of the form begin{equation} Big(r(t)big(x'(t)big)^gammaBig)' +sum_{i=1}^m q_i(t)f_ibig(x(sigma_i(t))big)=0 text{ for } t geq t_0,notag end{equation} We consider two cases when $f_i(u)/u^beta$ is non-increasing for $beta<gamma$, and non-decreasing for $beta>gamma$ where $beta$ and $gamma$ are the quotient of two positive odd integers. Our main tool is Lebesgue's Dominated Convergence theorem. Examples illustrating the applicability of the results are also given, and state an open problem.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78875088","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.02
G. Oros
"In this paper we introduce the Ruscheweyh-Bernardi differential-integral operator $T^m:Ato A$ defined by $$T^m[f](z)=(1-lambda )R^m [f](z)+lambda B^m[f](z), zin U,$$ where $R^m$ is the Ruscheweyh differential operator (Definition ref{d1.2}) and $B^m$ is the Bernardi integral operator (Definition ref{d1.1}). By using the operator $T^m$, the class of univalent functions denoted by $T^m(lambda ,beta )$, $0le lambda le 1$, $0le beta <1$, is defined and several differential subordinations are studied."
{"title":"Sufficient conditions for univalence obtained by using the Ruscheweyh-Bernardi differential-integral operator","authors":"G. Oros","doi":"10.24193/subbmath.2023.2.02","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.02","url":null,"abstract":"\"In this paper we introduce the Ruscheweyh-Bernardi differential-integral operator $T^m:Ato A$ defined by $$T^m[f](z)=(1-lambda )R^m [f](z)+lambda B^m[f](z), zin U,$$ where $R^m$ is the Ruscheweyh differential operator (Definition ref{d1.2}) and $B^m$ is the Bernardi integral operator (Definition ref{d1.1}). By using the operator $T^m$, the class of univalent functions denoted by $T^m(lambda ,beta )$, $0le lambda le 1$, $0le beta <1$, is defined and several differential subordinations are studied.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"119 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85254025","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.18
I. Rus
Let $(X,d)$ be a complete metric space, $(Y,rho)$ be a metric space and $f,g:Xto Y$ be two mappings. The problem is to give metric conditions which imply that, $C(f,g):={xin X | f(x)=g(x)}not=emptyset$. In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, emph{Teoria punctului fix ^in analiza funcc tionalu a}, Babec s-Bolyai Univ., Cluj-Napoca, 1973), A. Buicu a (A. Buicu a, emph{Principii de coincidenc tu a c si aplicac tii}, Presa Univ. Clujeanu a, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, emph{Co-vering mappings in metric spaces and fixed points}, Dokl. Math., 76(2007), no.2, 665-668) appear as corollaries. In the case of multivalued mappings our result generalizes some results given by A.V. Arutyunov and by A. Petruc sel (A. Petruc sel, emph{A generalization of Peetre-Rus theorem}, Studia Univ. Babec s-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied.
设$(X,d)$是一个完备的度量空间，$(Y,rho)$是一个度量空间，$f,g:Xto Y$是两个映射。问题是给出度量条件，这意味着$C(f,g):={xin X | f(x)=g(x)}not=emptyset$。本文给出了一个抽象的重合点结果，其中一些结果如peetrer -Rus (I.A. Rus, emph{Teoria punctului fix n analiza funcctionalua}, Babe c s-Bolyai university, Cluj-Napoca, 1973)， a . Buic u a (a . Buic u a, emph{Principii de coincidenctuacsi aplicactii}, Presa Univ. Clujean u a, Cluj-Napoca，A.V. Arutyunov, 2007)和A.V. Arutyunov emph{(A.V. Arutyunov)}。数学。， 76(2007)， no。(2665 -668)似乎是必然结果。在多值映射的情况下，我们的结果推广了A.V. Arutyunov和A. Petru c sel (A. Petru c sel，对peter emph{- rus定理的推广}，Studia university . Babe c s-Bolyai Math)给出的一些结果。， 35(1990)， 81-85)。研究了对度量不动点理论的影响。
{"title":"Around metric coincidence point theory","authors":"I. Rus","doi":"10.24193/subbmath.2023.2.18","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.18","url":null,"abstract":"Let $(X,d)$ be a complete metric space, $(Y,rho)$ be a metric space and $f,g:Xto Y$ be two mappings. The problem is to give metric conditions which imply that, $C(f,g):={xin X | f(x)=g(x)}not=emptyset$. In this paper we give an abstract coincidence point result with respect to which some results such as of Peetre-Rus (I.A. Rus, emph{Teoria punctului fix ^in analiza funcc tionalu a}, Babec s-Bolyai Univ., Cluj-Napoca, 1973), A. Buicu a (A. Buicu a, emph{Principii de coincidenc tu a c si aplicac tii}, Presa Univ. Clujeanu a, Cluj-Napoca, 2001) and A.V. Arutyunov (A.V. Arutyunov, emph{Co-vering mappings in metric spaces and fixed points}, Dokl. Math., 76(2007), no.2, 665-668) appear as corollaries. In the case of multivalued mappings our result generalizes some results given by A.V. Arutyunov and by A. Petruc sel (A. Petruc sel, emph{A generalization of Peetre-Rus theorem}, Studia Univ. Babec s-Bolyai Math., 35(1990), 81-85). The impact on metric fixed point theory is also studied.","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"402 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76591842","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 : 2023-06-13DOI: 10.24193/subbmath.2023.2.13
J. Jonnalagadda
"In this article, we give su cient conditions for the existence, uniqueness and Ulam{Hyers stability of solutions for a coupled system of two-point nabla fractional di erence boundary value problems subject to anti-periodic boundary conditions, using the vector approach of Precup [4, 14, 19, 21]. Some examples are included to illustrate the theory."
{"title":"A coupled system of fractional difference equations with anti-periodic boundary conditions","authors":"J. Jonnalagadda","doi":"10.24193/subbmath.2023.2.13","DOIUrl":"https://doi.org/10.24193/subbmath.2023.2.13","url":null,"abstract":"\"In this article, we give su cient conditions for the existence, uniqueness and Ulam{Hyers stability of solutions for a coupled system of two-point nabla fractional di erence boundary value problems subject to anti-periodic boundary conditions, using the vector approach of Precup [4, 14, 19, 21]. Some examples are included to illustrate the theory.\"","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87743116","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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