Pub Date : 2021-08-13DOI: 10.30538/psrp-oma2021.0090
M. Rossafi, A. Kari
In this paper, we present the notion of generalized (F)-expansive mapping incomplete rectangular metric spaces and study various fixed point theorems for such mappings. The findings of this paper, generalize and improve many existing results in the literature.
{"title":"Some fixed point theorems for (F)-expansive mapping in generalized metric spaces","authors":"M. Rossafi, A. Kari","doi":"10.30538/psrp-oma2021.0090","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0090","url":null,"abstract":"In this paper, we present the notion of generalized (F)-expansive mapping incomplete rectangular metric spaces and study various fixed point theorems for such mappings. The findings of this paper, generalize and improve many existing results in the literature.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42199588","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 : 2021-08-12DOI: 10.30538/psrp-oma2021.0089
Nour El Imane Khadidja Cheriet, B. Belaïdi
In this paper, we precise the hyper order of solutions for a class of higher-order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second-order case. These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon.
{"title":"The hyper order and fixed points of solutions of a class of linear differential equations","authors":"Nour El Imane Khadidja Cheriet, B. Belaïdi","doi":"10.30538/psrp-oma2021.0089","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0089","url":null,"abstract":"In this paper, we precise the hyper order of solutions for a class of higher-order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second-order case. These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46046716","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 : 2021-06-29DOI: 10.30538/psrp-oma2021.0086
C. Chesneau
Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.
{"title":"A study of the power-cosine copula","authors":"C. Chesneau","doi":"10.30538/psrp-oma2021.0086","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0086","url":null,"abstract":"Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69238008","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 : 2021-06-29DOI: 10.30538/psrp-oma2021.0087
W. L. Otae, N. B. Okelo, O. Ongati
In this paper, we give characterizations of orthogonality conditions in certain classes of normed spaces. We first consider Range-Kernel orthogonality in norm-attainable classes then we characterize orthogonality conditions for Jordan elementary operators.
{"title":"Characterization of orthogonality conditions in certain classes of normed spaces","authors":"W. L. Otae, N. B. Okelo, O. Ongati","doi":"10.30538/psrp-oma2021.0087","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0087","url":null,"abstract":"In this paper, we give characterizations of orthogonality conditions in certain classes of normed spaces. We first consider Range-Kernel orthogonality in norm-attainable classes then we characterize orthogonality conditions for Jordan elementary operators.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48976266","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 : 2021-06-11DOI: 10.30538/psrp-oma2021.0085
A. Al-Gonah, Ahmed Ali Atash
Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.
{"title":"On generalization of extended Gegenbauer polynomials of two variables","authors":"A. Al-Gonah, Ahmed Ali Atash","doi":"10.30538/psrp-oma2021.0085","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0085","url":null,"abstract":"Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46684849","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 : 2021-01-01DOI: 10.30538/psrp-oma2021.0080
T. Hamaizia
The purpose of this paper is to prove a fixed point theorem for (C)-class functions in complete (b)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.
{"title":"Fixed point theorems for generalized (left( psi ,varphi ,Fright) )-contraction type mappings in (b)-metric spaces with applications","authors":"T. Hamaizia","doi":"10.30538/psrp-oma2021.0080","DOIUrl":"https://doi.org/10.30538/psrp-oma2021.0080","url":null,"abstract":"The purpose of this paper is to prove a fixed point theorem for (C)-class functions in complete (b)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69237999","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 : 2020-12-27DOI: 10.30538/PSRP-OMA2020.0075
Benard Okelo
In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.
{"title":"On properties of inner product type integral transformers","authors":"Benard Okelo","doi":"10.30538/PSRP-OMA2020.0075","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2020.0075","url":null,"abstract":"In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49403830","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 : 2020-12-27DOI: 10.30538/PSRP-OMA2020.0076
B. Venkateswarlu, P. Reddy, Sujatha S. Sridevi
In this paper, we introduce a new class of analytic functions by using the lambda operator and obtain some subordination results.
本文利用lambda算子引入了一类新的解析函数，并得到了一些从属结果。
{"title":"Some applications of second-order differential subordination for a class of analytic function defined by the lambda operator","authors":"B. Venkateswarlu, P. Reddy, Sujatha S. Sridevi","doi":"10.30538/PSRP-OMA2020.0076","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2020.0076","url":null,"abstract":"In this paper, we introduce a new class of analytic functions by using the lambda operator and obtain some subordination results.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47727953","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 : 2020-12-21DOI: 10.30538/PSRP-OMA2020.0074
M. Omaba, L. Omenyi
Consider a class of two-point Boundary Value Problems (BVP) for a stochastic nonlinear fractional order differential equation (D^alpha u(t)=lambdasqrt{I^beta[sigma^2(t,u(t))]}dot{w}(t) ,0< t< 1) with boundary conditions (u(0)=0,,,u'(0)=u'(1)=0,) where (lambda>0) is a level of the noise term, (sigma:[0,1]timesmathbb{R}rightarrowmathbb{R}) is continuous, (dot{w}(t)) is a generalized derivative of Wiener process (Gaussian white noise), (D^alpha) is the Riemann-Liouville fractional differential operator of order (alphain (3,4)) and (I^beta,,,beta>0) is a fractional integral operator. We formulate the solution of the equation via a stochastic Volterra-type equation and investigate its existence and uniqueness under some precise linearity conditions using contraction fixed point theorem. A case of the above BVP for a stochastic nonlinear second order differential equation for (alpha=2) and (beta=0) with (u(0)=u(1)=0) is also studied.
{"title":"Boundary value problems for a class of stochastic nonlinear fractional order differential equations","authors":"M. Omaba, L. Omenyi","doi":"10.30538/PSRP-OMA2020.0074","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2020.0074","url":null,"abstract":"Consider a class of two-point Boundary Value Problems (BVP) for a stochastic nonlinear fractional order differential equation (D^alpha u(t)=lambdasqrt{I^beta[sigma^2(t,u(t))]}dot{w}(t) ,0< t< 1) with boundary conditions (u(0)=0,,,u'(0)=u'(1)=0,) where (lambda>0) is a level of the noise term, (sigma:[0,1]timesmathbb{R}rightarrowmathbb{R}) is continuous, (dot{w}(t)) is a generalized derivative of Wiener process (Gaussian white noise), (D^alpha) is the Riemann-Liouville fractional differential operator of order (alphain (3,4)) and (I^beta,,,beta>0) is a fractional integral operator. We formulate the solution of the equation via a stochastic Volterra-type equation and investigate its existence and uniqueness under some precise linearity conditions using contraction fixed point theorem. A case of the above BVP for a stochastic nonlinear second order differential equation for (alpha=2) and (beta=0) with (u(0)=u(1)=0) is also studied.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42552531","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 : 2020-12-16DOI: 10.30538/PSRP-OMA2020.0073
Abdissa Fekadu, Kidane Koyas, S. Gebregiorgis
The purpose of this article is to construct fixed point theorems and prove the existence and uniqueness of common fixed point results of ( s-alpha ) contraction for a pair of maps in the setting of ( b ) - dislocated metric spaces. Our results extend and generalize several well-known comparable results in the literature. The study procedure we used was that of Zoto and Kumari [1]. Furthermore, we provided an example in support of our main result.
本文的目的是构造( b )位错度量空间中一对映射的不动点定理，并证明了( s-alpha )收缩的公共不动点结果的存在唯一性。我们的结果扩展和推广了文献中几个著名的可比结果。我们采用Zoto和Kumari bbb的研究程序。此外，我们还提供了一个例子来支持我们的主要结果。
{"title":"Common fixed point results of $s$-$alpha $ contraction for a pair of maps in $b$-dislocated metric spaces","authors":"Abdissa Fekadu, Kidane Koyas, S. Gebregiorgis","doi":"10.30538/PSRP-OMA2020.0073","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2020.0073","url":null,"abstract":"The purpose of this article is to construct fixed point theorems and prove the existence and uniqueness of common fixed point results of ( s-alpha ) contraction for a pair of maps in the setting of ( b ) - dislocated metric spaces. Our results extend and generalize several well-known comparable results in the literature. The study procedure we used was that of Zoto and Kumari [1]. Furthermore, we provided an example in support of our main result.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45549502","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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