In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums. Let H denote the class of functions f that are harmonic univalent and sense-preserving in U =;fz :jzj > 1g which are of the form
{"title":"Partial sums of a certain harmonic univalent meromorphic functions","authors":"M. Aouf, R. El-Ashwah, J. Dziok, J. Stankiewicz","doi":"10.7862/RF.2014.1","DOIUrl":"https://doi.org/10.7862/RF.2014.1","url":null,"abstract":"In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums. Let H denote the class of functions f that are harmonic univalent and sense-preserving in U =;fz :jzj > 1g which are of the form","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122442794","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 problem of finding out the region which contains all or a prescribed number of zeros of a polynomial P (z) := n ∑ j=0 ajz j has a long history and dates back to the earliest days when the geometrical representation of complex numbers was introduced. In this paper, we present certain results concerning the location of the zeros of Lacunarytype polynomials P (z) := a0 + n ∑ j=μ ajz j in a disc centered at the origin.
{"title":"Number of Zeros of a Polynomial (Lacunary-type) in a Disk","authors":"Idrees Qasim, Tawheeda Rasool, A. Liman","doi":"10.7862/RF.2018.13","DOIUrl":"https://doi.org/10.7862/RF.2018.13","url":null,"abstract":"The problem of finding out the region which contains all or a prescribed number of zeros of a polynomial P (z) := n ∑ j=0 ajz j has a long history and dates back to the earliest days when the geometrical representation of complex numbers was introduced. In this paper, we present certain results concerning the location of the zeros of Lacunarytype polynomials P (z) := a0 + n ∑ j=μ ajz j in a disc centered at the origin.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122509100","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}
and let A (1) = A. For f ,F ∈ H(U), the function f(z) is said to be subordinate to F (z), or F (z) is superordinate to f(z), if there exists a function ω(z) analytic in U with ω(0) = 0 and |ω(z)| < 1(z ∈ U), such that f(z) = F (ω(z)). In such a case we write f(z) ≺ F (z). If F is univalent, then f(z) ≺ F (z) if and only if f(0) = F (0) and f(U) ⊂ F (U) (see [14] and [15]). Let φ : C×U → C and h (z) be univalent in U. If p (z) is analytic in U and satisfies the first order differential subordination:
{"title":"Preserving subordination and superordination results of generalized Srivastava-Attiya operator","authors":"M. Aouf, A. Mostafa, A. M. Shahin, S. Madian","doi":"10.7862/RF.2013.2","DOIUrl":"https://doi.org/10.7862/RF.2013.2","url":null,"abstract":"and let A (1) = A. For f ,F ∈ H(U), the function f(z) is said to be subordinate to F (z), or F (z) is superordinate to f(z), if there exists a function ω(z) analytic in U with ω(0) = 0 and |ω(z)| < 1(z ∈ U), such that f(z) = F (ω(z)). In such a case we write f(z) ≺ F (z). If F is univalent, then f(z) ≺ F (z) if and only if f(0) = F (0) and f(U) ⊂ F (U) (see [14] and [15]). Let φ : C×U → C and h (z) be univalent in U. If p (z) is analytic in U and satisfies the first order differential subordination:","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121123514","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}
Submitted by: Marian Mat loka Abstract: In the present paper we introduce some new generalized classes of dierence sequence spaces of fuzzy numbers dened by a se- quence of Orlicz functions. We also make an eort to study some topolog- ical properties and prove some inclusion relations between these spaces.
{"title":"Some new generalized classes of dierence sequences of fuzzy numbers dened by a sequence of Orlicz functions","authors":"S. Sharma","doi":"10.7862/RF.2013.8","DOIUrl":"https://doi.org/10.7862/RF.2013.8","url":null,"abstract":"Submitted by: Marian Mat loka Abstract: In the present paper we introduce some new generalized classes of dierence sequence spaces of fuzzy numbers dened by a se- quence of Orlicz functions. We also make an eort to study some topolog- ical properties and prove some inclusion relations between these spaces.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130835901","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}
: We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vector-valued ordinary differential equations. Our conclusions generalize many well-known results.
{"title":"Fixed Point Theorems for Monotone Mappings in Ordered Banach Spaces Under Weak Topology Features","authors":"A. Alahmari, M. Mabrouk, M. Taoudi","doi":"10.7862/rf.2019.1","DOIUrl":"https://doi.org/10.7862/rf.2019.1","url":null,"abstract":": We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vector-valued ordinary differential equations. Our conclusions generalize many well-known results.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132251473","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}
{"title":"Inequality for Polynomials with Prescribed Zeros","authors":"V. K. Jain","doi":"10.7862/rf.2020.5","DOIUrl":"https://doi.org/10.7862/rf.2020.5","url":null,"abstract":"","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"256 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132822873","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 sharp companion of the generalized trapezoid inequality is introduced. Applications to quadrature formula are pointed out.
给出了广义梯形不等式的一个尖锐伴形。指出了正交公式的应用。
{"title":"A Companion of the generalized trapezoid inequality and applications","authors":"M. Alomari","doi":"10.7862/RF.2013.1","DOIUrl":"https://doi.org/10.7862/RF.2013.1","url":null,"abstract":"A sharp companion of the generalized trapezoid inequality is introduced. Applications to quadrature formula are pointed out.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"294 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114095767","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 purpose of this review article is to present the concept of a regulated function and to indicate the connection of the class of regulated functions with other significant classes of functions. In par-ticular, we give a characterization of regulated functions in terms of step functions and we show that the linear space of regulated functions forms a Banach space under the classical supremum norm.
{"title":"On regulated functions","authors":"Józef Banaś, Mariola Kot","doi":"10.7862/RF.2017.2","DOIUrl":"https://doi.org/10.7862/RF.2017.2","url":null,"abstract":": The main purpose of this review article is to present the concept of a regulated function and to indicate the connection of the class of regulated functions with other significant classes of functions. In par-ticular, we give a characterization of regulated functions in terms of step functions and we show that the linear space of regulated functions forms a Banach space under the classical supremum norm.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116509791","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}
We propose a method of solving the problem with non- homogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace L H, in which the vec- tors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.
{"title":"Problem with integral condition for evolution equation","authors":"P. Kalenyuk, G. Kuduk, I. Kohút, Z. Nytrebych","doi":"10.7862/RF.2015.6","DOIUrl":"https://doi.org/10.7862/RF.2015.6","url":null,"abstract":"We propose a method of solving the problem with non- homogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace L H, in which the vec- tors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132140182","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}
Abstract: The paper discusses the existence of solutions for Cauchytype problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.
{"title":"On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order","authors":"M. Metwali","doi":"10.7862/RF.2017.8","DOIUrl":"https://doi.org/10.7862/RF.2017.8","url":null,"abstract":"Abstract: The paper discusses the existence of solutions for Cauchytype problem of fractional order in the space of Lebesgue integrable functions on bounded interval. Some qualitative properties of solutions are presented such as monotonicity, uniqueness and continuous dependence on the initial data. The main tools used are measure of weak (strong) noncompactness, Darbo fixed point theorem and fractional calculus.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121934922","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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