Abstract In this paper, we consider new subclasses 𝔗𝔖n(µ, a, b, ℓ, τ, γ) and 𝕽n(µ, a, b, ℓ, τ, γ) of analytic univalent functions defined by Erdelyi-Kober integral operator. We obtain coefficient inequalities, inclusion relationships involving the (n, δ)- neighborhoods, partial sums and integral mean inequalities for the functions that belongs to these classes. Also, subordinating factor sequence for the functions in the classes 𝔖n(µ, a, b, ℓ, τ, γ) and 𝕽n(µ, a, b, ℓ, τ, γ) are derived.
{"title":"On certain classes of analytic functions of Complex order defined by Erdelyi-Kober integral operator","authors":"T. Rosy, Asha Thomas","doi":"10.2478/gm-2021-0012","DOIUrl":"https://doi.org/10.2478/gm-2021-0012","url":null,"abstract":"Abstract In this paper, we consider new subclasses 𝔗𝔖n(µ, a, b, ℓ, τ, γ) and 𝕽n(µ, a, b, ℓ, τ, γ) of analytic univalent functions defined by Erdelyi-Kober integral operator. We obtain coefficient inequalities, inclusion relationships involving the (n, δ)- neighborhoods, partial sums and integral mean inequalities for the functions that belongs to these classes. Also, subordinating factor sequence for the functions in the classes 𝔖n(µ, a, b, ℓ, τ, γ) and 𝕽n(µ, a, b, ℓ, τ, γ) are derived.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"127 1","pages":"23 - 36"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76273427","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 In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses Dn,ρΣ,δ(Φ) and Fn,αΣ,δ(Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |a2| and |a3| of the bi-univalent function subclasses.
{"title":"New Subclasses of Bi-Univalent Functions based on the Fibonacci Numbers","authors":"Munirah Rossdy, R. Omar, S. C. Soh","doi":"10.2478/gm-2021-0016","DOIUrl":"https://doi.org/10.2478/gm-2021-0016","url":null,"abstract":"Abstract In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses Dn,ρΣ,δ(Φ) and Fn,αΣ,δ(Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |a2| and |a3| of the bi-univalent function subclasses.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"39 1","pages":"83 - 97"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80955090","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 In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fejér’s inequality for convex functions and of Grüss’ type inequalities are also provided.
{"title":"Integral Inequalities Related to Wirtinger’s Result","authors":"S. Dragomir","doi":"10.2478/gm-2021-0013","DOIUrl":"https://doi.org/10.2478/gm-2021-0013","url":null,"abstract":"Abstract In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fejér’s inequality for convex functions and of Grüss’ type inequalities are also provided.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"44 1","pages":"37 - 55"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86247579","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}
Covid-19 epidemic continues to escalate globally posing life threats to humans. Time series modeling plays a key role for the prediction of data-driven scenarios. A case for Covid-19 pandemic future numbers occurrence is one of the open forecasting scenario for application of the time series modeling. We applied the Autoregressive Integrated Moving Average (ARIMA) model to forecast the possible numbers of Covid-19 deaths in the Republic of South Africa using the previously reported data for a period of 17 months (May 2020 to September 2021). We adapted the Box-Jenkins’ methodology to step-by-step achieve the entire forecasting process. We identified the MA(1) (ARIMA(0,0,1)) as the best model based on the Akaike Information Criterion and the Bayesian Information Criterion. The forecasting done at 95% confidence interval for a period of 7 months (October 1, 2021 to April 31, 2022) indicated that the Covid-19 associated deaths in South Africa would slightly increase during the month of October 2021 but remain constant throughout the entire prediction period.
{"title":"Forecasting of Covid-19 deaths in South Africa using the autoregressive integrated moving average time series model","authors":"M. Kinyili, Maurice Wanyonyi","doi":"10.31559/glm2021.11.2.2","DOIUrl":"https://doi.org/10.31559/glm2021.11.2.2","url":null,"abstract":"Covid-19 epidemic continues to escalate globally posing life threats to humans. Time series modeling plays a key role for the prediction of data-driven scenarios. A case for Covid-19 pandemic future numbers occurrence is one of the open forecasting scenario for application of the time series modeling. We applied the Autoregressive Integrated Moving Average (ARIMA) model to forecast the possible numbers of Covid-19 deaths in the Republic of South Africa using the previously reported data for a period of 17 months (May 2020 to September 2021). We adapted the Box-Jenkins’ methodology to step-by-step achieve the entire forecasting process. We identified the MA(1) (ARIMA(0,0,1)) as the best model based on the Akaike Information Criterion and the Bayesian Information Criterion. The forecasting done at 95% confidence interval for a period of 7 months (October 1, 2021 to April 31, 2022) indicated that the Covid-19 associated deaths in South Africa would slightly increase during the month of October 2021 but remain constant throughout the entire prediction period.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46273471","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 formalize new findings on formal Arabic language by constructing equivalence classes on letters depending on inversion principle. This equivalent relation furnishes a conjecture that Arabic language has a DNA-like inversion controller, called language DNA (LDNA) (Al-Rawajfeh, 2020, Ref [2]) and it can be even considered as a part of the full language DNA that can be discovered by more investigations similar to this work.
{"title":"Mathematical formalism on \"Arabic Language DNA\"","authors":"Aiman Eid Al-Rawajfeh, Z. Altawallbeh","doi":"10.31559/glm2021.11.1.2","DOIUrl":"https://doi.org/10.31559/glm2021.11.1.2","url":null,"abstract":"In this work we formalize new findings on formal Arabic language by constructing equivalence classes on letters depending on inversion principle. This equivalent relation furnishes a conjecture that Arabic language has a DNA-like inversion controller, called language DNA (LDNA) (Al-Rawajfeh, 2020, Ref [2]) and it can be even considered as a part of the full language DNA that can be discovered by more investigations similar to this work.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48739555","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}
Dindar Saeed Saeed, Sadeq Taha Abdulazeez, Sarbast Kamal Rasheed, Rogash Younis Masiha, Diyar Hashim Malo
Petroleum is one of the world's most important economic products. It is widely accepted that petroleum is not only an energy product, but also a financial asset. Therefore, it is important to understand the dependence of petroleum prices on economic conditions and financial markets and how they can affect the world economy. The fluctuations in world petroleum prices affect the economies of petroleum importing countries through different channels. One of the most important of these influence channels is the exchange rate. Because changes in exchange rates cause different economic problems in fragile economies. Changes in petroleum prices affect the economic performance of any country through various channels. One of the channels of influence is exchange rates. Petroleum prices affect the transfer of income from petroleum exporting countries to petroleum importing countries through trade and thus determine the exchange rate. In this study, the Relationship between Petroleum Price and Real Exchange Rate in Iraq was examined by ADF unit root test, Johansen-Juselius cointegration test and Granger causality analysis. For the analysis, the Petroleum Price and Real Exchange Rate data of Iraq were taken from the official website of the World Bank and transferred to the Eviews 10 program and necessary analyzes were made. The results of the analysis were analyzed and interpreted in tables.
{"title":"The relationship between petroleum price and real exchange rate: an example of Iraq","authors":"Dindar Saeed Saeed, Sadeq Taha Abdulazeez, Sarbast Kamal Rasheed, Rogash Younis Masiha, Diyar Hashim Malo","doi":"10.31559/glm2021.11.1.3","DOIUrl":"https://doi.org/10.31559/glm2021.11.1.3","url":null,"abstract":"Petroleum is one of the world's most important economic products. It is widely accepted that petroleum is not only an energy product, but also a financial asset. Therefore, it is important to understand the dependence of petroleum prices on economic conditions and financial markets and how they can affect the world economy. The fluctuations in world petroleum prices affect the economies of petroleum importing countries through different channels. One of the most important of these influence channels is the exchange rate. Because changes in exchange rates cause different economic problems in fragile economies. Changes in petroleum prices affect the economic performance of any country through various channels. One of the channels of influence is exchange rates. Petroleum prices affect the transfer of income from petroleum exporting countries to petroleum importing countries through trade and thus determine the exchange rate. In this study, the Relationship between Petroleum Price and Real Exchange Rate in Iraq was examined by ADF unit root test, Johansen-Juselius cointegration test and Granger causality analysis. For the analysis, the Petroleum Price and Real Exchange Rate data of Iraq were taken from the official website of the World Bank and transferred to the Eviews 10 program and necessary analyzes were made. The results of the analysis were analyzed and interpreted in tables.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45579623","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, a new formula of 𝛽𝑘 is suggested for the conjugate gradient method of solving unconstrained optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent condition, sufficient descent condition, conjugacy condition, and global convergence properties. Numerical comparisons with two standard conjugate gradient algorithms show that this algorithm is very effective depending on the number of iterations and the number of functions evaluated.
{"title":"Global convergence of new three terms conjugate gradient for unconstrained optimization","authors":"Ahmed Anwer Mustafa, Salah Gazi Shareef","doi":"10.31559/glm2021.11.1.1","DOIUrl":"https://doi.org/10.31559/glm2021.11.1.1","url":null,"abstract":"In this paper, a new formula of 𝛽𝑘 is suggested for the conjugate gradient method of solving unconstrained optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent condition, sufficient descent condition, conjugacy condition, and global convergence properties. Numerical comparisons with two standard conjugate gradient algorithms show that this algorithm is very effective depending on the number of iterations and the number of functions evaluated.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42382057","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 main purpose of this paper is to establish some common fixed point theorems for single and set-valued mappings, under strict contractive conditions with no continuity, no completeness, no inclusions and without using neither compactness nor closeness. These theorems improve the results of Fisher [8], Ahmed [1] and [2], and others. Also, common fixed point theorems for two hybrid pairs satisfying a contractive condition of integral type are given improving the results of [3], [4] and [6].
{"title":"A unique common fixed point for a family of set-valued mappings","authors":"H. Bouhadjera, S. Beloul","doi":"10.2478/gm-2021-0007","DOIUrl":"https://doi.org/10.2478/gm-2021-0007","url":null,"abstract":"Abstract The main purpose of this paper is to establish some common fixed point theorems for single and set-valued mappings, under strict contractive conditions with no continuity, no completeness, no inclusions and without using neither compactness nor closeness. These theorems improve the results of Fisher [8], Ahmed [1] and [2], and others. Also, common fixed point theorems for two hybrid pairs satisfying a contractive condition of integral type are given improving the results of [3], [4] and [6].","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"45 1","pages":"79 - 94"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75265568","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 purpose of this paper is to prove a common fixed point theorem for a pair of mappings satisfying an implicit relation, generalizing the main results from [6], [10], [11], [13] and other papers.
{"title":"A general common fixed point theorem for a pair of mappings in S - metric spaces","authors":"V. Popa, A. Patriciu","doi":"10.2478/gm-2021-0003","DOIUrl":"https://doi.org/10.2478/gm-2021-0003","url":null,"abstract":"Abstract The purpose of this paper is to prove a common fixed point theorem for a pair of mappings satisfying an implicit relation, generalizing the main results from [6], [10], [11], [13] and other papers.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"13 1","pages":"31 - 39"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77276003","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 In this article, by making use of Horadam polynomials, we introduce and investigate a certain family 𝔗Σ (λ, α, β, k, γ; x) of analytic and biunivalent functions associated with Wanas operator which defined in the open unit disk 𝕌. We establish upper bounds for the initial Taylor-Maclaurin coefficients and obtain the Fekete-Szegö inequality of functions belonging to this family. We also point out several certain special cases for our results.
{"title":"Horadam polynomials and their applications to a certain family of bi-univalent functions defined by Wanas operator","authors":"A. Wanas, T. G. Shaba","doi":"10.2478/gm-2021-0009","DOIUrl":"https://doi.org/10.2478/gm-2021-0009","url":null,"abstract":"Abstract In this article, by making use of Horadam polynomials, we introduce and investigate a certain family 𝔗Σ (λ, α, β, k, γ; x) of analytic and biunivalent functions associated with Wanas operator which defined in the open unit disk 𝕌. We establish upper bounds for the initial Taylor-Maclaurin coefficients and obtain the Fekete-Szegö inequality of functions belonging to this family. We also point out several certain special cases for our results.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"27 1","pages":"103 - 119"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76652179","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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