This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient conditions for JRα,βz to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis.
{"title":"Properties of a Linear Operator Involving Lambert Series and Rabotnov Function","authors":"Jamal Salah","doi":"10.1155/2024/3657721","DOIUrl":"https://doi.org/10.1155/2024/3657721","url":null,"abstract":"This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient conditions for JRα,βz to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102745","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}
M. Shanmugapriya, R. Sundareswaran, S. G. K. Subramanian, A. Alameri
An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter β and the unsteadiness parameter S strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter Rd becomes larger. In addition, the Biot numbers Bi1 & Bi2 lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient S˜fxRex0.5, heat transfer rate H˜tx Rex0.5, and nanoparticle transfer rate C˜txRex0.5. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict S˜fxRex0.5,H˜tx Rex0.5, and C˜txRex0.5. Statistical metrics including RMSE, MAE, MAPE, MSE, R2, and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an R2 value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models.
{"title":"Investigation of Magnetized Casson Nanofluid Flow along Wedge: Gaussian Process Regression","authors":"M. Shanmugapriya, R. Sundareswaran, S. G. K. Subramanian, A. Alameri","doi":"10.1155/2024/2880748","DOIUrl":"https://doi.org/10.1155/2024/2880748","url":null,"abstract":"An unsteady two-dimensional magnetized Casson nanofluid flow model is constructed over a wedge under the effect of thermal radiation and chemical reaction. The multiple slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. This study investigates the application of soft computing techniques to address the challenges posed by the complexity of problem modeling and numerical methods. Traditional approaches incorporating various model factors may struggle to provide accurate solutions. To resolve this issue, Gaussian process regression (GPR) is employed to predict the solution of the proposed flow model. With the help of the numerical shooting method together with Runge–Kutta–Fehlberg fourth-fifth-order (RKF-45) reference data, the GPR model is trained. The numerical simulation illustrated that the Casson fluid parameter β and the unsteadiness parameter S strengthen the friction factor, and the heat transfer rate is enhanced as the radiation parameter Rd becomes larger. In addition, the Biot numbers Bi1 & Bi2 lead to strengthen nanoparticle temperature; an opposite behavior is noticed with the skin friction coefficient S˜fxRex0.5, heat transfer rate H˜tx Rex0.5, and nanoparticle transfer rate C˜txRex0.5. The GPR model with the exponential Kernel function provided better performance than other functions on both training and checking datasets to predict S˜fxRex0.5,H˜tx Rex0.5, and C˜txRex0.5. Statistical metrics including RMSE, MAE, MAPE, MSE, R2, and R are employed to check the accuracy and convergences of the predicted and numerical solutions obtained through GPR and RKF-45. It is observed that all three GPR models had an R2 value of higher than 0.9. The proposed study demonstrates the advantages of employing soft computing methods (GPR) to effectively analyse the behavior of complex flow models.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139445845","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, we introduce and investigate a class of biunivalent functions, denoted by Hn,r,α, that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients a2 and a3. Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class.
{"title":"Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator","authors":"Waleed Al-Rawashdeh","doi":"10.1155/2023/2573044","DOIUrl":"https://doi.org/10.1155/2023/2573044","url":null,"abstract":"In this paper, we introduce and investigate a class of biunivalent functions, denoted by Hn,r,α, that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients a2 and a3. Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139145403","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 study the space of prime fuzzy ideals (and the space of maximal fuzzy ideals as a subspace) equipped with the hull-kernel topology in partially ordered sets. Mainly, we investigate the conditions for which the fuzzy prime spectrum of a poset is compact, Hausdorff, and normal, respectively.
{"title":"The Fuzzy Prime Spectrum of Partially Ordered Sets","authors":"Derso Abeje Engidaw, Gezahagne Mulat Addis, Wondwosen Zemene Norahun, Dereje Kifle Boku, Habtu Bayafers Demrew, T. Degefa","doi":"10.1155/2023/4526348","DOIUrl":"https://doi.org/10.1155/2023/4526348","url":null,"abstract":"We study the space of prime fuzzy ideals (and the space of maximal fuzzy ideals as a subspace) equipped with the hull-kernel topology in partially ordered sets. Mainly, we investigate the conditions for which the fuzzy prime spectrum of a poset is compact, Hausdorff, and normal, respectively.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138997628","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}
This study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order.
本文提出了一种利用Adomian多项式混合显式有限差分技术有效求解非线性耦合Drinfeld - sokolov - wilson (DSW)系统的新算法。该方法解决了DSW系统的精确求解问题。通过一个测试问题，将精确解与绝对误差和均方误差进行比较，以评估EFD- ap与精确解和传统显式有限差分(EFD)方法的精度，从而获得数值结果。结果表明，该方法在求解高阶非线性偏微分系统时具有较好的精度和效率，是一种很有前途的求解方法。
{"title":"Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System","authors":"Israa Th. Younis, Ekhlass S. Al-Rawi","doi":"10.1155/2023/6916596","DOIUrl":"https://doi.org/10.1155/2023/6916596","url":null,"abstract":"This study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138598103","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}
Let be a group and be a -graded ring with non-zero unity. The goal of our article is reconsidering some well-known concepts on graded rings using a group homomorphism . Next is to examine the new concepts compared to the known concepts. For example, it is known that is weak if whenever such that , then
同样，我们建立并研究了 α 非退化环、α 规则环、α 强环、α 第一强级环和α 弱交叉积的概念。
{"title":"On Properties of Graded Rings with respect to Group Homomorphisms","authors":"A. Alshehry, R. Abu-Dawwas, Muhsen Al-Bashayreh","doi":"10.1155/2023/3803873","DOIUrl":"https://doi.org/10.1155/2023/3803873","url":null,"abstract":"<jats:p>Let <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mi>G</mi> </math> </jats:inline-formula> be a group and <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <mi>R</mi> </math> </jats:inline-formula> be a <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <mi>G</mi> </math> </jats:inline-formula>-graded ring with non-zero unity. The goal of our article is reconsidering some well-known concepts on graded rings using a group homomorphism <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mi>α</mi> <mo>:</mo> <mi>G</mi> <mo>⟶</mo> <mi>G</mi> </math> </jats:inline-formula>. Next is to examine the new concepts compared to the known concepts. For example, it is known that <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\"> <mfenced open=\"(\" close=\")\" separators=\"|\"> <mrow> <mi>R</mi> <mo>,</mo> <mi>G</mi> </mrow> </mfenced> </math> </jats:inline-formula> is weak if whenever <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\"> <mi>g</mi> <mo>∈</mo> <mi>G</mi> </math> </jats:inline-formula> such that <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\"> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </math> </jats:inline-formula>, then <jats:inline-formula> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\"> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <msup> <mrow> <mi>g</mi> </mrow> ","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139274681","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, we establish some inequalities involving the modulus of the derivative of rational functions with prescribed poles and restricted zeros. The obtained results generalize some known inequalities for rational functions. Moreover, our results also contain certain known polynomial inequalities.
{"title":"Some Inequalities Involving the Derivative of Rational Functions","authors":"Arnisa Rasri, Jiraphorn Somsuwan Phanwan","doi":"10.1155/2023/5541585","DOIUrl":"https://doi.org/10.1155/2023/5541585","url":null,"abstract":"In this paper, we establish some inequalities involving the modulus of the derivative of rational functions with prescribed poles and restricted zeros. The obtained results generalize some known inequalities for rational functions. Moreover, our results also contain certain known polynomial inequalities.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063862","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}
Ildephonse Nizeyimana, George Otieno Orwa, Michael Arthur Ofori, Samuel Musili Mwalili
Weighted Cox regression models were proposed as an alternative to the standard Cox proportional hazards models where consistent estimators can be obtained with more relative strength compared to unweighted cases. We proposed censoring balancing functions which can be built in a way that allows us to obtain the maximum possible significant treatment effects that may have gone undetected due to censoring. The harm caused by this is compensated and new weighted parameter estimates are found. These functions are constructed to be monotonic because even the hazard ratios are not exactly constant as in the ideal case, but are violated by monotonic deviations in time. For more than one covariate, even the interaction between covariates in addition to censoring can lead to the loss of significance for some covariates’ effects. Undetected significant effects of one covariate can be obtained, still keeping the significance and approximate size of the remaining one(s). This is performed by keeping the consistency of the parameter estimates. The results from both the simulated datasets and their application to real datasets supported the importance of the suggested censoring balancing functions in both one covariate and more than one covariate cases.
{"title":"Censoring Balancing Functions for Undetected Probably Significant Effects in Cox Regression","authors":"Ildephonse Nizeyimana, George Otieno Orwa, Michael Arthur Ofori, Samuel Musili Mwalili","doi":"10.1155/2023/6676767","DOIUrl":"https://doi.org/10.1155/2023/6676767","url":null,"abstract":"Weighted Cox regression models were proposed as an alternative to the standard Cox proportional hazards models where consistent estimators can be obtained with more relative strength compared to unweighted cases. We proposed censoring balancing functions which can be built in a way that allows us to obtain the maximum possible significant treatment effects that may have gone undetected due to censoring. The harm caused by this is compensated and new weighted parameter estimates are found. These functions are constructed to be monotonic because even the hazard ratios are not exactly constant as in the ideal case, but are violated by monotonic deviations in time. For more than one covariate, even the interaction between covariates in addition to censoring can lead to the loss of significance for some covariates’ effects. Undetected significant effects of one covariate can be obtained, still keeping the significance and approximate size of the remaining one(s). This is performed by keeping the consistency of the parameter estimates. The results from both the simulated datasets and their application to real datasets supported the importance of the suggested censoring balancing functions in both one covariate and more than one covariate cases.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134886422","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 well‐known matrix‐generated tree structure for Pythagorean triplets is extended to the primitive solutions of the Diophantine equation where is a positive square‐free integer. The proof is based on a parametrization of these solutions as well as on a dual version of the Fermat’s method of descent.
{"title":"On Parametric and Matrix Solutions to the Diophantine Equation <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi mathvariant=\"normal\">d</mi> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mi>z</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> </math> Where <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <mi>d</mi> </math> Is a …","authors":"James D. Shaw, James Guyker","doi":"10.1155/2023/1505337","DOIUrl":"https://doi.org/10.1155/2023/1505337","url":null,"abstract":"The well‐known matrix‐generated tree structure for Pythagorean triplets is extended to the primitive solutions of the Diophantine equation <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi mathvariant=\"normal\">d</mi> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mi>z</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> </math> where <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mi>d</mi> </math> is a positive square‐free integer. The proof is based on a parametrization of these solutions as well as on a dual version of the Fermat’s method of descent.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135814914","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}
Hadeel Z. Alzumi, Hakima Bouhadjera, Mohammed S. Abdo
In this work, we establish three common fixed point results for expansive maps satisfying implicit relations in metric and dislocated metric spaces. We do this by utilizing recently developed concept of occasionally weakly biased maps of type . These studies about the theory of common fixed points refine several earlier ones. Some illustrative examples are offered to support our theorems, and even better, a pertinent application is supplied to demonstrate the viability and applicability of one of these results.
{"title":"Unique Common Fixed Points for Expansive Maps","authors":"Hadeel Z. Alzumi, Hakima Bouhadjera, Mohammed S. Abdo","doi":"10.1155/2023/6689743","DOIUrl":"https://doi.org/10.1155/2023/6689743","url":null,"abstract":"In this work, we establish three common fixed point results for expansive maps satisfying implicit relations in metric and dislocated metric spaces. We do this by utilizing recently developed concept of occasionally weakly biased maps of type <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mfenced open=\"(\" close=\")\" separators=\"|\"> <mrow> <mi mathvariant=\"script\">A</mi> </mrow> </mfenced> </math> . These studies about the theory of common fixed points refine several earlier ones. Some illustrative examples are offered to support our theorems, and even better, a pertinent application is supplied to demonstrate the viability and applicability of one of these results.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981958","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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