Pub Date : 2023-11-28DOI: 10.28924/2291-8639-21-2023-129
Salahuddin
The aim of this paper is to consider a general non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. We apply a two-step technique where approximate solutions of a sequence of a generalized mixed variational inequality problem (GMVIP) are inserted in the iterative method of a selective coordinate-wise decomposition descent method. Its convergence is achieved under coercivity-type assumptions.
{"title":"The Study of Coordinate-Wise Decomposition Descent Method for Optimization Problems","authors":"Salahuddin","doi":"10.28924/2291-8639-21-2023-129","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-129","url":null,"abstract":"The aim of this paper is to consider a general non-stationary optimization problem whose objective function need not be smooth in general and only approximation sequences are known instead of exact values of the functions. We apply a two-step technique where approximate solutions of a sequence of a generalized mixed variational inequality problem (GMVIP) are inserted in the iterative method of a selective coordinate-wise decomposition descent method. Its convergence is achieved under coercivity-type assumptions.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"102 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139224172","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 : 2023-11-28DOI: 10.28924/2291-8639-21-2023-128
Gundeti Soujanya, P. Kavyasree, B. S. Reddy
Pythagorean fuzzy sets and interval valued Pythagorean fuzzy sets have an important role in decision making techniques. Pythagorean hesitant fuzzy sets are time and again used in dealing with uncertain and vague data. The motive of this paper is to introduce the notion cubic Pythagorean hesitant fuzzy linear spaces. We also present the notion of P(R)-intersection, P(R)-union of cubic Pythagorean hesitant fuzzy linear spaces with examples. Secondly, a series of operators like cubic Pythagorean hesitant fuzzy weighted averaging aggregation operators, cubic Pythagorean hesitant fuzzy order weighted averaging aggregation operators and cubic Pythagorean hesitant fuzzy hybrid order weighted averaging aggregation operators are developed. Then, these aggregation operators are further extended to cubic Pythagorean hesitant fuzzy prioritized weighted averaging aggregation operators by assigning priorities to the criteria. A real life MCDM problem has been illustrated and the effectiveness of the results are compared with those solved using cubic picture hesitant fuzzy prioritized weighted averaging aggregation operators.
{"title":"Cubic Pythagorean Hesitant Fuzzy Linear Spaces and Its Relevance in Multi Criteria Decision Making","authors":"Gundeti Soujanya, P. Kavyasree, B. S. Reddy","doi":"10.28924/2291-8639-21-2023-128","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-128","url":null,"abstract":"Pythagorean fuzzy sets and interval valued Pythagorean fuzzy sets have an important role in decision making techniques. Pythagorean hesitant fuzzy sets are time and again used in dealing with uncertain and vague data. The motive of this paper is to introduce the notion cubic Pythagorean hesitant fuzzy linear spaces. We also present the notion of P(R)-intersection, P(R)-union of cubic Pythagorean hesitant fuzzy linear spaces with examples. Secondly, a series of operators like cubic Pythagorean hesitant fuzzy weighted averaging aggregation operators, cubic Pythagorean hesitant fuzzy order weighted averaging aggregation operators and cubic Pythagorean hesitant fuzzy hybrid order weighted averaging aggregation operators are developed. Then, these aggregation operators are further extended to cubic Pythagorean hesitant fuzzy prioritized weighted averaging aggregation operators by assigning priorities to the criteria. A real life MCDM problem has been illustrated and the effectiveness of the results are compared with those solved using cubic picture hesitant fuzzy prioritized weighted averaging aggregation operators.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"43 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139221955","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 : 2023-11-28DOI: 10.28924/2291-8639-21-2023-127
B. Alshammari, D. Mashat, F. Mallawi
We propose a mathematical model for the vibrio cholerae spread under the influence of a seasonal environment with two routes of infection. We proved the existence of a unique bounded positive solution, and that the system admits a global attractor set. The basic reproduction number R0 was calculated for both cases, the fixed and seasonal environment which permits to characterise both, the extinction and the persistence of the disease. We proved that the phage-free equilibrium point is globally asymptotically stable if R0≤1, while the disease will be persist if R0>1. Finally, extensive numerical simulations are given to confirm the theoretical findings.
{"title":"Mathematical and Numerical Investigations for a Cholera Dynamics With a Seasonal Environment","authors":"B. Alshammari, D. Mashat, F. Mallawi","doi":"10.28924/2291-8639-21-2023-127","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-127","url":null,"abstract":"We propose a mathematical model for the vibrio cholerae spread under the influence of a seasonal environment with two routes of infection. We proved the existence of a unique bounded positive solution, and that the system admits a global attractor set. The basic reproduction number R0 was calculated for both cases, the fixed and seasonal environment which permits to characterise both, the extinction and the persistence of the disease. We proved that the phage-free equilibrium point is globally asymptotically stable if R0≤1, while the disease will be persist if R0>1. Finally, extensive numerical simulations are given to confirm the theoretical findings.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"50 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139222328","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 : 2023-11-21DOI: 10.28924/2291-8639-21-2023-126
Siham Bayad, Abdelmajid El Hajaj, Khalid Hilal
In this study, we propose a more comprehensive and realistic option pricing model based on approximative fractional Brownian motion, building upon recent advancements in this area. Specifically, we utilize the double 3/2-volatility Jump-Diffusion model, which incorporates approximative fractional Brownian motion with 3/2-volatility, stochastic interest rate, and stochastic intensity. To account for the stochastic interest rate, we employ a two-factor Vasicek model. Notably, our model accommodates negative interest rates. Consequently, we develop a multi-factor model with a stochastic interest rate structure for pricing European options and derive a closed-form pricing formula with an analytical solution by applying some algebraic calculations and Lie symmetries. In order to demonstrate the superiority of our proposed model over other classical approaches, we present numerical results that showcase the value of a European call option. This comparative analysis underscores the advantages of our model in comparison to traditional models.
{"title":"Valuing European Option Under Double 3/2-Volatility Jump-Diffusion Model With Stochastic Interest Rate and Stochastic Intensity Under Approximative Fractional Brownian Motion","authors":"Siham Bayad, Abdelmajid El Hajaj, Khalid Hilal","doi":"10.28924/2291-8639-21-2023-126","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-126","url":null,"abstract":"In this study, we propose a more comprehensive and realistic option pricing model based on approximative fractional Brownian motion, building upon recent advancements in this area. Specifically, we utilize the double 3/2-volatility Jump-Diffusion model, which incorporates approximative fractional Brownian motion with 3/2-volatility, stochastic interest rate, and stochastic intensity. To account for the stochastic interest rate, we employ a two-factor Vasicek model. Notably, our model accommodates negative interest rates. Consequently, we develop a multi-factor model with a stochastic interest rate structure for pricing European options and derive a closed-form pricing formula with an analytical solution by applying some algebraic calculations and Lie symmetries. In order to demonstrate the superiority of our proposed model over other classical approaches, we present numerical results that showcase the value of a European call option. This comparative analysis underscores the advantages of our model in comparison to traditional models.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"17 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139252311","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 : 2023-11-21DOI: 10.28924/2291-8639-21-2023-125
M. A. Bakhit, N. M. Dahshan, Ranya Tahier, Omniat O. Y. Karrar, Mehreen S. Khan, M. A. Orsud
The paper investigate a necessary and sufficient condition for the composition operator from harmonic Lipschitz spaces LipHα, (0<α<1) into weighted harmonic Zygmund spaces ZHβ, (0<β<∞) to be bounded and compact on the open unit disk. As an application, it estimates the essential norms of such an operator from LipHα into ZHβ spaces.
{"title":"Composition Operators From Harmonic Lipschitz Space Into Weighted Harmonic Zygmund Space","authors":"M. A. Bakhit, N. M. Dahshan, Ranya Tahier, Omniat O. Y. Karrar, Mehreen S. Khan, M. A. Orsud","doi":"10.28924/2291-8639-21-2023-125","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-125","url":null,"abstract":"The paper investigate a necessary and sufficient condition for the composition operator from harmonic Lipschitz spaces LipHα, (0<α<1) into weighted harmonic Zygmund spaces ZHβ, (0<β<∞) to be bounded and compact on the open unit disk. As an application, it estimates the essential norms of such an operator from LipHα into ZHβ spaces.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"2 ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139250961","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 : 2023-11-13DOI: 10.28924/2291-8639-21-2023-121
K. Vidhya, A. Saraswathi
The Shortest Path Problem is a core problem in network optimization, with applications in various scientific and engineering fields, such as communication, transportation, routing, scheduling, and computer networks. Many studies and algorithms have been proposed to solve the traditional shortest path problem, but they often fail to provide optimal solutions when dealing with the uncertainties and vagueness that exist in real-world situations. This study aims to address the Bi-objective Shortest Path Problem using intuitionistic fuzzy arc numbers. The main goal is to find the path that minimizes both cost and time between a given source node and destination node. To handle the complexities introduced by trapezoidal intuitionistic fuzzy numbers, an accuracy function is used. The study suggests a simple yet effective method to solve this problem and shows its efficiency through a numerical example. The research tries to offer innovative solutions for optimizing paths in scenarios where cost and time factors are important, navigating the complex landscape of uncertainty inherent in practical applications.
{"title":"A Novel Method for Finding the Shortest Path With Two Objectives Under Trapezoidal Intuitionistic Fuzzy Arc Costs","authors":"K. Vidhya, A. Saraswathi","doi":"10.28924/2291-8639-21-2023-121","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-121","url":null,"abstract":"The Shortest Path Problem is a core problem in network optimization, with applications in various scientific and engineering fields, such as communication, transportation, routing, scheduling, and computer networks. Many studies and algorithms have been proposed to solve the traditional shortest path problem, but they often fail to provide optimal solutions when dealing with the uncertainties and vagueness that exist in real-world situations. This study aims to address the Bi-objective Shortest Path Problem using intuitionistic fuzzy arc numbers. The main goal is to find the path that minimizes both cost and time between a given source node and destination node. To handle the complexities introduced by trapezoidal intuitionistic fuzzy numbers, an accuracy function is used. The study suggests a simple yet effective method to solve this problem and shows its efficiency through a numerical example. The research tries to offer innovative solutions for optimizing paths in scenarios where cost and time factors are important, navigating the complex landscape of uncertainty inherent in practical applications.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"68 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139278666","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 : 2023-11-13DOI: 10.28924/2291-8639-21-2023-123
T. Gaketem
For the purpose of this research, we give the new concept of essential implicative UPfilter from the concept of essential UP-filters in UP-algebras. Although we know that the concept of implicative UP-filters is UP-filters, we have an example showing that the concept of essential UPfilters does not necessarily be essential implicative UP-filters. After that, we extend the concept of essential implicative UP-filters to t-essential fuzzy implicative UP-filters of UP-algebras and study their relationship based on characteristic functions and upper level subsets.
为了本研究的目的，我们从 UP 架构中的本质蕴涵式 UP 滤波器概念出发，给出了本质蕴涵式 UP 滤波器这一新概念。虽然我们知道蕴涵式 UP 滤波器的概念是 UP 滤波器，但我们有一个例子说明本质 UP 滤波器的概念不一定是本质蕴涵式 UP 滤波器。之后，我们将本质蕴涵型 UP 滤波器的概念扩展到 UP 架构的 t-本质模糊蕴涵型 UP 滤波器，并基于特征函数和上层子集研究它们之间的关系。
{"title":"Essential Implicative UP-Filters and t-Essential Fuzzy Implicative UP-Filters of UP-Algebras","authors":"T. Gaketem","doi":"10.28924/2291-8639-21-2023-123","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-123","url":null,"abstract":"For the purpose of this research, we give the new concept of essential implicative UPfilter from the concept of essential UP-filters in UP-algebras. Although we know that the concept of implicative UP-filters is UP-filters, we have an example showing that the concept of essential UPfilters does not necessarily be essential implicative UP-filters. After that, we extend the concept of essential implicative UP-filters to t-essential fuzzy implicative UP-filters of UP-algebras and study their relationship based on characteristic functions and upper level subsets.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"86 1-2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139278759","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 : 2023-11-13DOI: 10.28924/2291-8639-21-2023-124
R. Rajalakshmi, C. Carpintero, N. Rajesh, E. Rosas
In this paper, we introduce the notions of minimal u-ω-closed sets, maximal u-ω-open sets, u-ω-paraopen sets, u-ω-paraclosed sets, u-ω-mean open sets and u-ω-mean closed sets in bitopological spaces and obtain several characterizations and some of its properties.
{"title":"Some Subsets of Bitopological Spaces","authors":"R. Rajalakshmi, C. Carpintero, N. Rajesh, E. Rosas","doi":"10.28924/2291-8639-21-2023-124","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-124","url":null,"abstract":"In this paper, we introduce the notions of minimal u-ω-closed sets, maximal u-ω-open sets, u-ω-paraopen sets, u-ω-paraclosed sets, u-ω-mean open sets and u-ω-mean closed sets in bitopological spaces and obtain several characterizations and some of its properties.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"54 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139278046","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 : 2023-11-13DOI: 10.28924/2291-8639-21-2023-122
M. Folly-Gbetoula
We obtain symmetries of a family of difference equations and we prove a relationship between these symmetries and similarity variables. We proceed with reduction and eventually derive formula solutions of the difference equations. Furthermore, we discuss the periodic nature of the solutions and analyze the stability of the fixed points. We use Lie point symmetry analysis as our tool in obtaining the solutions. Though we have analyzed a specific family of difference equations in this paper, the algorithmic techniques presented can be utilized to tackle many other difference equations.
{"title":"Solvability and Dynamical Analysis of Difference Equations","authors":"M. Folly-Gbetoula","doi":"10.28924/2291-8639-21-2023-122","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-122","url":null,"abstract":"We obtain symmetries of a family of difference equations and we prove a relationship between these symmetries and similarity variables. We proceed with reduction and eventually derive formula solutions of the difference equations. Furthermore, we discuss the periodic nature of the solutions and analyze the stability of the fixed points. We use Lie point symmetry analysis as our tool in obtaining the solutions. Though we have analyzed a specific family of difference equations in this paper, the algorithmic techniques presented can be utilized to tackle many other difference equations.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"35 11","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139278192","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 : 2023-10-30DOI: 10.28924/2291-8639-21-2023-119
M. Khalifa Saad, R. A. Abdel-Baky
Curves on surfaces and their frames play an important role in differential geometry and in many branches of science such as mechanics and physics. So, we are interested in studying one of these surfaces along a curve lying on a surface. In this paper, we define a surface normal to a surface along a curve lying on a surface in Euclidean 3-space E3. Then, we analyze the necessary and sufficient conditions for that surface to be a ruled surface. Finally, we illustrate the convenience and efficiency of this approach with some representative examples.
{"title":"Normal Surfaces along a Curve on a Surface in Euclidean 3-Space","authors":"M. Khalifa Saad, R. A. Abdel-Baky","doi":"10.28924/2291-8639-21-2023-119","DOIUrl":"https://doi.org/10.28924/2291-8639-21-2023-119","url":null,"abstract":"Curves on surfaces and their frames play an important role in differential geometry and in many branches of science such as mechanics and physics. So, we are interested in studying one of these surfaces along a curve lying on a surface. In this paper, we define a surface normal to a surface along a curve lying on a surface in Euclidean 3-space E3. Then, we analyze the necessary and sufficient conditions for that surface to be a ruled surface. Finally, we illustrate the convenience and efficiency of this approach with some representative examples.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":"180 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136068151","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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