Pub Date : 2024-07-01DOI: 10.21608/ejmaa.2024.251590.1096
Swayamprabha Tiwari, Sameena Saba, Mohammad Ahmad
. S. Ramanujan in his last letter to G.H. Hardy has introduced sev-enteen mock theta functions of di erenct orders ( 3,5 and 7) without explicitly mentioning the reason for his levelling of order, later Watson added to this set three more third order mock theta function. Watson also de ned bilateral form of some mock theta function of order ve and expressed them in terms of lerch transendetal functions . Patial mock theta functions of sixth order were studied by Y.S. Choi and partial mock theta functions of third order were studied by G.E. Andrews. In this paper we have given generalization of partial sixth and third order mock theta functions and it is shown that these generalized partial mock theta functions are F q functions. q-integral representation of these generalized partial mock theta functions are also given. we have also expressed some bilateral mock theta functions in terms of lerch transcendental functions f ( x, ξ ; q,p ).
{"title":"A Study of Generalized Partial Mock Theta Functions","authors":"Swayamprabha Tiwari, Sameena Saba, Mohammad Ahmad","doi":"10.21608/ejmaa.2024.251590.1096","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.251590.1096","url":null,"abstract":". S. Ramanujan in his last letter to G.H. Hardy has introduced sev-enteen mock theta functions of di erenct orders ( 3,5 and 7) without explicitly mentioning the reason for his levelling of order, later Watson added to this set three more third order mock theta function. Watson also de ned bilateral form of some mock theta function of order ve and expressed them in terms of lerch transendetal functions . Patial mock theta functions of sixth order were studied by Y.S. Choi and partial mock theta functions of third order were studied by G.E. Andrews. In this paper we have given generalization of partial sixth and third order mock theta functions and it is shown that these generalized partial mock theta functions are F q functions. q-integral representation of these generalized partial mock theta functions are also given. we have also expressed some bilateral mock theta functions in terms of lerch transcendental functions f ( x, ξ ; q,p ).","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"2 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141694047","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.252405.1100
F. Siepe
{"title":"Some remarks on the higher regularity of minimizers of anisotropic functionals","authors":"F. Siepe","doi":"10.21608/ejmaa.2024.252405.1100","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.252405.1100","url":null,"abstract":"","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"31 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141699684","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.280116.1166
Thirupathi Reddy Pinninti
{"title":"SOME PROPERTIES OF ANALYTIC FUNCTIONS DEFINED BY POLYLOGARITHM FUNCTIONS","authors":"Thirupathi Reddy Pinninti","doi":"10.21608/ejmaa.2024.280116.1166","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.280116.1166","url":null,"abstract":"","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"236 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141692443","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.272451.1136
Thokchom Chhatrajit
. One of the research gaps in the study of best proximity for two pairs of mappings in multiplicative metric spaces may lie in the exploration of its applications in speci c elds such as computer science or biology, where understanding the behavior of mappings is critical for modeling and analysis. Emphasizing the signi cance of proximity in multiplicative metric spaces, the investigation seeks to unveil insights into the behavior and interaction of mappings, thereby o ering valuable contributions to the broader eld of mathematical analysis. Through rigorous theoretical analysis and computational experimentation, the study endeavors to provide actionable insights and methodologies for optimizing proximity in multiplicative metric spaces, thereby advancing the theoretical foundations and practical applications within this specialized domain. Many issues in many elds, including di erential equations, optimisation, and computer science, may be modelled by xed-point equations of the type fx = x . In this work, two pairs of proximally commuting mappings in a complete multiplicative metric space are given the idea of optimal proximity. An example is also given to support the results.
.研究乘法度量空间中两对映射的最佳邻近性的一个研究空白可能在于探索其在计算机科学或生物学等特定 c 领域的应用，在这些领域，理解映射的行为对于建模和分析至关重要。本研究强调乘法度量空间中接近性的重要，试图揭示映射的行为和相互作用，从而为更广泛的数学分析，做出有价值的贡献。通过严谨的理论分析和计算实验，该研究致力于为优化乘法度量空间中的邻近性提供可行的见解和方法，从而推进这一专业领域的理论基础和实际应用。许多 领域的许多问题，包括二 连续方程、优化和计算机科学，都可以用 fx = x 类型的 xed-point 方程来建模。在这项工作中，给出了在一个完整的乘法度量空间中两对近似换向映射的最优近似性思想。还给出了一个例子来支持这些结果。
{"title":"BEST PROXIMITY FOR TWO PAIRS OF MAPPINGS IN MULTIPLICATIVE METRIC SPACE","authors":"Thokchom Chhatrajit","doi":"10.21608/ejmaa.2024.272451.1136","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.272451.1136","url":null,"abstract":". One of the research gaps in the study of best proximity for two pairs of mappings in multiplicative metric spaces may lie in the exploration of its applications in speci c elds such as computer science or biology, where understanding the behavior of mappings is critical for modeling and analysis. Emphasizing the signi cance of proximity in multiplicative metric spaces, the investigation seeks to unveil insights into the behavior and interaction of mappings, thereby o ering valuable contributions to the broader eld of mathematical analysis. Through rigorous theoretical analysis and computational experimentation, the study endeavors to provide actionable insights and methodologies for optimizing proximity in multiplicative metric spaces, thereby advancing the theoretical foundations and practical applications within this specialized domain. Many issues in many elds, including di erential equations, optimisation, and computer science, may be modelled by xed-point equations of the type fx = x . In this work, two pairs of proximally commuting mappings in a complete multiplicative metric space are given the idea of optimal proximity. An example is also given to support the results.","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"6 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141702555","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.280883.1168
H. Waghamore, Manjunath B. E.
. This study explores the uniqueness of entire and meromorphic functions with equal weights l ≥ 0 by investigating the general di erence-di erential polynomial Ψ ( z,f ). We have extended the ndings attributed to [3] and derived a new result. Additionally, we examine the implications when a polynomial of degree n shares a common value with the general di erence-di erential polynomial. We have also posed an open problem for future research work.
.本研究通过研究一般 di erence-di erential 多项式 Ψ ( z,f ) 来探索等权重 l≥ 0 的全等函数和同态函数的唯一性。我们扩展了归因于 [3] 的 ndings，并得出了一个新结果。此外，我们还研究了当 n 度多项式与一般 di erence-di erential 多项式共享一个共同值时的影响。我们还为未来的研究工作提出了一个开放性问题。
{"title":"Uniqueness of General Difference Differential Polynomials and Meromorphic(Entire) Functions","authors":"H. Waghamore, Manjunath B. E.","doi":"10.21608/ejmaa.2024.280883.1168","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.280883.1168","url":null,"abstract":". This study explores the uniqueness of entire and meromorphic functions with equal weights l ≥ 0 by investigating the general di erence-di erential polynomial Ψ ( z,f ). We have extended the ndings attributed to [3] and derived a new result. Additionally, we examine the implications when a polynomial of degree n shares a common value with the general di erence-di erential polynomial. We have also posed an open problem for future research work.","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"39 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697041","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.269610.1128
S. Porwal, Omendra Mishra
{"title":"Starlike and Convex functions associated with Hypergeometric Matrix functions","authors":"S. Porwal, Omendra Mishra","doi":"10.21608/ejmaa.2024.269610.1128","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.269610.1128","url":null,"abstract":"","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141711233","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.276458.1148
Ritam Biswas, Tanmay Biswas
. At present time, theory of complex numbers is a very renowned subject area in Mathematics as well as various other elds of science and technology. In nineteenth century, di erent number systems had been introduced for examining algebra regarding multiple imaginary units. The notion of bi-complex numbers, perhaps, would be the most important among those. Later on, as an extension of this number system, generalized bicomplex number had been introduced. On the other hand, the concept of fuzzy logic has been considered to be signi cant in Mathematics to solve problems having imprecise spectrum of data. In this paper, our intension is to fuzzify generalized bicomplex number. For this purpose, here we rst de ne generalized fuzzy bicomplex numbers from two alternative aspects and then, based upon these we propose some basic mathematical tools such as generalized fuzzy bicomplex norm, basic arithmetic operations etc. which help to study some fundamental properties in this regard.
.目前，复数理论是数学以及其他各种 科学和技术领域中一个非常著名的学科领域。19 世纪，为了研究有关多重虚数单位的代数，人们引入了不同的数系 erent。其中最重要的可能是双复数的概念。后来，作为这个数系的扩展，又引入了广义二复数。另一方面，模糊逻辑的概念被认为是数学中解决数据不精确问题的重要。在本文中，我们的目的是对广义双复数进行模糊化。为此，我们 rst de ne 广义模糊二叉数从两个方面进行了研究，并在此基础上提出了一些基本数学工具，如广义模糊二叉法、基本算术运算等，这些工具有助于研究这方面的一些基本特性。
{"title":"Generalized fuzzy bicomplex numbers and some of their properties.","authors":"Ritam Biswas, Tanmay Biswas","doi":"10.21608/ejmaa.2024.276458.1148","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.276458.1148","url":null,"abstract":". At present time, theory of complex numbers is a very renowned subject area in Mathematics as well as various other elds of science and technology. In nineteenth century, di erent number systems had been introduced for examining algebra regarding multiple imaginary units. The notion of bi-complex numbers, perhaps, would be the most important among those. Later on, as an extension of this number system, generalized bicomplex number had been introduced. On the other hand, the concept of fuzzy logic has been considered to be signi cant in Mathematics to solve problems having imprecise spectrum of data. In this paper, our intension is to fuzzify generalized bicomplex number. For this purpose, here we rst de ne generalized fuzzy bicomplex numbers from two alternative aspects and then, based upon these we propose some basic mathematical tools such as generalized fuzzy bicomplex norm, basic arithmetic operations etc. which help to study some fundamental properties in this regard.","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"10 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141693993","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 : 2024-07-01DOI: 10.21608/ejmaa.2024.270077.1129
Megha M. Manakame
. In this research article, we investigates the value distribution of linear q -di erence operators L k ( f, ∆ q,c ) and L k ( g, ∆ q,c ), for a transcendental entire functions of zero order. At the same time we also investigate the uniqueness problems when two linear q - di erence operators of entire functions share one value with nite weight. Our results extends the previous theorems of existing studies [11], [12]
.本文研究了零阶超越全函数的线性 q -di erence 算子 L k ( f, ∆ q,c ) 和 L k ( g, ∆ q,c ) 的值分布。同时，我们还研究了当两个线性 q - di erence 整函数算子共享一个具有 nite weight 的值时的唯一性问题。我们的结果扩展了已有研究[11]、[12]的定理
{"title":"WEIGHTED SHARING OF ENTIRE FUNCTIONS CONCERNING LINEAR DIFFERENCE OPERATORS","authors":"Megha M. Manakame","doi":"10.21608/ejmaa.2024.270077.1129","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.270077.1129","url":null,"abstract":". In this research article, we investigates the value distribution of linear q -di erence operators L k ( f, ∆ q,c ) and L k ( g, ∆ q,c ), for a transcendental entire functions of zero order. At the same time we also investigate the uniqueness problems when two linear q - di erence operators of entire functions share one value with nite weight. Our results extends the previous theorems of existing studies [11], [12]","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"19 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141691343","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 : 2024-01-01DOI: 10.21608/ejmaa.2023.241678.1082
Orhan Dişkaya, H. Menken
{"title":"On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions","authors":"Orhan Dişkaya, H. Menken","doi":"10.21608/ejmaa.2023.241678.1082","DOIUrl":"https://doi.org/10.21608/ejmaa.2023.241678.1082","url":null,"abstract":"","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"5 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139126439","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 : 2024-01-01DOI: 10.21608/ejmaa.2024.264470.1121
N. Hooda, Pardeep Kumar, Monika Sihag
. The aim of this research paper is to extend the results of Karapinar and Khojasteh [13], Karapinar and Fulga [12] in super metric space by using weakly compatible mappings. Further, the analogue results of Jungck[10], Das and Naik [6], and Ciric [5] in quasi-contraction mappings are generalized in super metric space.
{"title":"Weakly compatible maps and fixed point results in Super Metric Space","authors":"N. Hooda, Pardeep Kumar, Monika Sihag","doi":"10.21608/ejmaa.2024.264470.1121","DOIUrl":"https://doi.org/10.21608/ejmaa.2024.264470.1121","url":null,"abstract":". The aim of this research paper is to extend the results of Karapinar and Khojasteh [13], Karapinar and Fulga [12] in super metric space by using weakly compatible mappings. Further, the analogue results of Jungck[10], Das and Naik [6], and Ciric [5] in quasi-contraction mappings are generalized in super metric space.","PeriodicalId":91074,"journal":{"name":"Electronic journal of mathematical analysis and applications","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140517573","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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