This paper presents axiomatic as well as constructive definitions of intuitionistic fuzzy bi-implicators based on intuitionistic fuzzy t-norms and their intuitionistic fuzzy residual implicators. The inter-relationship among different proposed classes is presented along with a detailed study of the properties of one of these intuitionistic fuzzy bi-implicators called the intuitionistic fuzzy β−bi-implicator operator constructed using Lukasiewicz intuitionistic fuzzy t-norm and its R-implicator.
{"title":"INTUITIONISTIC FUZZY BI-IMPLICATOR AND PROPERTIES OF LUKASIEWICZ INTUITIONISTIC FUZZY BI-IMPLICATOR","authors":"S. Ashraf, M. Qayyum, E. Kerre","doi":"10.26837/JAEM.482887","DOIUrl":"https://doi.org/10.26837/JAEM.482887","url":null,"abstract":"This paper presents axiomatic as well as constructive definitions of intuitionistic fuzzy bi-implicators based on intuitionistic fuzzy t-norms and their intuitionistic fuzzy residual implicators. The inter-relationship among different proposed classes is presented along with a detailed study of the properties of one of these intuitionistic fuzzy bi-implicators called the intuitionistic fuzzy β−bi-implicator operator constructed using Lukasiewicz intuitionistic fuzzy t-norm and its R-implicator.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43560532","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 aim of this paper is to establish a general de finite integrals involving product of the Aleph function and generalized incomplete hypergeometric function with general arguments. Being unifi ed and general in nature, this integral yields a number of known and new results as special cases. For the sake of illustration, several corollaries are also recorded here as special case of our main results.
{"title":"INTEGRAL INVOLVING ALEPH-FUNCTION AND THE GENERALIZED INCOMPLETE HYPERGEOMETRIC FUNCTION","authors":"D. Kumar, F. Ayant, Faruk Uçar","doi":"10.26837/JAEM.572066","DOIUrl":"https://doi.org/10.26837/JAEM.572066","url":null,"abstract":"The aim of this paper is to establish a general de finite integrals involving product of the Aleph function and generalized incomplete hypergeometric function with general arguments. Being unifi ed and general in nature, this integral yields a number of known and new results as special cases. For the sake of illustration, several corollaries are also recorded here as special case of our main results.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42780560","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 present article deals with the general family of summation-integral type operators. Here, we introduce the Stancu type generalization of the Jakimovski-LeviatanPǎltǎnea operators and study Voronovskaja-type asymptotic theorem, local approximation, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Also, we propose a king type modification of these operators to obtain better estimates.
{"title":"APPROXIMATION BY STANCU TYPE JAKIMOVSKI-LEVIATAN-PALTANEA OPERATORS","authors":"Alok Kumar, Vandana Rai","doi":"10.26837/JAEM.556533","DOIUrl":"https://doi.org/10.26837/JAEM.556533","url":null,"abstract":"The present article deals with the general family of summation-integral type operators. Here, we introduce the Stancu type generalization of the Jakimovski-LeviatanPǎltǎnea operators and study Voronovskaja-type asymptotic theorem, local approximation, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Also, we propose a king type modification of these operators to obtain better estimates.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47193375","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 object of this paper is to present certain new image formulas for the product of general class of polynomial and (p, q)–extended Gauss’s hypergeometric function by applying the Saigo-Maeda fractional integral operators involving Appell’s function F3. Certain interesting special cases of our main results are also considered.
{"title":"FRACTIONAL INTEGRALS FOR THE PRODUCT OF SRIVASTAVA'S POLYNOMIAL AND (p; q) - EXTENDED HYPERGEOMETRIC FUNCTION","authors":"D.L. Suthar, L. Mishra, A. M. Khan, Anita Alaria","doi":"10.26837/jaem.446155","DOIUrl":"https://doi.org/10.26837/jaem.446155","url":null,"abstract":"The main object of this paper is to present certain new image formulas for the product of general class of polynomial and (p, q)–extended Gauss’s hypergeometric function by applying the Saigo-Maeda fractional integral operators involving Appell’s function F3. Certain interesting special cases of our main results are also considered.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44298983","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}
For all q ∈ (0; 1) and 0 ≤ ∝ < 1 we define a class of analytic functions, so-called q -starlike functions of order ∝ on the open unit disc 𝔻 = { 𝓏 : | 𝓏| < 1 }. We will study this class of functions and explore some inclusion properties with the well-known class Starlike functions of order ∝.
{"title":"q-STARLIKE FUNCTIONS OF ORDER ALPHA","authors":"Y. Polatoglu, Faruk Uçar, Bülent Yilmaz","doi":"10.26837/JAEM.428337","DOIUrl":"https://doi.org/10.26837/JAEM.428337","url":null,"abstract":"For all q ∈ (0; 1) and 0 ≤ ∝ < 1 we define a class of analytic functions, so-called q -starlike functions of order ∝ on the open unit disc 𝔻 = { 𝓏 : | 𝓏| < 1 }. We will study this class of functions and explore some inclusion properties with the well-known class Starlike functions of order ∝.","PeriodicalId":44094,"journal":{"name":"TWMS Journal of Applied and Engineering Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45107176","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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