Josip Pecaric, Anamarija Perusic-Pribanic, Ksenija Smoljak-Kalamir
In this paper, we obtain some new weighted Hermite-Hadamard-type inequalities which involve generalizations of Steffensen?s inequality obtained by using the extension of Montgomery identity via Taylor?s formula. Further, we show that by using the extension of Montgomery identity via Fink?s identity we can obtain some other weighted Hermite-Hadamard-type inequalities.
{"title":"Weighted Hermite-Hadamard-type inequalities for generalizations of Steffensen’s inequality via the extension of Mongomery identity","authors":"Josip Pecaric, Anamarija Perusic-Pribanic, Ksenija Smoljak-Kalamir","doi":"10.2298/aadm220523015p","DOIUrl":"https://doi.org/10.2298/aadm220523015p","url":null,"abstract":"In this paper, we obtain some new weighted Hermite-Hadamard-type inequalities which involve generalizations of Steffensen?s inequality obtained by using the extension of Montgomery identity via Taylor?s formula. Further, we show that by using the extension of Montgomery identity via Fink?s identity we can obtain some other weighted Hermite-Hadamard-type inequalities.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we analyze multi-dimensional Weyl almost periodic type functions in Lebesgue spaces with variable exponents. The introduced classes seem to be new and not considered elsewhere even in the constant coefficient case. We provide certain applications to the abstract Volterra integrodifferential equations in Banach spaces.
{"title":"Multi-dimensional Weyl almost periodic type functions and applications","authors":"Marko Kostic, Vladimir Fedorov","doi":"10.2298/aadm221130016k","DOIUrl":"https://doi.org/10.2298/aadm221130016k","url":null,"abstract":"In this paper, we analyze multi-dimensional Weyl almost periodic type functions in Lebesgue spaces with variable exponents. The introduced classes seem to be new and not considered elsewhere even in the constant coefficient case. We provide certain applications to the abstract Volterra integrodifferential equations in Banach spaces.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers and polynomials of order with complex numbers with the aid of the Euler operator and partial derivatives of the generating function. Relations among the these numbers and polynomials of neqative integer order, the beta-type rational functions, finite combinatorial sums, the Stirling numbers, and the Lah numbers are given. Finally, new classes of polynomials and modification exponential Euler type splines are constructed.
{"title":"Modification exponential Euler type splines derived from Apostol-Euler numbers and polynomials of complex order","authors":"Damla Gun, Y. Simsek","doi":"10.2298/aadm220712011g","DOIUrl":"https://doi.org/10.2298/aadm220712011g","url":null,"abstract":"The purpose of this paper is to give formulas and Recurrence relations for the Apostol-Euler numbers and polynomials of order with complex numbers with the aid of the Euler operator and partial derivatives of the generating function. Relations among the these numbers and polynomials of neqative integer order, the beta-type rational functions, finite combinatorial sums, the Stirling numbers, and the Lah numbers are given. Finally, new classes of polynomials and modification exponential Euler type splines are constructed.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, new sharp Mitrinovic-Adamovic inequalities for circular functions are established.
本文建立了圆函数的新的尖锐Mitrinovic-Adamovic不等式。
{"title":"New sharp inequalities of Mitrinovic-Adamovic type","authors":"Weidong Jiang","doi":"10.2298/aadm210507010j","DOIUrl":"https://doi.org/10.2298/aadm210507010j","url":null,"abstract":"In this paper, new sharp Mitrinovic-Adamovic inequalities for circular functions are established.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The first aim of this paper is to show how the Huygens? and Wilker?s inequalities are related. In this sense, we establish and prove a class of inequalities depending on a parameter n, where Huygens? and Wilker?s inequalities are obtained when n = 1 and n = 2, respectively. By exploiting the above idea, we introduce other classes of inequalities depending on a parameter, extending an inequality of Wilker type and also the classical Cusa inequality. Finally, some open problems are posed.
{"title":"The relationship between Huygens’ and Wilker’s inequalities and further remarks","authors":"Chao-Ping Chen, C. Mortici","doi":"10.2298/aadm210727012c","DOIUrl":"https://doi.org/10.2298/aadm210727012c","url":null,"abstract":"The first aim of this paper is to show how the Huygens? and Wilker?s inequalities are related. In this sense, we establish and prove a class of inequalities depending on a parameter n, where Huygens? and Wilker?s inequalities are obtained when n = 1 and n = 2, respectively. By exploiting the above idea, we introduce other classes of inequalities depending on a parameter, extending an inequality of Wilker type and also the classical Cusa inequality. Finally, some open problems are posed.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For an anisotropic discrete nonlinear problem with variable exponent, we demonstrate both the existence and multiplicity of nontrivial solutions in this study. The variational principle and critical point theory are the key techniques employed here.
{"title":"Anisotropic discrete boundary value problems","authors":"O. Hammouti, S. Taarabti, R. Agarwal","doi":"10.2298/aadm220824008h","DOIUrl":"https://doi.org/10.2298/aadm220824008h","url":null,"abstract":"For an anisotropic discrete nonlinear problem with variable exponent, we demonstrate both the existence and multiplicity of nontrivial solutions in this study. The variational principle and critical point theory are the key techniques employed here.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let the sequences Gn and gn be defined by Gn := ?10 dt/(1?t2n)1/n (n ? 2) and gn := ??0 dt/(1 + t2n)1/n (n ? 1). In this paper, we first derive analytical representations for these two sequences Gn and gn in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for Gn and gn.
{"title":"Analytical and asymptotic representations for two sequence related to Gauss’ lemniscate functions","authors":"Xue-Feng Han, Chao-Ping Chen, H.M. Srivastava","doi":"10.2298/aadm220810024h","DOIUrl":"https://doi.org/10.2298/aadm220810024h","url":null,"abstract":"Let the sequences Gn and gn be defined by Gn := ?10 dt/(1?t2n)1/n (n ? 2) and gn := ??0 dt/(1 + t2n)1/n (n ? 1). In this paper, we first derive analytical representations for these two sequences Gn and gn in terms of the gamma function. By using the obtained analytical representations, we then deduce asymptotic expansions for Gn and gn.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136304077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For r, s ? R and ? = min {r, s}, let D[x + r, x + s; ?n?1] ? ??n (x) be the divided difference of the functions ?n?1 = (?1)n ?(n?1) (n ? N) on (??,?), where ?(n) stands for the polygamma functions. In this paper, we present the necessary and sufficient conditions for the functions x ? ?k i=1 ?mi (x) ? ?k ?k i=1 ?ni (x) , x ? ?k i=1 ?ni (x) ? ?k?snk (x) to be completely monotonic on (??,?), where mi, ni ? N for i = 1,..., k with k ? 2 and snk = ?k i=1 ni. These generalize known results and gives an answer to a problem.
对于r s ?R和?= min {r, s}，让D[x + r, x + s;n ?1) ??？N (x)是两个函数的除差? N ?1 = (?1)n ?(n?1) (n?N) on(??，?)，其中?(N)表示多元函数。本文给出了函数x ?k i=1 ?mi (x) ?k k i=1 ni (x) x ?k i=1 ni (x) ?k ?SNK (x)在(??，?)上是完全单调的，其中mi, ni ?N对于i = 1，…k和k ?2和SNK = ?k i=1 ni。这些方法概括了已知的结果，并给出了问题的答案。
{"title":"Complete monotonicity involving the divided difference of polygamma functions","authors":"Zhen-Hang Yang, Jingfeng Tian","doi":"10.2298/aadm210630007y","DOIUrl":"https://doi.org/10.2298/aadm210630007y","url":null,"abstract":"For r, s ? R and ? = min {r, s}, let D[x + r, x + s; ?n?1] ? ??n (x) be the divided difference of the functions ?n?1 = (?1)n ?(n?1) (n ? N) on (??,?), where ?(n) stands for the polygamma functions. In this paper, we present the necessary and sufficient conditions for the functions x ? ?k i=1 ?mi (x) ? ?k ?k i=1 ?ni (x) , x ? ?k i=1 ?ni (x) ? ?k?snk (x) to be completely monotonic on (??,?), where mi, ni ? N for i = 1,..., k with k ? 2 and snk = ?k i=1 ni. These generalize known results and gives an answer to a problem.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68353884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Inverse interpolation with rational functions is investigated for the use in iterative refinement of the root approximation. A new family of optimal methods of arbitrary large order of convergence for solving nonlinear equations is presented. Experiments are conducted to check the influence of polynomial degrees in numerator and denominator on convergence properties of the proposed methods. Wolfram Mathematica 12 software was used to carry the computation due to its capabilities of arbitrary large precision arithmetic.
{"title":"New family of root-finding algorithms based on inverse rational interpolation","authors":"J. Dzunic","doi":"10.2298/aadm220708003d","DOIUrl":"https://doi.org/10.2298/aadm220708003d","url":null,"abstract":"Inverse interpolation with rational functions is investigated for the use in iterative refinement of the root approximation. A new family of optimal methods of arbitrary large order of convergence for solving nonlinear equations is presented. Experiments are conducted to check the influence of polynomial degrees in numerator and denominator on convergence properties of the proposed methods. Wolfram Mathematica 12 software was used to carry the computation due to its capabilities of arbitrary large precision arithmetic.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68354325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We aim to investigate the four types of variant Euler harmonic sums. Also, as corollaries, we provide particular examples of our core findings, some of whose further instances are evaluated in terms of basic and well-known functions as well as certain mathematical constants. We explore relevant linkages between our results and those of other previously established studies. An examination of a specific case of one result shows a relationship to series involving zeta functions, which is also a popular area of research.
{"title":"Four types of variant Euler harmonic sums","authors":"Necdet Batır, Junesang Choi","doi":"10.2298/aadm200411021b","DOIUrl":"https://doi.org/10.2298/aadm200411021b","url":null,"abstract":"We aim to investigate the four types of variant Euler harmonic sums. Also, as corollaries, we provide particular examples of our core findings, some of whose further instances are evaluated in terms of basic and well-known functions as well as certain mathematical constants. We explore relevant linkages between our results and those of other previously established studies. An examination of a specific case of one result shows a relationship to series involving zeta functions, which is also a popular area of research.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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