Demonstratio Mathematica最新文献

{"title":"Properties of a subclass of analytic functions defined by Riemann-Liouville fractional integral applied to convolution product of multiplier transformation and Ruscheweyh derivative","authors":"A. Alb Lupaș, M. Acu","doi":"10.1515/dema-2022-0249","DOIUrl":"https://doi.org/10.1515/dema-2022-0249","url":null,"abstract":"Abstract The contribution of fractional calculus in the development of different areas of research is well known. This article presents investigations involving fractional calculus in the study of analytic functions. Riemann-Liouville fractional integral is known for its extensive applications in geometric function theory. New contributions were previously obtained by applying the Riemann-Liouville fractional integral to the convolution product of multiplier transformation and Ruscheweyh derivative. For the study presented in this article, the resulting operator is used following the line of research that concerns the study of certain new subclasses of analytic functions using fractional operators. Riemann-Liouville fractional integral of the convolution product of multiplier transformation and Ruscheweyh derivative is applied here for introducing a new class of analytic functions. Investigations regarding this newly introduced class concern the usual aspects considered by researchers in geometric function theory targeting the conditions that a function must meet to be part of this class and the properties that characterize the functions that fulfil these conditions. Theorems and corollaries regarding neighborhoods and their inclusion relation involving the newly defined class are stated, closure and distortion theorems are proved, and coefficient estimates are obtained involving the functions belonging to this class. Geometrical properties such as radii of convexity, starlikeness, and close-to-convexity are also obtained for this new class of functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49152583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New inertial forward–backward algorithm for convex minimization with applications","authors":"K. Kankam, W. Cholamjiak, P. Cholamjiak","doi":"10.1515/dema-2022-0188","DOIUrl":"https://doi.org/10.1515/dema-2022-0188","url":null,"abstract":"Abstract In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46734314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions","authors":"H. Olğar","doi":"10.1515/dema-2022-0210","DOIUrl":"https://doi.org/10.1515/dema-2022-0210","url":null,"abstract":"Abstract The goal of this study is to analyse the eigenvalues and weak eigenfunctions of a new type of multi-interval Sturm-Liouville problem (MISLP) which differs from the standard Sturm-Liouville problems (SLPs) in that the Strum-Liouville equation is defined on a finite number of non-intersecting subintervals and the boundary conditions are set not only at the endpoints but also at finite number internal points of interaction. For the self-adjoint treatment of the considered MISLP, we introduced some self-adjoint linear operators in such a way that the considered multi-interval SLPs can be interpreted as operator-pencil equation. First, we defined a concept of weak solutions (eigenfunctions) for MISLPs with interface conditions at the common ends of the subintervals. Then, we found some important properties of eigenvalues and corresponding weak eigenfunctions. In particular, we proved that the spectrum is discrete and the system of weak eigenfunctions forms a Riesz basis in appropriate Hilbert space.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49041957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces","authors":"Choonkil Park, Mohammad Amin Tareeghee, Abbas Najati, Yavar Khedmati Yengejeh, Siriluk Paokanta","doi":"10.1515/dema-2023-0265","DOIUrl":"https://doi.org/10.1515/dema-2023-0265","url":null,"abstract":"Abstract This article presents the general solution <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> <m:mo>:</m:mo> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">G</m:mi> <m:mo>→</m:mo> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">V</m:mi> </m:math> f:{mathcal{G}}to {mathcal{V}} of the following functional equation: <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mn>6</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mn>2</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> <m:mn>4</m:mn> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mn>3</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>+</m:mo> <m:mn>4</m:mn> <m:mi>y</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>,</m:mo> <m:mspace width=\"1.0em\" /> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mi>y</m:mi> <m:mo>∈</m:mo> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">G</m:mi> <m:mo>,</m:mo> </m:math> fleft(x)-4fleft(x+y)+6fleft(x+2y)-4fleft(x+3y)+fleft(x+4y)=0,hspace{1.0em}x,yin {mathcal{G}}, where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">G</m:mi> <m:mo>,</m:mo> <m:mo>+</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left({mathcal{G}},+) is an abelian group and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">V</m:mi> </m:math> {mathcal{V}} is a linear space. We also investigate its Hyers-Ulam stability on some restricted domains. We apply the obtained results to present some asymptotic behaviors of this functional equation in the framework of normed spaces. Finally, we provide some characterizations of inner product spaces associated with the mentioned functional equation.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximation of the image of the Lp ball under Hilbert-Schmidt integral operator","authors":"N. Huseyin","doi":"10.1515/dema-2022-0219","DOIUrl":"https://doi.org/10.1515/dema-2022-0219","url":null,"abstract":"Abstract In this article, an approximation of the image of the closed ball of the space L p {L}_{p} ( p > 1 pgt 1 ) centered at the origin with radius r r under Hilbert-Schmidt integral operator F ( ⋅ ) : L p → L q Fleft(cdot ):{L}_{p}to {L}_{q} , 1 p + 1 q = 1 frac{1}{p}+frac{1}{q}=1 is considered. An error evaluation for the given approximation is obtained.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43580821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniqueness of solutions for a ψ-Hilfer fractional integral boundary value problem with the p-Laplacian operator","authors":"A. Alsaedi, M. Alghanmi, B. Ahmad, Boshra Alharbi","doi":"10.1515/dema-2022-0195","DOIUrl":"https://doi.org/10.1515/dema-2022-0195","url":null,"abstract":"Abstract In this article, we discuss the existence of a unique solution to a ψ psi -Hilfer fractional differential equation involving the p p -Laplacian operator subject to nonlocal ψ psi -Riemann-Liouville fractional integral boundary conditions. Banach’s fixed point theorem is the main tool of our study. Examples are given for illustrating the obtained results.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42501432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hyers-Ulam stability of isometries on bounded domains-II","authors":"Ginkyu Choi, Soon-Mo Jung","doi":"10.1515/dema-2022-0196","DOIUrl":"https://doi.org/10.1515/dema-2022-0196","url":null,"abstract":"Abstract The question of whether there is a true isometry approximating the ε varepsilon -isometry defined in the bounded subset of the n n -dimensional Euclidean space has long been considered an interesting question. In 1982, Fickett published the first article on this topic, and in early 2000, Alestalo et al. and Väisälä improved Fickett’s result significantly. Recently, the second author of this article published a paper improving the previous results. The main purpose of this article is to significantly improve all of the aforementioned results by applying a basic and intuitive method.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46318442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A certain class of fractional difference equations with damping: Oscillatory properties","authors":"Sivakumar Arundhathi, J. Alzabut, V. Muthulakshmi, Hakan Adıgüzel","doi":"10.1515/dema-2022-0236","DOIUrl":"https://doi.org/10.1515/dema-2022-0236","url":null,"abstract":"Abstract In this study, we have investigated the oscillatory properties of the following fractional difference equation: ∇ α + 1 χ ( κ ) ⋅ ∇ α χ ( κ ) − p ( κ ) г ( ∇ α χ ( κ ) ) + q ( κ ) G ∑ μ = κ − α + 1 ∞ ( μ − κ − 1 ) ( − α ) χ ( μ ) = 0 , {nabla }^{alpha +1}chi left(kappa )cdot {nabla }^{alpha }chi left(kappa )-pleft(kappa )гleft({nabla }^{alpha }chi left(kappa ))+qleft(kappa ){mathcal{G}}left(mathop{sum }limits_{mu =kappa -alpha +1}^{infty }{left(mu -kappa -1)}^{left(-alpha )}chi left(mu )right)=0, where κ ∈ N 0 kappa in {{mathbb{N}}}_{0} , ∇ α {nabla }^{alpha } denotes the Liouville fractional difference operator of order α ∈ ( 0 , 1 ) alpha in left(0,1) , p p , and q q are nonnegative sequences, and г г and G {mathcal{G}} are real valued continuous functions, all of which satisfy certain assumptions. Using the generalized Riccati transformation technique, mathematical inequalities, and comparison results, we have found a number of new oscillation results. A few examples have been built up in this context to illustrate the main findings. The conclusion of this study is regarded as an expansion of continuous time to discrete time in fractional contexts.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48733253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic behavior of resolvents of equilibrium problems on complete geodesic spaces","authors":"Y. Kimura, Keisuke Shindo","doi":"10.1515/dema-2022-0187","DOIUrl":"https://doi.org/10.1515/dema-2022-0187","url":null,"abstract":"Abstract In this article, we discuss equilibrium problems and their resolvents on complete geodesic spaces. In particular, we consider asymptotic behavior and continuity of resolvents with positive parameter in a complete geodesic space whose curvature is bounded above. Furthermore, we apply these results to resolvents of convex functions.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45236415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A dimension expanded preconditioning technique for block two-by-two linear equations","authors":"Wei-Hua Luo, Bruno Carpentieri, Jun Guo","doi":"10.1515/dema-2023-0260","DOIUrl":"https://doi.org/10.1515/dema-2023-0260","url":null,"abstract":"Abstract In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}