Pub Date : 2024-08-12DOI: 10.1186/s13660-024-03173-7
Fatimah Rahoumah, Kai Siong Yow, Nik Mohd Asri Nik Long, Menshawi Gasim
Complex neutrosophic soft groups represent a significant advancement in handling uncertainty by integrating the concepts of fuzzy logic, soft sets, and neutrosophic logic. These groups generalize complex fuzzy soft groups and introduce an additional dimension through neutrosophic membership functions, namely truth, indeterminacy, and falsity. This creates a richer framework for dealing with uncertainty and ambiguity, making it well-suited for managing complex data structures in real-world applications. We explore some important definitions and theoretical frameworks surrounding complex neutrosophic soft groups, highlighting the unique aspect of neutrosophic membership functions. Additionally, we present an overview of neutrosophic soft groups, exploring some of their key operations and fundamental properties. We then examine the basics of homogeneous complex neutrosophic soft sets and their roles in establishing complex neutrosophic soft groups.
{"title":"On properties and operations of complex neutrosophic soft groups","authors":"Fatimah Rahoumah, Kai Siong Yow, Nik Mohd Asri Nik Long, Menshawi Gasim","doi":"10.1186/s13660-024-03173-7","DOIUrl":"https://doi.org/10.1186/s13660-024-03173-7","url":null,"abstract":"Complex neutrosophic soft groups represent a significant advancement in handling uncertainty by integrating the concepts of fuzzy logic, soft sets, and neutrosophic logic. These groups generalize complex fuzzy soft groups and introduce an additional dimension through neutrosophic membership functions, namely truth, indeterminacy, and falsity. This creates a richer framework for dealing with uncertainty and ambiguity, making it well-suited for managing complex data structures in real-world applications. We explore some important definitions and theoretical frameworks surrounding complex neutrosophic soft groups, highlighting the unique aspect of neutrosophic membership functions. Additionally, we present an overview of neutrosophic soft groups, exploring some of their key operations and fundamental properties. We then examine the basics of homogeneous complex neutrosophic soft sets and their roles in establishing complex neutrosophic soft groups.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947980","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}
Pub Date : 2024-08-05DOI: 10.1186/s13660-024-03182-6
Ohud Bulayhan Almutairi, Sid Ahmed Ould Ahmed Mahmoud
In recent years, the study of bounded linear operators in several variables has received great interest from many authors, including the second author’s previous contributions. In our present work, we define a new class of multivariable operator theory, which we have called M-hyponormal tuple. We present some algebraic and spectral properties associated with them.
{"title":"M-hyponormality in several variables operator theory","authors":"Ohud Bulayhan Almutairi, Sid Ahmed Ould Ahmed Mahmoud","doi":"10.1186/s13660-024-03182-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03182-6","url":null,"abstract":"In recent years, the study of bounded linear operators in several variables has received great interest from many authors, including the second author’s previous contributions. In our present work, we define a new class of multivariable operator theory, which we have called M-hyponormal tuple. We present some algebraic and spectral properties associated with them.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969616","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}
Pub Date : 2024-07-30DOI: 10.1186/s13660-024-03177-3
Qin Li, Zonghu Xiu, Lin Chen
In this paper, we deal with the following fractional $p&q$ -Laplacian problem: $$ left { textstylebegin{array}{l@{quad }l} (-Delta )_{p}^{s}u +(-Delta )_{q}^{s}u =lambda a(x)|u|^{theta -2}u+ mu b(x)|u|^{r-2}u&text{in}; Omega , u(x)=0 &text{in}; mathbb{R}^{N}setminus Omega , end{array}displaystyle right . $$ where $Omega subset mathbb{R}^{N}$ is a bounded domain with smooth boundary, $sin (0,1)$ , $(-Delta )_{m}^{s}$ $(min {p,q})$ is the fractional m-Laplacian operator, $p,q,r,theta in (1,p_{s}^{*}]$ , $p_{s}^{*}=frac{Np}{N-sp}$ , $lambda , mu >0$ , and the weights $a(x)$ and $b(x)$ are possibly sign changing. Using the concentration compactness principle for fractional Sobolev spaces and the Ekeland variational principle, we prove that the problem admits a nonnegative solution for the critical case $r=p_{s}^{*}$ . Moreover, for the subcritical case $r< p_{s}^{*}$ , we obtain two existence results by applying the Ekeland variational principle and the mountain pass theorem.
{"title":"Existence of nontrivial solutions for a fractional (p&q)-Laplacian equation with sandwich-type and sign-changing nonlinearities","authors":"Qin Li, Zonghu Xiu, Lin Chen","doi":"10.1186/s13660-024-03177-3","DOIUrl":"https://doi.org/10.1186/s13660-024-03177-3","url":null,"abstract":"In this paper, we deal with the following fractional $p&q$ -Laplacian problem: $$ left { textstylebegin{array}{l@{quad }l} (-Delta )_{p}^{s}u +(-Delta )_{q}^{s}u =lambda a(x)|u|^{theta -2}u+ mu b(x)|u|^{r-2}u&text{in}; Omega , u(x)=0 &text{in}; mathbb{R}^{N}setminus Omega , end{array}displaystyle right . $$ where $Omega subset mathbb{R}^{N}$ is a bounded domain with smooth boundary, $sin (0,1)$ , $(-Delta )_{m}^{s}$ $(min {p,q})$ is the fractional m-Laplacian operator, $p,q,r,theta in (1,p_{s}^{*}]$ , $p_{s}^{*}=frac{Np}{N-sp}$ , $lambda , mu >0$ , and the weights $a(x)$ and $b(x)$ are possibly sign changing. Using the concentration compactness principle for fractional Sobolev spaces and the Ekeland variational principle, we prove that the problem admits a nonnegative solution for the critical case $r=p_{s}^{*}$ . Moreover, for the subcritical case $r< p_{s}^{*}$ , we obtain two existence results by applying the Ekeland variational principle and the mountain pass theorem.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871643","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}
Pub Date : 2024-07-30DOI: 10.1186/s13660-024-03181-7
Meizhong Wang, Dashan Fan
It is known that the damped fractional wave equation has the diffusive structure as $trightarrow infty $ . Let $u(t,x)=e^{-t}cosh (tsqrt{L})f(x)+e^{-t} frac{sinh (tsqrt{L})}{sqrt{L}}(f(x)+g(x))$ be the solution of the Cauchy problem for the damped fractional wave equation, where $sqrt{L}$ involves the fractional Laplacian $(-triangle )^{alpha}$ on the space variable. We can study the decay estimate of the solution $u(t,x)$ over the time t by means of the Cauchy problem for the parabolic equation. In this paper, we consider, for $0
{"title":"Asymptotic estimates of solution to damped fractional wave equation","authors":"Meizhong Wang, Dashan Fan","doi":"10.1186/s13660-024-03181-7","DOIUrl":"https://doi.org/10.1186/s13660-024-03181-7","url":null,"abstract":"It is known that the damped fractional wave equation has the diffusive structure as $trightarrow infty $ . Let $u(t,x)=e^{-t}cosh (tsqrt{L})f(x)+e^{-t} frac{sinh (tsqrt{L})}{sqrt{L}}(f(x)+g(x))$ be the solution of the Cauchy problem for the damped fractional wave equation, where $sqrt{L}$ involves the fractional Laplacian $(-triangle )^{alpha}$ on the space variable. We can study the decay estimate of the solution $u(t,x)$ over the time t by means of the Cauchy problem for the parabolic equation. In this paper, we consider, for $0<alpha <1$ , the Cauchy problem in the two- and three-dimensional spaces for the damped fractional wave equation and the corresponding parabolic equation and obtain the Triebel–Lizorkin space estimate of the difference of solutions. At the same time, we also consider, for $alpha =1$ , the case of the Cauchy problem in the four-dimensional space and obtain a Triebel–Lizorkin space estimate.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871452","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}
Pub Date : 2024-07-25DOI: 10.1186/s13660-024-03174-6
Takeshi Suguro
We consider the logarithmic Sobolev inequality on the Heisenberg group. One can derive the logarithmic Sobolev inequality from the Sobolev inequality, and we consider an application to the uncertainty inequality on the Heisenberg group. Moreover, one can also obtain a dissipative estimate of a solution of the heat equation on the Heisenberg group from the logarithmic Sobolev inequality.
{"title":"The logarithmic Sobolev inequality on the Heisenberg group and applications to the uncertainty inequality and heat equation","authors":"Takeshi Suguro","doi":"10.1186/s13660-024-03174-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03174-6","url":null,"abstract":"We consider the logarithmic Sobolev inequality on the Heisenberg group. One can derive the logarithmic Sobolev inequality from the Sobolev inequality, and we consider an application to the uncertainty inequality on the Heisenberg group. Moreover, one can also obtain a dissipative estimate of a solution of the heat equation on the Heisenberg group from the logarithmic Sobolev inequality.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141783079","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}
Pub Date : 2024-07-25DOI: 10.1186/s13660-024-03175-5
Mingyang Zhao, Liangjin Zhou
This article presents the HDG approximation as a solution to the unilateral contact problem, leveraging the regularization method and an iterative procedure for resolution. In our study, u represents the potential (displacement of the elastic body) and q represents the flux (the force exerted on the body). Our analysis establishes that the utilization of polynomials of degree $k (k ge 1)$ leads to achieving an optimal convergence rate of order $k+1$ in $L^{2}$ -norm for both u and q. Importantly, this optimal convergence is maintained irrespective of whether the domain is discretized through a structured or unstructured grid. The numerical results consistently align with the theoretical findings, underscoring the effectiveness and reliability of the proposed HDG approximation method for unilateral contact problems.
本文利用正则化方法和迭代程序，提出了单边接触问题的 HDG 近似解。在我们的研究中，u 代表势（弹性体的位移），q 代表通量（施加在弹性体上的力）。我们的分析表明，使用度数为 $k (k ge 1)$ 的多项式可使 u 和 q 在 $L^{2}$ -norm（L^{2}$ 正态）下达到最佳收敛率 $k+1$。数值结果与理论研究结果一致，凸显了针对单边接触问题提出的 HDG 近似方法的有效性和可靠性。
{"title":"HDG methods for the unilateral contact problem","authors":"Mingyang Zhao, Liangjin Zhou","doi":"10.1186/s13660-024-03175-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03175-5","url":null,"abstract":"This article presents the HDG approximation as a solution to the unilateral contact problem, leveraging the regularization method and an iterative procedure for resolution. In our study, u represents the potential (displacement of the elastic body) and q represents the flux (the force exerted on the body). Our analysis establishes that the utilization of polynomials of degree $k (k ge 1)$ leads to achieving an optimal convergence rate of order $k+1$ in $L^{2}$ -norm for both u and q. Importantly, this optimal convergence is maintained irrespective of whether the domain is discretized through a structured or unstructured grid. The numerical results consistently align with the theoretical findings, underscoring the effectiveness and reliability of the proposed HDG approximation method for unilateral contact problems.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782889","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}
Pub Date : 2024-07-25DOI: 10.1186/s13660-024-03176-4
Koti N. V. V. Vara Prasad, Vinay Mishra, Zoran D. Mitrović, Dania Santina, Nabil Mlaiki
In this paper, we introduce the notion of unified interpolative contractions of the Reich–Rus–Ćirić type and give some results about the fixed points for these mappings in the framework of relational metric spaces. We present examples where the results of some previous research are not relevant. Also, we apply our results to solving problems related to nonlinear matrix equations, emphasizing their practical importance.
{"title":"Unified interpolative of a Reich-Rus-Ćirić-type contraction in relational metric space with an application","authors":"Koti N. V. V. Vara Prasad, Vinay Mishra, Zoran D. Mitrović, Dania Santina, Nabil Mlaiki","doi":"10.1186/s13660-024-03176-4","DOIUrl":"https://doi.org/10.1186/s13660-024-03176-4","url":null,"abstract":"In this paper, we introduce the notion of unified interpolative contractions of the Reich–Rus–Ćirić type and give some results about the fixed points for these mappings in the framework of relational metric spaces. We present examples where the results of some previous research are not relevant. Also, we apply our results to solving problems related to nonlinear matrix equations, emphasizing their practical importance.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782891","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}
Pub Date : 2024-07-25DOI: 10.1186/s13660-024-03178-2
Jurica Perić
The concept of strong ${mathcal {F}}$ -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong ${mathcal {F}}$ -concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.
{"title":"Strong (mathcal {F})-convexity and concavity and refinements of some classical inequalities","authors":"Jurica Perić","doi":"10.1186/s13660-024-03178-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03178-2","url":null,"abstract":"The concept of strong ${mathcal {F}}$ -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong ${mathcal {F}}$ -concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782890","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}
In this article, we study the structure of a multiple variable mapping. Indeed, we reduce the system of several mixed additive-quadratic equations defining a multivariable mapping to obtain a single functional equation, say, the multimixed additive-quadratic equation. We also show that such mappings under some conditions can be multi-additive, multi-quadratic and multi-additive-quadratic. Moreover, we establish the Hyers–Ulam stability of the multimixed additive-quadratic equation, using the so-called direct (Hyers) method. Additionally, we present a concrete example (the numerical approximation) regarding the stability of some two variable mappings into real numbers. Applying some characterization results, we indicate two examples for the case that a multimixed additive-quadratic mapping (in the special cases) cannot be stable.
{"title":"The system of mixed type additive-quadratic equations and approximations","authors":"Abasalt Bodaghi, Hesam Mahzoon, Nasser Mikaeilvand","doi":"10.1186/s13660-024-03180-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03180-8","url":null,"abstract":"In this article, we study the structure of a multiple variable mapping. Indeed, we reduce the system of several mixed additive-quadratic equations defining a multivariable mapping to obtain a single functional equation, say, the multimixed additive-quadratic equation. We also show that such mappings under some conditions can be multi-additive, multi-quadratic and multi-additive-quadratic. Moreover, we establish the Hyers–Ulam stability of the multimixed additive-quadratic equation, using the so-called direct (Hyers) method. Additionally, we present a concrete example (the numerical approximation) regarding the stability of some two variable mappings into real numbers. Applying some characterization results, we indicate two examples for the case that a multimixed additive-quadratic mapping (in the special cases) cannot be stable.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141783080","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}
Pub Date : 2024-07-18DOI: 10.1186/s13660-024-03171-9
Abhay Pratap Singh, Uaday Singh
Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space $L^{p,w}$ , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function $fin L^{p,w}$ . We use the modulus of continuity of the functions to measure the rate of convergence.
{"title":"Approximation properties of a modified Gauss–Weierstrass singular integral in a weighted space","authors":"Abhay Pratap Singh, Uaday Singh","doi":"10.1186/s13660-024-03171-9","DOIUrl":"https://doi.org/10.1186/s13660-024-03171-9","url":null,"abstract":"Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space $L^{p,w}$ , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function $fin L^{p,w}$ . We use the modulus of continuity of the functions to measure the rate of convergence.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740766","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}
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