This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem.
{"title":"Strong convergence of split equality variational inequality, variational inclusion, and multiple sets fixed point problems in Hilbert spaces with application","authors":"Charu Batra, Renu Chugh, Rajeev Kumar, Khaled Suwais, Sally Almanasra, Nabil Mlaiki","doi":"10.1186/s13660-024-03118-0","DOIUrl":"https://doi.org/10.1186/s13660-024-03118-0","url":null,"abstract":"This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"86 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302524","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 : 2024-03-21DOI: 10.1186/s13660-024-03119-z
Yi Li, Mengjiao Wang
In this paper, we study the weak-type regularity of the Bergman projection on n-dimensional classical Hartogs triangles. We extend the results of Huo–Wick on the 2-dimensional classical Hartogs triangle to the n-dimensional classical Hartogs triangle and show that the Bergman projection is of weak type at the upper endpoint of $L^{q}$ -boundedness but not of weak type at the lower endpoint of $L^{q}$ -boundedness.
本文研究了 n 维经典哈托格三角形上伯格曼投影的弱型正则性。我们将 Huo-Wick 关于 2 维经典哈托格三角形的结果推广到 n 维经典哈托格三角形，并证明伯格曼投影在 $L^{q}$ 有界的上端点是弱类型的，但在 $L^{q}$ 有界的下端点不是弱类型的。
{"title":"Weak-type regularity for the Bergman projection over N-dimensional classical Hartogs triangles","authors":"Yi Li, Mengjiao Wang","doi":"10.1186/s13660-024-03119-z","DOIUrl":"https://doi.org/10.1186/s13660-024-03119-z","url":null,"abstract":"In this paper, we study the weak-type regularity of the Bergman projection on n-dimensional classical Hartogs triangles. We extend the results of Huo–Wick on the 2-dimensional classical Hartogs triangle to the n-dimensional classical Hartogs triangle and show that the Bergman projection is of weak type at the upper endpoint of $L^{q}$ -boundedness but not of weak type at the lower endpoint of $L^{q}$ -boundedness.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"30 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196979","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 : 2024-03-21DOI: 10.1186/s13660-024-03113-5
Jacob A. Abuchu, Austine E. Ofem, Hüseyin Işık, Godwin C. Ugwunnadi, Ojen K. Narain
In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed point constraint of quasi-nonexpansive mappings under the scope of real Hilbert spaces when the underlying cost operator is quasi-monotone. The method involves inertial viscosity approximation and a constructed self-adjustable step size condition that depends solely on the information of the previous step. We establish a strong convergence result of the proposed method under certain mild conditions on the algorithm parameters. Finally, to demonstrate the gain of our method, some numerical examples are presented in comparison with some related methods in literature.
{"title":"Modified inertial viscosity extrapolation method for solving quasi-monotone variational inequality and fixed point problems in real Hilbert spaces","authors":"Jacob A. Abuchu, Austine E. Ofem, Hüseyin Işık, Godwin C. Ugwunnadi, Ojen K. Narain","doi":"10.1186/s13660-024-03113-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03113-5","url":null,"abstract":"In this paper, we introduce and study a viscous-type extrapolation algorithm for finding a solution of the variational inequality problem and a fixed point constraint of quasi-nonexpansive mappings under the scope of real Hilbert spaces when the underlying cost operator is quasi-monotone. The method involves inertial viscosity approximation and a constructed self-adjustable step size condition that depends solely on the information of the previous step. We establish a strong convergence result of the proposed method under certain mild conditions on the algorithm parameters. Finally, to demonstrate the gain of our method, some numerical examples are presented in comparison with some related methods in literature.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"27 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196906","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 : 2024-03-21DOI: 10.1186/s13660-024-03109-1
Naim Latif Braha
The main object of this paper is to construct a new class of modified $(p,q)$ -Gamma-type operators. For this new class of operators, in section one, the general moments are find; in section two, the Korovkin-type theorem and some direct results are proved by considering the modulus of continuity and modulus of smoothness and their behavior in Lipschitz-type spaces. In section three, some results in the weighted spaces are given, and in the end, some shape-preserving properties are proven.
{"title":"Approximation by modified ((p,q))-gamma-type operators","authors":"Naim Latif Braha","doi":"10.1186/s13660-024-03109-1","DOIUrl":"https://doi.org/10.1186/s13660-024-03109-1","url":null,"abstract":"The main object of this paper is to construct a new class of modified $(p,q)$ -Gamma-type operators. For this new class of operators, in section one, the general moments are find; in section two, the Korovkin-type theorem and some direct results are proved by considering the modulus of continuity and modulus of smoothness and their behavior in Lipschitz-type spaces. In section three, some results in the weighted spaces are given, and in the end, some shape-preserving properties are proven.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205761","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 study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a power-law type kernel. We prove the existence and uniqueness of a solution for the model and establish the stability conditions by employing Banach’s contraction principle and a generalized α-ψ-Geraghty type contraction. We perform stability analysis based on the Ulam–Hyers concept. To calculate the approximate solution, we utilize Gegenbauer polynomials via the spectral collocation method. The presented model includes two fractal and fractional order derivatives. The influence of the fractional and fractal derivatives on the outbreak of HIV is investigated by utilizing real data from the Cape Verde Islands in 1987–2014.
{"title":"On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative","authors":"Yanru Wu, Monireh Nosrati Sahlan, Hojjat Afshari, Maryam Atapour, Ardashir Mohammadzadeh","doi":"10.1186/s13660-024-03098-1","DOIUrl":"https://doi.org/10.1186/s13660-024-03098-1","url":null,"abstract":"In this study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a power-law type kernel. We prove the existence and uniqueness of a solution for the model and establish the stability conditions by employing Banach’s contraction principle and a generalized α-ψ-Geraghty type contraction. We perform stability analysis based on the Ulam–Hyers concept. To calculate the approximate solution, we utilize Gegenbauer polynomials via the spectral collocation method. The presented model includes two fractal and fractional order derivatives. The influence of the fractional and fractal derivatives on the outbreak of HIV is investigated by utilizing real data from the Cape Verde Islands in 1987–2014.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"31 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140170936","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 : 2024-03-19DOI: 10.1186/s13660-024-03085-6
Ayman M. Mahmoud, Cemil Tunç
In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature.
{"title":"On the qualitative behaviors of stochastic delay integro-differential equations of second order","authors":"Ayman M. Mahmoud, Cemil Tunç","doi":"10.1186/s13660-024-03085-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03085-6","url":null,"abstract":"In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"35 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171188","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 : 2024-03-15DOI: 10.1186/s13660-024-03112-6
S. Balamoorthy, T. Kavaskar, K. Vinothkumar
In this paper, we obtain the Harary index and the hyper-Wiener index of the H-generalized join of graphs and the generalized corona product of graphs. As a consequence, we deduce some of the results in (Das et al. in J. Inequal. Appl. 2013:339, 2013) and (Khalifeh et al. in Comput. Math. Appl. 56:1402–1407, 2008). Moreover, we calculate the Harary index and the hyper-Wiener index of the ideal-based zero-divisor graph of a ring.
在本文中，我们得到了图的 H 广义连接和图的广义日冕积的哈拉里指数和超维纳指数。因此，我们推导出了（Das 等人，载于《不等式应用》2013:339，2013 年）和（Khalifeh 等人，载于《计算数学应用》56:1402-1407，2008 年）中的一些结果。此外，我们还计算了基于理想的环零分维图的哈拉里指数和超维纳指数。
{"title":"Harary and hyper-Wiener indices of some graph operations","authors":"S. Balamoorthy, T. Kavaskar, K. Vinothkumar","doi":"10.1186/s13660-024-03112-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03112-6","url":null,"abstract":"In this paper, we obtain the Harary index and the hyper-Wiener index of the H-generalized join of graphs and the generalized corona product of graphs. As a consequence, we deduce some of the results in (Das et al. in J. Inequal. Appl. 2013:339, 2013) and (Khalifeh et al. in Comput. Math. Appl. 56:1402–1407, 2008). Moreover, we calculate the Harary index and the hyper-Wiener index of the ideal-based zero-divisor graph of a ring.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140148947","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 : 2024-03-12DOI: 10.1186/s13660-024-03110-8
Amjad Hussain, Ilyas Khan, Abdullah Mohamed
As a first attempt, we obtain the boundedness of the rough fractional Hausdorff operator on variable exponent Herz-type spaces. The method used in this paper enables us to study the operator on some other function spaces with variable exponents.
{"title":"Variable Herz–Morrey estimates for rough fractional Hausdorff operator","authors":"Amjad Hussain, Ilyas Khan, Abdullah Mohamed","doi":"10.1186/s13660-024-03110-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03110-8","url":null,"abstract":"As a first attempt, we obtain the boundedness of the rough fractional Hausdorff operator on variable exponent Herz-type spaces. The method used in this paper enables us to study the operator on some other function spaces with variable exponents.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"2019 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126801","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 : 2024-03-12DOI: 10.1186/s13660-024-03108-2
Hanaa M. Zayed, Teodor Bulboacă
The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function $mathfrak{J}_{lambda ,mu}^{nu ,m}(z):=Gamma ^{m}(lambda +1) Gamma (lambda +mu +1)2^{2lambda +mu}z^{1-(nu /2)-lambda} mathcal{J}_{lambda ,mu }^{nu ,m}(sqrt{z})$ , where the function $mathcal{J}_{lambda ,mu}^{nu ,m}$ satisfies the differential equation $mathcal{J}_{lambda ,mu}^{nu ,m}(z):=(1-2lambda -nu )J_{ lambda ,mu}^{nu ,m}(z)+z (J_{lambda ,mu }^{nu ,m}(z) )^{prime}$ with $$ J_{nu ,lambda}^{mu ,m}(z)= biggl(frac{z}{2} biggr)^{2lambda + nu} sum_{k=0}^{infty} frac{(-1)^{k}}{Gamma ^{m} (k+lambda +1 )Gamma (kmu +nu +lambda +1 )} biggl(frac{z}{ 2} biggr)^{2k} $$ for $lambda in mathbb{C}setminus mathbb{Z}^{-}$ , $mathbb{Z}^{-}:= { -1,-2,-3,ldots }$ , $min mathbb{N}$ , $nu in mathbb{C}$ , and $mu in mathbb{N}_{0}:=mathbb{N}cup {0}$ . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, $0leq alpha <1$ . Ultimately, we discuss the starlikeness and convexity of order zero for $mathfrak{J}_{lambda ,mu} ^{nu ,m}$ , and it turns out that they are useful to extend the range of validity for the parameter λ to $lambda geq 0$ where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates.
{"title":"Geometric characterization of the generalized Lommel–Wright function in the open unit disc","authors":"Hanaa M. Zayed, Teodor Bulboacă","doi":"10.1186/s13660-024-03108-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03108-2","url":null,"abstract":"The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function $mathfrak{J}_{lambda ,mu}^{nu ,m}(z):=Gamma ^{m}(lambda +1) Gamma (lambda +mu +1)2^{2lambda +mu}z^{1-(nu /2)-lambda} mathcal{J}_{lambda ,mu }^{nu ,m}(sqrt{z})$ , where the function $mathcal{J}_{lambda ,mu}^{nu ,m}$ satisfies the differential equation $mathcal{J}_{lambda ,mu}^{nu ,m}(z):=(1-2lambda -nu )J_{ lambda ,mu}^{nu ,m}(z)+z (J_{lambda ,mu }^{nu ,m}(z) )^{prime}$ with $$ J_{nu ,lambda}^{mu ,m}(z)= biggl(frac{z}{2} biggr)^{2lambda + nu} sum_{k=0}^{infty} frac{(-1)^{k}}{Gamma ^{m} (k+lambda +1 )Gamma (kmu +nu +lambda +1 )} biggl(frac{z}{ 2} biggr)^{2k} $$ for $lambda in mathbb{C}setminus mathbb{Z}^{-}$ , $mathbb{Z}^{-}:= { -1,-2,-3,ldots }$ , $min mathbb{N}$ , $nu in mathbb{C}$ , and $mu in mathbb{N}_{0}:=mathbb{N}cup {0}$ . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, $0leq alpha <1$ . Ultimately, we discuss the starlikeness and convexity of order zero for $mathfrak{J}_{lambda ,mu} ^{nu ,m}$ , and it turns out that they are useful to extend the range of validity for the parameter λ to $lambda geq 0$ where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"4 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126730","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 : 2024-03-07DOI: 10.1186/s13660-023-03062-5
D. Sagheer, S. Batul, A. Daim, A. Saghir, H. Aydi, S. Mansour, W. Kallel
The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established.
{"title":"Well-posed fixed point results and data dependence problems in controlled metric spaces","authors":"D. Sagheer, S. Batul, A. Daim, A. Saghir, H. Aydi, S. Mansour, W. Kallel","doi":"10.1186/s13660-023-03062-5","DOIUrl":"https://doi.org/10.1186/s13660-023-03062-5","url":null,"abstract":"The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"52 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054666","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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