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 Journal of Inequalities and ApplicationsJournal Prestige (SJR): 0.546 Citation Impact (citeScore): 1Number of Followers: 0     Open Access journal ISSN (Print) 1025-5834 - ISSN (Online) 1029-242X Published by SpringerOpen  [228 journals]
• The inertial iterative extragradient methods for solving pseudomonotone
equilibrium programming in Hilbert spaces

• Abstract: In this paper, we present new iterative techniques for approximating the solution of an equilibrium problem involving a pseudomonotone and a Lipschitz-type bifunction in Hilbert spaces. These techniques consist of two computing steps of a proximal-type mapping with an inertial term. Improved simplified stepsize rules that do not involve line search are investigated, allowing the method to be implemented more quickly without knowing the Lipschitz-type constants of a bifunction. The iterative sequences converge weakly on a specific solution to the problem when the control parameter conditions are properly specified. The numerical tests were carried out, and the results demonstrated the applicability and quick convergence of innovative approaches over earlier ones.
PubDate: 2022-05-10

• Using ρ-cone arcwise connectedness on parametric set-valued
optimization problems

• Abstract: Within the inquiry about work, we explore a parametric set-valued optimization problem, where the objective as well as constraint maps are set-valued. A generalization of cone arcwise associated set-valued maps is presented named ρ-cone arcwise connectedness of set-valued maps. We set up adequate Karush–Kuhn–Tucker optimality conditions for the problem beneath contingent epiderivative and ρ-cone arcwise connectedness presumptions. Assist, Mond–Weir, Wolfe, and blended sorts duality models are examined. We demonstrate the related theorems between the primal and the comparing dual problems beneath the presumption.
PubDate: 2022-05-08

• A Caputo discrete fractional-order thermostat model with one and two
sensors fractional boundary conditions depending on positive parameters by
using the Lipschitz-type inequality

• Abstract: A thermostat model described by a second-order fractional difference equation is proposed in this paper with one sensor and two sensors fractional boundary conditions depending on positive parameters by using the Lipschitz-type inequality. By means of well-known contraction mapping and the Brouwer fixed-point theorem, we provide new results on the existence and uniqueness of solutions. In this work by use of the Caputo fractional difference operator and Hyer–Ulam stability definitions we check the sufficient conditions and solution of the equations to be stable, while most researchers have examined the necessary conditions in different ways. Further, we also establish some results regarding Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability for our discrete fractional-order thermostat models. To support the theoretical results, we present suitable examples describing the thermostat models that are illustrated by graphical representation.
PubDate: 2022-05-08

• On the domain of generalized mean in Nakano sequence space, and its
prequasi ideal with some applications

• Abstract: Some topological and geometric behavior of the space of all sequences whose generalized mean transforms are in Nakano sequence space, the multiplication mappings acting on it, and the eigenvalue distribution of mappings ideal generated by this space and s-numbers are discussed. We construct the existence of a fixed point of Kannan contraction mapping on these spaces. Several numerical experiments are presented to illustrate our results. Moreover, some successful applications to the existence of solutions of nonlinear difference equations are explained. The strength here is that the current results are constructed under flexible setups given by controlling the weight and power of these spaces.
PubDate: 2022-05-07

variational inequalities

• Abstract: In this paper, we introduce two subgradient extragradient-type algorithms for solving variational inequality problems in the real Hilbert space. The first one can be applied when the mapping f is strongly pseudomonotone (not monotone) and Lipschitz continuous. The first algorithm only needs two projections, where the first projection onto closed convex set C and the second projection onto a half-space $$C_{k}$$ . The strong convergence theorem is also established. The second algorithm is relaxed and self-adaptive; that is, at each iteration, calculating two projections onto some half-spaces and the step size can be selected in some adaptive ways. Under the assumption that f is monotone and Lipschitz continuous, a weak convergence theorem is provided. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms.
PubDate: 2022-05-07

system of variational inequality problems and fixed point problem

• Abstract: Abstract We introduce a new subgradient extragradient algorithm utilizing the concept of the set of solutions of the split modified system of variational inequality problems (SMSVIP). Our main theorem is weak convergence theorem for such an algorithm for approximating the fixed point problem in a real Hilbert space. We also apply these results to approximate the split minimization problem. In the last section, we provide an example to illustrate the potential of our main theorem.
PubDate: 2022-05-03

• Continuous controlled cone metric-type spaces over real Banach algebras
and fixed-point results

• Abstract: Abstract In this article, we introduce a new geometrical structure that is the hybrid of a cone metric space over Banach algebra and a controlled metric-type space. We introduce a new metric space and prove analogs of Banach-, Kannan- and Reich-type fixed-point theorems. We also furnish various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in the literature.
PubDate: 2022-05-03

• An analysis concerning approximate controllability results for
second-order Sobolev-type delay differential systems with impulses

• Abstract: Abstract This paper is devoted to studying the approximate controllability for second-order impulsive differential inclusions with infinite delay. For proving the main results, we use the results related to the cosine and sine function of operators, Martelli’s fixed point theorem, and the results when combined with the properties of differential inclusions. Firstly, we prove the approximate controllability for second-order impulsive differential inclusions with initial conditions. Then, we extend the discussion to the second-order impulsive system with nonlocal conditions. Finally, we provide an example for the illustration of the obtained theoretical results.
PubDate: 2022-05-03

• Extended Jensen’s functional for diamond integral via Green’s function
and Hermite polynomial

• Abstract: Abstract In this paper, with the help of Green’s function and Hermite interpolating polynomial, an extension of Jensen’s functional for n-convex functions is deduced from Jensen’s inequality involving diamond integrals. Special Hermite conditions, including Taylor two point formula and Lagrange’s interpolation, are also deployed to find the further extensions of Jensen’s functional. This paper also includes discussion on bounds for Grüss inequality, Ostrowski inequality, and Čebyšev functional associated to the newly defined Jensen’s functional.
PubDate: 2022-04-28

• On a system of monotone variational inclusion problems with fixed-point
constraint

• Abstract: Abstract In this paper, we study the problem of finding the solution of the system of monotone variational inclusion problems recently introduced by Chang et al. (Optimization 70(12):2511–2525, 2020) with the constraint of a fixed-point set of quasipseudocontractive mappings. We propose a new iterative method that employs an inertial technique with self-adaptive step size for approximating the solution of the problem in Hilbert spaces and prove a strong-convergence result for the proposed method under more relaxed conditions. Moreover, we apply our results to study related optimization problems. Finally, we present some numerical experiments to demonstrate the performance of our proposed method, compare it with a related method as well as experiment on the dependency of the key parameters on the performance of our method.
PubDate: 2022-04-27

• Lyapunov-type inequalities for fractional Langevin-type equations

• Abstract: Abstract In this study, some new Lyapunov-type inequalities are presented for Caputo-Hadamard fractional Langevin-type equations of the forms \begin{aligned} &{}_{H}^{C}D_{a + }^{\beta } \bigl({}_{H}^{C}D_{a + }^{\alpha }+ p(t)\bigr)x(t) + q(t)x(t) = 0,\quad 0 < a < t < b, \end{aligned} and \begin{aligned} &{}_{H}^{C}D_{a + }^{\eta }{ \phi _{p}}\bigl[\bigl({}_{H}^{C}D_{a + }^{\gamma }+ u(t)\bigr)x(t)\bigr] + v(t){\phi _{p}}\bigl(x(t)\bigr) = 0,\quad 0 < a < t < b, \end{aligned} subject to mixed boundary conditions, respectively, where $$p(t)$$ , $$q(t)$$ , $$u(t)$$ , $$v(t)$$ are real-valued functions and $$0 < \beta < 1 < \alpha < 2$$ , $$1 < \gamma$$ , $$\eta < 2$$ , $${\phi _{p}}(s) = s{ ^{p - 2}}s$$ , $$p > 1$$ . The boundary value problems of fractional Langevin-type equations were firstly converted into the equivalent integral equations with corresponding kernel functions, and then the Lyapunov-type inequalities were derived by the analytical method. Noteworthy, the Langevin-type equations are multi-term differential equations, creating significant challenges and difficulties in investigating the problems. Consequently, this study provides new results that can enrich the existing literature on the topic.
PubDate: 2022-04-27

• A new reverse Hardy–Hilbert inequality with the power function as
intermediate variables

• Abstract: Abstract In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients and use them to establish a reverse Hardy–Hilbert inequality with the power function as intermediate variables. Then, we obtain the equivalent forms and some equivalent statements of the best possible constant factor related to several parameters. Finally, we illustrate how the obtained results can generate some particular reverse Hardy–Hilbert inequalities.
PubDate: 2022-04-27

• Multilinear strongly singular integral operators on non-homogeneous metric
measure spaces

• Abstract: Abstract Let $$(X,d,\mu )$$ be a non-homogeneous metric measure space satisfying the geometrically and upper doubling measure conditions. In this paper, the boundedness in Lebesgue spaces for multilinear strongly singular integral operators on non-homogeneous metric measure spaces is proved. As an application, the boundedness in Morrey spaces for multilinear strongly singular integral operators is also obtained.
PubDate: 2022-04-25

• Some new dynamic Gronwall–Bellman–Pachpatte type inequalities with
delay on time scales and certain applications

• Abstract: Abstract The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall–Bellman–Pachpatte type on time scales. We introduce very important generalized results with the help of Leibniz integral rule on time scales. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Our results can be used as handy tools for the study of qualitative and quantitative properties of solutions of dynamic equations on time scales. Some examples are provided to demonstrate the applications of the results.
PubDate: 2022-04-18

• Quadruple fixed-point techniques for solving integral equations involved
with matrices and the Markov process in generalized metric spaces

• Abstract: Abstract The goal of this manuscript is to establish quadruple fixed-point and coincidence-point consequences in the setting of generalized metric spaces equipped with vector-valued metrics and matrix equations. Moreover, some supportive examples and corollaries are presented here to support the theoretical results. Ultimately, the theoretical results are presented here to discuss some applications to support our study.
PubDate: 2022-04-18

• Blow-up time estimate for porous-medium problems with gradient terms under
Robin boundary conditions

• Abstract: This paper deals with the blow-up phenomena connected to the following porous-medium problem with gradient terms under Robin boundary conditions: $$\textstyle\begin{cases} u_{t}=\Delta u^{m}+k_{1}u^{p}-k_{2} \vert \nabla u \vert ^{q} & \text{in } \Omega\times(0,t^{*}), \\ \frac{\partial u}{\partial\nu}+\gamma u=0 &\text{on } \partial\Omega\times(0,t^{*}), \\ u(x,0)=u_{0}(x)\geq0 &\text{in } \overline{\Omega}, \end{cases}$$ where $$\Omega\subset\mathbb{R}^{n}$$ ( $$n\geq3$$ ) is a bounded and convex domain with smooth boundary ∂Ω. The constants p, q, m are positive, and $$p>q>m>1$$ , $$q>2$$ . By making use of the Sobolev inequality and the differential inequality technique, we obtain a lower bound for the blow-up time of the solution. In addition, an example is given as an application of the abstract results obtained in this paper. Our results can be regarded as an answer to the open question raised by Li et al. in (Z. Angew. Math. Phys. 70:1–18, 2019).
PubDate: 2022-04-18

• Some results of neutrosophic normed space VIA Tribonacci convergent
sequence spaces

• Abstract: Abstract The concept of Tribonacci sequence spaces by the domain of a regular Tribonacci matrix was introduced by Yaying and Hazarika (Math. Slovaca 70(3):697–706, 2000). In this paper, by using the domain of regular Tribonacci matrix $$T = (t _{ik} )$$ and the concept of neutrosophic convergence, we introduce some neutrosophic normed space in Tribonacci convergent spaces and prove some topological and algebraic properties based results with respect to these spaces.
PubDate: 2022-04-14

• Extremal properties of the beta-normal distribution

• Abstract: Abstract Asymptotic behaviors of the extremes of the beta-normal distribution are derived. The higher-order asymptotic expansions of the probability density and cumulative distribution functions for the maximum are given under an optimal normalizing constants. In particular, the associated rates of convergence are explicitly calculated.
PubDate: 2022-04-13

• Some parameterized Simpson-, midpoint- and trapezoid-type inequalities for
generalized fractional integrals

• Abstract: Abstract In this paper, we first obtain an identity for differentiable mappings. Then, we establish some new generalized inequalities for differentiable convex functions involving some parameters and generalized fractional integrals. We show that these results reduce to several new Simpson-, midpoint- and trapezoid-type inequalities. The results given in this study are the generalizations of results proved in several earlier papers.
PubDate: 2022-04-11

• A smooth approximation approach for optimization with probabilistic
constraints based on sigmoid function

• Abstract: Abstract Many practical problems, such as computer science, communications network, product design, system control, statistics and finance, etc.,can be formulated as a probabilistic constrained optimization problem (PCOP) which is challenging to solve since it is usually nonconvex and nonsmooth. Effective methods for the probabilistic constrained optimization problem mostly focus on approximation techniques, such as convex approximation, D.C. (difference of two convex functions) approximation, and so on. This paper aims at studying a smooth approximation approach. A smooth approximation to the probabilistic constraint function based on a sigmoid function is analyzed. Equivalence of PCOP and the corresponding approximation problem are shown under some appropriate assumptions. Sequential convex approximation (SCA) algorithm is implemented to solve the smooth approximation problem. Numerical results suggest that the smooth approximation approach proposed is effective for optimization problems with probabilistic constraints.
PubDate: 2022-04-08

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