In this paper some enriched rational type contractive mappings are introduced and related fixed point theorems are proved by using Krasnselskii iteration procedure. Some examples are cited in support of our theorems to show that our theorems are more generalized. Finally, two different applications of our proved theorems are given to ensure the existence of a unique solution to a nonlinear boundary value problem and also to get solutions for some functional equations relating to the problem of dynamical programming.
In the work, the authors consider the Schur-convexity, the Schur-geometric convexity, and the Schur-harmonic convexity of two means defined by the inverse sine and tangent functions. They also apply these convexity properties to construct several inequalities for special means. These convexity properties correct and modify relevant results discussed in the paper [D.-S. Chen, The Schur-convexity and inequality chains of two anti-trigonometric mean, Math. Pract. Theory 50 2020, 5, 268-275].
Consider a configuration space Omega whose boundary is made up of an asymptotically straight curve and its reflection (in two dimensions) or rotation (in three dimensions) about an axis of symmetry. We prove that by imposing an infinite net-area condition on the profile curve along just one end of Omega, the Dirichlet Laplacian - Delta {-\Delta} on Omega has at least one isolated eigenvalue (hence at least one bound state) below a natural threshold. The varying eigenvalue of the cross-section along the axis of symmetry plays a central role in our analysis, and integrals of the Bessel function are also of crucial importance.
In this paper, we investigate the existence of best proximity points for classes of multivalued mappings that are not necessarily self mappings, defined on a pair of subsets in strictly convex and reflexive Banach spaces. A fixed point framework based on the Himmelberg fixed point theorem is used to derive the existence of best proximity point in the absence of self-mapping properties. Several examples are provided to illustrate the applicability of our results. The work contributes to the development of best proximity theory for multivalued nonlinear operators in Banach spaces and enriches the existing literature on approximation of fixed points through nearest point relations.
This study explores the approximate boundary controllability of certain nonlinear stochastic partial functional integrodifferential equations with finite delay and Rosenblatt process. By assuming that the linear undelayed component is approximately controllable and possesses a resolvent operator as defined by Grimmer, the research utilizes the Banach fixed-point theorem and the uniform norm-topology continuity of the resolvent operator to establish sufficient conditions for the system's approximate controllability. This approach generalizes several significant results existing in the literature without necessitating the compactness of the resolvent operator or the uniform boundedness of the nonlinear term. An illustrative example is provided to demonstrate the applicability of the findings.
In this paper, we introduce a new subclass of analytic and multivalent functions by means of the Salagean's differential operator, and obtain the sharp upper bound of Zaleman functional |a(p+1)(2) - a(p+2)| for functions belong to this class.
This paper establishes sharp Gaussian upper bounds for Schrodinger semigroups generated by operators of the form-Delta(D) + V on the positive orthant (0,infinity )d with Dirichlet boundary conditions, where V is a singular complex-valued potential. We prove that if V satisfies a dissipativity condition Re V <= 0, a weighted global Kato condition integral(Q)II(i=1 )(d)xi]IV(x)I dx
We solve the problem AX = y, where A : K -> R-N IRN is a linear, continuous operator, and K is a class of functions with prescribed bounds defined on a compact domain in R-m. We restate the problem as consisting of minimizing an entropy of Fermi-Dirac type, subject to AX = y as a constraint. We prove that the solution is robust respect to small perturbations of the data and converges to a true solution as the number of data points increases.
In this paper, we show that every expansive linear homeomorphism on a Banach space with the eventual shadowing property is topologically stable. Moreover, for finite-dimensional Banach spaces, the eventual shadowing property and topological stability are equivalent.
In this article, we explore several sufficient conditions under which an eventually shadowable point can be approximated by entropy points. Moreover, we derive distinct conditions for an eventually shadowable point to be an entropy point. We also study the situation where a system related to an eventually shadowable point is conjugated to an odometer. On the other hand, we introduce the concept of orbital shadowable points and obtain the following results: The set of orbital shadowable points of a homeomorphism on a compact metric space is invariant; a homeomorphism has the orbital shadowing property if and only if every point is orbital shadowable; a homeomorphism has the orbital shadowing property if and only if the set of orbital shadowable points has full measure with respect to every ergodic measure.
In this paper, we study pointwise, uniform, and L (R) (0 < r < 1) convergence of the Legendre series with coefficients of bounded variation. We also show that "coefficients being of generalized bounded variation" gives a Tauberian theorem for Legendre series, that is, if the coefficients of Legendre series is of generalized bounded variation, then the Legendre series is (C, 1) summable if and only if the series is convergent.
We present Leray-Schauder alternatives and Schauder-type fixed point theorems for compact maps with a selection-type property.
We build a universal set in omega omega x 2 omega {\omega<^>{\omega}\times 2<^>{\omega}} for the family of summable ideals. We investigate its Borel complexity and topological properties, such as meagerness and sigma-porosity.
This paper explores integral inequalities within the framework of fractional integrals having exponential kernels through a parameterized approach. A novel integral identity with a parameter is introduced, forming the basis for deriving a general inequality. From this, several classical inequalities, including midpoint, trapezium, Bullen, Simpson, and corrected Simpson types, are obtained for differentiable convex functions. Numerical examples and graphical analyses are presented to verify the validity of the proposed results. The findings are further demonstrated through applications to special functions, showcasing the versatility of the developed framework.
The current work focuses on statistical Riemann summability, statistical Riemann integrability, statistical Lebesgue summability, and statistical Lebesgue integrability using Deferred Ces & agrave;ro and Deferred N & ouml;rlund means. First, we explore key theorems that connect these concepts, providing examples for illustration. In our newly established sequence spaces, we illustrate the application of Korovkin-type approximation theorems, supported by some examples of positive linear operators showcasing the significance of our results.
In this paper, we give an alternative proof for the proof of Theorem 2.23 shown in the paper [J. Borzov & aacute;-Moln & aacute;rov & aacute;, L. Hal & ccaron;inov & aacute; and O. Hutn & iacute;k, The smallest semicopula-based universal integrals II: Convergence theorems, Fuzzy Sets and Systems 271 2015, 18-30] by exploiting the uniform continuity of the underlying semicopula together with using epsilon-techniques of limit. Thus, our proof avoids using the way interchanging the supremum and infimum which is not valid in general.
The study of changes in population size and reasons for these changes appear as population dynamics. These dynamics generally focus on change in population size over time. Mathematical modeling is used to make sense of these changes. In this study, three population models have been reconstructed and solved using proportional derivative on time scales. Equilibrium points and stability states of these solutions were examined.
The NLS equation can be derived from the Zakharov system in a singular limit. The goal of this paper is to add some new aspects to the existing analysis about this approximation. We outline the differences between the situation x ∈ ℝ {x\in{\mathbb{R}}} and x ∈ 𝕋 = ℝ / ( 2 π ℤ ) {x\in\mathbb{T}={\mathbb{R}}/(2\pi{\mathbb{Z}})} . We explain the difficulties occurring in the construction of higher order approximations and use these approximations to improve the approximation rate. Moreover, we point out that the standard validity proof requires a smallness condition which was not stated in the existing literature.
In this paper, we present a brief survey of recent results about various classes of almost periodic-type functions and their applications to the abstract Volterra integro-differential equations, nonlinear evolution equations of first order, ordinary differential equations and some classes of integro-differential-difference equations. We consider the Poincaré–Perron problem for higher-order ordinary differential equations in the class of almost periodic-type functions and the almost periodic points and minimal sets in ω-regular spaces, among many other interesting topics, providing also some perspectives for expanding the theory of almost periodic functions.
In this paper, we study an improvement on convergence in the measure theorem of a sequence of seminormed fuzzy integrals which has been proposed by Xuecheng. Furthermore, some other forms of convergence in measure are also presented.
