Type Integral Operators Research Articles

Volterra type integral operator acting between Fock spaces

Volterra type integral operator acting between Fock spaces

Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Some α − ϕ -Fuzzy Cone Contraction Results with Integral Type Application

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

Kantorovich-type operators associated with a variant of Jain operators

"This note focuses on a sequence of linear positive operators of integral type in the sense of Kantorovich. The construction is based on a class of discrete operators representing a new variant of Jain operators. By our statements, we prove that the integral family turns out to be useful in approximating continuous signals de ned on unbounded intervals. The main tools in obtaining these results are moduli of smoothness of rst and second order, K-functional and Bohman- Korovkin criterion."

Three-Dimensional Nonlinear Integral Operator with the Modelling of Majorant Function

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model. Mathematical Subject Classification (2010): 45P05, 45G10, 47H99

Simultaneous Approximation by a New Sequence of Integral Type Based on Two Parameters

This paper introduces a generalization sequence of positive and linear operators of integral type based on two parameters to improve the order of approximation. First, the simultaneous approximation is studied and a Voronovskaja-type asymptotic formula is introduced. Next, an error of the estimation in the simultaneous approximation is found. Finally, a numerical example to approximate a test function and its first derivative of this function is given for some values of the parameters.

Note on norm of an m-linear integral-type operator between weighted-type spaces

We find a necessary and sufficient condition for the boundedness of an m-linear integral-type operator between weighted-type spaces of functions, and calculate norm of the operator, complementing some results by L. Grafakos and his collaborators. We also present an inequality which explains a detail in the proof of the boundedness of the linear integral-type operator on L^{p}({mathbb {R}}^{n}) space.

On Landau-Type Approximation Operators

In this paper, we define and study a general class of convolution operators based on Landau operators. A property of these new operators is that they reproduce the affine functions, a feature less commonly encountered by integral type operators. Approximation properties in different function spaces are obtained, including quantitative Voronovskaya-type results.

Operator-Orthoregressive Method for Identifying Coefficients of Linear Differential Equations

We propose an approach to identify coefficients of linear differential equations from observations of solutions with additive perturbations, based on the algebraic Fliess–Sira-Ramirez method combined with the orthogonal regression method in the space of observed functions that are transformed by convolution type integral operators. We establish the consistency of the operator-orthoregressive method and numerically analyze asymptotical properties and computational complexity of the proposed method in comparison with the asymptotically optimal variational method of identification.

Approximation of generalized nonlinear Urysohn operators using positive linear operators

There are presented two methods for approximation of generalized Urysohn type operators. The first of them is the natural generalization of the method considered first by Demkiv in [1]. The convergence results are given in quantitative form, using certain moduli of continuity. In the final part there are given a few exemplifications for discrete and integral type operators and, in particular, for Bernstein and Durrmeyer operators.

Alternative criteria for boundedness of one class of integral operators in Lebesgue spaces

The paper discusses weighted Hardy type inequalities for a certain class of Volterra type integral operators with kernels. Criteria for the validity of the presented inequalities are found, which are different from the criteria obtained earlier.

New characterizations for differences of integral-type operators from α-Bloch space to β-Bloch-Orlicz space

New characterizations for differences of integral-type operators from α-Bloch space to β-Bloch-Orlicz space

Approximation of New Sequence of Integral Type Operators with two Parameters

In our paper, we provide and study a new sequence of positive and linear operators of integral type. This sequence depends on two parameters, positive integers and. We mention some of the properties of this sequence and describe a Voronovskaja type asymptotic formula. Besides, we find the error estimates of this approximation in terms of the modulus of continuity. lastly, we introduce a numerical example and compare the results obtained.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

Abstract In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

Improving the order of approximation by a generalization of new bivariate sequence of integral type operators with parameters

In this study, we define the bivariate new sequence of integral type operators which is denote by Hn(f(t, t); x, y) to approximation the functions in the spaces Ca ([0, ∞) × [0, ∞)), a > 0 and define a generalization of this sequence depends on a natural number S denote it by Hn, s(f; x, y) to get a better order of approximation by the sequence Hn, s(f; x, y). Firstly, we study some approximation properties for these sequences. Then, we discuss the simultaneous approximation for the r-th order partial derivatives for the sequence Hn, s(f; x, y). Also, we illustrate the order of approximation by Voronovskaja-type theorem. Finally, we demonstrate the convergence of the sequence Hn, s(f(t, t); x, y) to the function f by given some numerical examples and compare the numerical results obtained with the numerical results occurs from the sequence Hn(f; x, y).

On the optimal numerical parameters related with two weighted estimates for commutators of classical operators and extrapolation results

We give two-weighted norm estimates for higher order commutator of classical operators such as singular integral and fractional type operators, between weighted $$L^p$$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of non-trivial weights in the optimal region satisfying the conditions required. Finally, we exhibit an extrapolation result that allows us to obtain boundedness results of the type described above in the variable setting and for a great variety of operators, by starting from analogous inequalities in the classical context. In order to get this result we prove a Calderon–Scott type inequality with weights that connects adequately the spaces involved.

Approximation properties of a family of integral type operators

In this paper we consider a general class of linear positive processes of integral type. These operators act on functions defined on unbounded interval. Among the particular cases included are Durrmeyer–Jain operators, Păltănea–Szasz–Mirakjan operators and operators using Baskakov–Szasz type bases. We focus on highlighting some approximation targeting different classes of functions. The main working tools are Bohman–Korovkin theorem, weighted K-functionals and moduli of smoothness.

Essential Norm of Integral Type Operators Mapping into Certain Banach Spaces of Analytic Functions

We study certain integral type operators acting on a large class of Banach spaces of analytic functions on the open unit disc. The operators map into weighted Banach spaces of analytic functions, Bloch type spaces or Zygmund type spaces. Besides characterizing boundedness, we give essential norm estimates of these operators. In order to investigate these operators, we also study weighted differentiation composition operators between these spaces.

On a q‐Laplace–type integral operator and certain class of series expansion

AbstractIn this paper, we develop a q‐theory of the q‐Laplace–type integral operators qL2 and ql2 introduced by Uçar and Albayrak in 2011. We derive several identities and establish various results related to the q‐Laplace–type integral operators of various classes of q‐special functions and q‐series expansions. By using a q‐series representation of the q‐analogues, we obtain results enfolding power series of even orders. Further, by utilizing the new results, we obtain formulas and conclusions associated with q‐hypergeometric functions of first and second types. In a brief reading, we finally establish new formulas involving q‐trigonometric and q‐Bessel functions as well.

Mappings of Generalized Condensing Type in Metric Spaces with Busemann Convex Structure

Related to earlier work on existence results of best proximity points (pairs) for cyclic (noncyclic) condensing operators of integral type in the setting of reflexive Busemann convex spaces, in this paper, we introduce another class of cyclic (noncyclic) condensing operators and study the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in such spaces. Then, we present an application of our main existence result to study the existence of an optimal solution for a system of differential equations.