This paper establishes new fixed point theorems based on the concept of F-contractions. The results are formulated for multivalued mappings of rational type defined on spherically complete ultrametric spaces. Several special cases are discussed, some of which generalize or improve upon known results. Illustrative examples are provided to support the theoretical findings. Furthermore, an alternative generalization involving almost contractive multivalued mappings of rational type is also presented within the framework of F-contractions.
This study presents a comparison of various inverse soft covering upper approximations, focusing specifically on the differences between them. A key finding of our work is the introduction of a new type of inverse soft covering upper approximation which is a new approach in developing inverse soft covering based rough sets. We demonstrate that this new approximation is smaller than the three existing approximations described in the literature. Based on this result, we aim to manage the decision-making processes, especially for the uncertainty problems, in a more ideal way.
In this paper, we introduce the notion of semi uniform alpha convergence for sequences of functions between metric spaces. We also provide some results concerning the relationship between uniform exhaustiveness, semi uniform exhaustiveness and semi uniform alpha convergence. Finally, we give a Korovkin-type theorem related to uniform exhaustiveness.
This research presents a comprehensive theoretical and computational analysis of the Kirk order-2 iteration method for approximating fixed points of operators that satisfy a weak contractive condition within the framework of a real Banach space. The primary objectives are to establish the strong convergence, stability, and computational efficiency of this iterative scheme. A key contribution of this work is a detailed self-comparative analysis of the convergence rate among six distinct permutations of the iterative scheme's coefficients. We derive a precise analytical condition that determines which permutation yields a faster convergence rate, providing a theoretical framework for optimizing the algorithm's performance. Numerical results are presented to validate the theoretical findings and demonstrate the algorithm's efficiency, confirming that specific permutations of the coefficients can significantly accelerate convergence.
We give some new embeddings results for weighted grand Lebesgue spaces L-omega(p)),delta (Omega), where Omega subset of R-d is a open bounded subset. We also obtain the boundedness of the Kantorovich operator K-n in L-omega(p),delta) [0, 1]. In addition, we establish two direct estimates by K-functionals of the rate of approximation in L-omega(p),delta) [0,1].We generalize the direct estimate inequality in classical Lebesgue spaces L-p [0,1] to L-omega(p),delta)[0,1] using the boundedness of the Hardy-Littlewood maximal operator in L-omega(p),delta) [0,1]. Finally, we obtain similar results in [8] for the spaces L-omega(p),delta) [0,1].
The aim of this study is to investigate the variation detracting property and convergence in variation of the generalized Kantorovich type Szasz-Mirakyan operators constructed via Appell polynomials in the space of functions of bounded variation. These problems are examined with respect to the variation seminorm. Additionally, the rate of convergence is analyzed in terms of total variation.
In the present paper, we state a quantitative version of the convergence utilizing the logarithmic weighted modulus of continuity for a new generalization of the Mellin-Gauss-Weierstrass operators which preserve logarithmic functions. Later, we express logarithmic moments of the modified operators, and then we give Voronovskaya-type theorem. Moreover, a rate of convergence is achieved, and onwards the global smoothness preservation feature is stated via the logarithmic weighted modulus of continuity in the weighted Mellin-Lebesgue spaces comprising all Lebesgue measurable functions.
This study introduces 2D Bell polynomials alongside Appell polynomials, examining their properties through generating functions. We delve into various characteristics of these polynomials, such as explicit forms, summation formulae, recurrence relations, and addition formulas. Additionally, we introduce the 2D Bell-Appell-based Stirling polynomials of the second kind, detailing their associated outcomes. This research aims to deepen the understanding of 2D Bell-based Appell and 2D Bell-Appell-based Stirling polynomials within mathematical analysis, with significant implications for approximation techniques. The findings could inform the development of new mathematical theories and applications, enhancing methods for approximation in various contexts.
In this paper, we present a new three-parameter semi-classical Laguerre matrix weight function and explore the associated sequence of matrix orthogonal polynomials. We derive explicit expressions for the corresponding three-term recurrence relations, both in terms of their scalar counterparts and scalar Hankel determinants. Finally, we analyze the asymptotic behavior of the recurrence coefficients with respect to the variables t and n.
In this article, we present the best possible proof of the conjectures posed by re-searchers Li Yin et al. and Riku Klen et al., along with the appropriate bounds invol-ving generalized trigonometric and hyperbolic functions. These inequalities are further generalized with the best possible bounds. Alternative proofs of the Cusa-Huygens inequality were given using particular cases.
The paper delves the problem of approximating Lauricella-Saran's hypergeometric functions by a special family of functions - branched continued fractions. Under certain conditions of the parameters of the Lauricella-Saran's hypergeometric functions F-M, new domains of the analytic continuation of these functions and their ratios are established, using their expansions into branched continued fractions, the elements of which are polynomials of three complex variables. At the end, several numerical experiments are presented that illustrate the efficient approximation of special function by branched continued fraction.
In this paper, we introduce 2-variable truncated Tricomi functionsh(n)(x,y) and 2-parameter 2-variable truncated Tricomi functions h(n,nu)((alpha))(x, y) employing integral forms and establish their characteristics, such as series definitions and generating functions. Also, we derive the higher-order truncated Tricomi functions and study their features.
This paper introduces a new approximation theorem, type of Korovkin, for positive linear operators (pLO) defined on the Banach space C-* [0, infinity) comprising all real-valued continuous functions on [0, infinity) that converge to a finite limit as their argument approaches infinity. By applying statistical convergence with respect to power series methods and employing the test functions 1, exp(-u) and exp(-2u), we derive a novel approximation result. Our findings demonstrate that the proposed method outperforms classical and statistical approaches, as illustrated by a concrete example. Furthermore, we explore the rate of convergence associated with this new approximation theorem.
This study focuses on solving finite minimax problems. A new reformulation for the minimax problems is established based on indicator functions. The relations between the original and reformulated problems are investigated. Based on the new formulation of minimax problems, a new smoothing approach is proposed via the approximation of the indicator functions. A new algorithm is developed to solve the reformulated and smoothed problems. Finally, the performance of the algorithm is illustrated on some test problems, and the comparison of the obtained numerical results with the other methods is presented.
The main aim of this paper is to derive new Ostrowski type inequalities for 3-convex functions and for functions whose modulus of derivatives are convex, using the weighted Montgomery identity and the weighted Hermite-Hadamard inequalities. Additionally, certain Hermite-Hadamard inequalities for 3-convex functions are provided.
The purpose of this paper is to study the Legendre spectral method for solving a particular case of the heat convection-diffusion equation, wich is formulated as a mixed initial boundary value problem within the finite regular domain A = (-1, 1). To tackle this problem, we employ certain techniques to transform it into a system of ordinary differential equations. Through matrix analysis, we derive a general term that characterizes all the ordinary differential equations in this system. solving this general term, provides the desired approximate solution, and we also present the error estimation.
The article addresses systems of Hammerstein integral equations of the first kind, in which the determinant of the non-diagonal matrix-kernel is identically equal to zero.The class of problems under consideration has fundamental differences from standard cases: the solution may not exist, be non-unique, or depend on high derivatives of the input data. In terms of matrix pencils, sufficient conditions for the local existence of a unique solution in the class of continuous functions are formulated. Illustrative examples are given. Difficulties arising in the construction of numerical methods for solving these problems are discussed.
In this paper we establish a quantitative estimate for the order of approximation for the generalized and the Kantorovich sampling series based upon kernels with asymptotic decay as the function u-2, that are characterized by an infinite first order discrete absolute moment. The key point of the above proof is provided by the application of a special case of the Euler-MacLaurin summation formula. Concrete examples are discussed, such as the critical case of the Fejer kernel.
In this paper, we consider a new generalization of complex Stancu operators. We obtain quantitative upper estimates for the convergence, lower estimates from a qualitative Voronovskaja-type theorem and then the exact degree of simultaneous approximation by these operators attached to analytic functions in a disk centered at the origin with radius greater than 1. Also, we give some graphical and numerical examples.
In this paper, Appell-type Changhee F-polynomials, which correspond of Appell-type Changhee polynomials in Fibonomial Calculus, are introduced. Furthermore, the Appell-type Changhee F-polynomial matrix is defined. Some relations and identities involving these polynomials and matrices are established.
