In this paper, the existence of fixed point results of Leray Schauder type for the sum and the product of nonlinear operators acting on RWC-Banach algebras under weak topology is proved. Our results are formulated in terms of a sequential characterization of the RWC-Banach algebra and the De Blasi measure of weak noncompactness. Application to Chandrasekhar Integral equations is also given.

The creation of new nonlinear multivariate integral operators is motivated by the need for mathematical tools that can handle the complex interdependencies that naturally arise in contemporary applications. From an abstract scientific point of view, it is also necessary to develop new operator theories beyond existing ones to offer original research perspectives. This article contributes to these complementary aspects. We present two nonlinear multivariate integral operators that have the particularity of incorporating trigonometric transformations of the main function. Thanks to their trigonometric nature, they completely stand out from existing operators, offering a new and complete framework. Therefore, we take advantage of advanced mathematical techniques for trigonometric functions to address the challenges they pose. In particular, we show that they have manageable integrals and series expansions, that they are solutions of specific differential and functional equations, and that they are involved in general inequalities of various types (Hölder-type, convex-type, etc.). In the application part, we use some of these properties to propose a wide collection of trigonometric inequalities that are both original and precise. Figures are produced to illustrate them for a direct visual check.

We consider the analogue of measure on a ring of sets, by defining a lattice-measure on a lattice-ring of elements of a lattice of infinite tuples of real numbers. We obtain various results about the convergence of sequences of tuples in the lattice with respect to the lattice-measure and use these results to show that the limit of a convergent sequence in a lattice sigma-ring is also in the lattice sigma-ring under certain conditions.

In this work, we consider the following mixed local-nonlocal quasilinear ellipic problem$$(P_\lambda)\left\{\begin{array}{rcll} -\Delta_p u+(-\Delta)_p^s u = \lambda f(u) \text{in}\Omega,\\ u 0 \text{in }\Omega,\\ u = 0 \text{in }\mathbb{R}^N \setminus\Omega,\end{array}\right.$$where Ω⊂RN is a bounded regular domain in RN with 0s1pN and f: R→R is a continuous function, that have a finite number of zeroes, changing sign between them. The main goal of this paper is to prove the existence and multiplicity of positive solutions for such problems by using variational methods.

The Ali-Mikhail-Haq copula is a bivariate ratio-type Archimedean copula known for its simplicity and flexibility in modeling moderate negative and positive dependence structures, making it widely used in various fields. However, it is limited to capturing asymmetric dependence features, significant negative correlations, or versatile tail dependence properties. This research paper proposes two modifications of the Ali-Mikhail-Haq copula that overcome these limitations, but at the price of the loss of the positive dependence nature. Contrary to the common approach that focuses on modifying the corresponding generator function, we apply direct functional changes to the Ali-Mikhail-Haq copula. We thus perturb its Archimedean identity. The first copula has the particularity of being non-exchangeable, capable of reaching an interesting level of negative dependence correlations, and possessing flexible tail dependence properties. The second copula offers another modeling option; it is exchangeable like the Ali-Mikhail-Haq copula, but it benefits from a broader range of negative dependence correlations and more adaptable tail dependence properties. For the two proposed copulas, we investigate their main characteristics, including quadrant dependence, copula density function, conditional copulas, couples of value generation, extended variants via standard copula schemes, comprehensive copula orders, and weighted harmonic mean copula transformations. An application on two new bivariate logistic distributions in a two-component system context is given. When possible, numerical and graphical studies are given to strengthen the theory.

Recent direction of studies shows that there is a kin connection between regular functions and orthogonal polynomials. In this paper, we study a new class of regular and bi-univalent functions that involve the familiar Gegenbauer polynomials. Some achieved results include some early coefficient bounds and the upper estimates for the Fekete-Szegö inequalities with real and complex parameters.

In this paper we investigate a mathematical model for the unilateral contact between an electro-viscoelastic body and a conductive foundation. The Signorini conditions are used to model the contact, and adhesion between the contact surfaces is also taken into account. We establish the existence and uniqueness of a weak solution to this problem. Furthermore, we propose a fully discrete numerical scheme to approximate the solution, and we present and prove the main result concerning the estimation of errors.

Our research is primarily focused on applying the tempered (κ, ψ)-fractional operators to investigate the existence, uniqueness, and κ-Mittag-Leffler-Ulam-Hyers stability of a specific class of boundary value problems involving implicit nonlinear fractional differential equations and tempered (κ, ψ)-Hilfer fractional derivatives. To accomplish this, we make use of the fixed point theorem of Banach and a generalization of the well-known Gronwall inequality. Additionally, we provide illustrative examples to demonstrate the practical effectiveness of our main findings.

In this article, we consider a quasilinear parabolic system under fair general conditions with form-boundary conditions on the singular coefficients. We establish the requirements on the structural coefficients of the parabolic system under which the quasilinear system has the unique solution in the Holder functional space.