We introduce and study a topology on nominal sets induced by a support closure operator, which arises naturally from the action of finitary permutations on a countable set of atoms. This topology is generated by support classes and is closely related to a metric defined via symmetric differences of supports. We characterize continuous maps between nominal sets in this topological setting, investigate compactness and Hausdorffness properties and analyze the interplay between equivariance, support closure and topological structure. Our results provide new insights into the algebraic and topological aspects of nominal sets, enriching their theory and potential applications in areas such as logic, computer science and algebraic structures with name-binding.
Let G be a locally compact group and 1 <= p < oo. In this paper, we show that the mapping pi : G & times; L-p(G) -> L-p(G) with the assignment (t, f) bar right arrow T(t)f = phi/delta(t)*phi delta(t) * f, is separately continuous which ensures that {T-t}(t is an element of G) forms a C-0-semigroup. Also, it is proved that the C-0-semigroup {T-t}(t is an element of G) admits a universal vector only when G is noncompact and second countable. The hypercyclic phenomenon is studied for the single weighted translation as well. Finally, we give examples of universal C-0-semigroups.
Dense fuzzy sets play an inevitable role in exploring various aspects of fuzzy topological spaces. The present paper aims at investigating the properties of dense fuzzy sets in different fuzzy topological spaces. Several characterization theorems and other novel results are obtained by means of dense fuzzy sets in specific contexts as well as in general settings. The relationship between quasi-coincidence of fuzzy sets and denseness property is also analyzed. Additionally, the concepts of separability, Q-separability, beta-separability and Q-beta-separability are examined.
This research work deals with generalizations and refinements of bounds of the first inequality of the celebrated Her-mite Hadamard dual inequality via Riemann-Liouville fractional integrals. Specifically, we explore generalized integral inequalities for several kinds of convexities using fractional integrals by utilizing the newly defined class of (s1, s2, t1, t2)-convex functions. The proposed research work establishes the superiority of an enhanced version of the power-mean integral inequality and H & ouml;lder integral inequality, termed as improved power-mean and H & ouml;lder-& Idot;& scedil;can integral inequalities, over the traditional ones.
In mathematical interpretations, integral inequalities constitute a significant and continuous body of research. Recently, numerous studies have been conducted on fractional calculus approaches due to their widespread usage in science. The tempered fractional integral is a fundamental notion in fractional calculus. Our main goal in this work is to obtain some Bullen-type inequalities utilizing the tempered fractional integral operators. From a new identity, we derive several novel Bullen-type inequalities for differentiable convex functions.
Convexity assumptions play an important role in mathematical analysis. In this work, we establish a midpoint-type inequality for the average value of (s, t)-convex functions of the second kind within the framework of quantum calculus. We begin by presenting a new identity for functions that are twice partially quantum differentiable. Using this identity, we derive two inequalities that provide error estimates for a generalized Hadamard inequality. We also demonstrate how these results apply to continuous functions whose second-order quantum partial derivatives are (s, t)-convex of the second kind in absolute value. Graphical examples are included to illustrate and compare the results. Finally, we present applications involving special means of positive real numbers.
In this work, we introduce new subclasses Sigma & lowast;Sq (sigma, & rhov;) and Sigma & lowast;Cq (sigma, & rhov;) of meromorphic functions defined on a punctured unit disk and constructed using the q-derivative. We explore the properties coefficient estimates and the convexity of these classes. The study also includes the radius of meromorphically q-starlikeness, the radius of meromorphically q-convexity, modified Hadamard product and integral operators of class Sigma & lowast;Sq (sigma, & rhov;). We have provided a graphical explanation to clarify how changing the values of q affects the theoretical conclusions. This visual approach provides a clearer view of the variations that appear when q changes and supplements the analytical results. This work increases our understanding of the properties of meromorphic functions by integrating analytical findings with graphical representations.
This paper explores a solution method for a nonlinear Erd & eacute;lyi-Kober type fractional integral equation (NLFIE), leveraging fixed point theory, particularly the Darbo fixed point theory. The equation, with deviating arguments and the Erd & eacute;lyi-Kober operator, offers insights applicable to diverse scientific domains. Notably, by specializing parameters, it aligns with models describing infectious disease propagation. Additionally, it underscores the utility of Erd & eacute;lyi-Kober fractional integrals in characterizing media with non-integer mass dimensions, with applications spanning porous media to electrochemistry. This analysis advances our understanding of solving complex nonlinear integral equations, offering interdisciplinary insights with practical implications.
The objective of this paper is to prove fixed point results in rectangular quasi-b metric spaces using w-distance function. We establish some results for the existence and uniqueness of fixed points and introduce a new class of contractive mappings to generalize. We also analyze the existence of solutions to integral equations of the volterra type in order to show the significance of our theoretical results. Additionally, examples are provided. Furthermore, we applied one of our results to determine the existence of a solution to an integral equation.
The purpose of this research is to incorporate the new class of functions called (m, (5)-convex functions. In addition, we establish several inequalities for (m, (5)-convex functions. Furthermore, we give some applications of the main results in Tsallis entropy and analysis.
A many-level abstract approximation system on a quantale L is introduced and studied. Based on this fact, a pair of lower quantic and upper quantic M-approximation operators is specified and discussed. In addition, the concepts of an Alexandrov M-Hutton quasi-fuzzy topology and an Alexandrov M-Hutton fuzzy co-topology on L are introduced. Moreover, the relationships between them and a lower quantic M-approximation operator (a lower QM-ApprX operator for short) and an upper quantic Mapproximation operator (an upper QM-ApprX operator for short) are discussed, respectively. Furthermore, the notion of an M-open structure and its relationships with a lower QM-ApprX operator and the concept of an M-closed structure are established.
Let S-sin(& lowast;) be the class of normalized analytic functions f defined on the unit disk such that z f '(z) / f(z) lies in an eight-shaped region in the right-half plane which is the image of the unit disk under an entire function 1 + sin z. For this class we determine the sharp estimates for certain Hermitian Toeplitz determinants whose elements are coefficients of starlike functions governed by the subordination relation to the Sine function.
Fuzzy delay mixed Volterra-Fredholm integro differential equations arise naturally in the mathematical modeling of real-world phenomena involving uncertainty, memory effects, and time delays in engineering and applied sciences. This paper investigates the convergence behavior of the Adomian Decomposition Method (ADM) when applied to a class of such equations with fuzzy parameters and delay terms. Fuzzy set theory is employed to rigorously represent parametric uncertainty, thereby enhancing the realism and flexibility of the mathematical model. Sufficient conditions guaranteeing the convergence of the ADM series solution are derived using fixed-point arguments in appropriate function spaces. The theoretical analysis is supported by numerical examples that demonstrate the accuracy and efficiency of the proposed approach. The results confirm that ADM provides a reliable and effective framework for solving fuzzy delay mixed Volterra-Fredholm integrodifferential equations.
We use the notion of radial derivative of analytic functions to introduce a new composition-differentiation operator on the classical spaces of analytic functions on the unit disk. These classical spaces of analytic functions include the Hardy space, the Bergman space, and the Dirichlet space. We then obtain necessary and sufficient conditions on the symbol function to ensure that the induced operator is Hilbert-Schmidt.
Taking into account the recent view of fixed point theory as expressed by Jalali and Samet [On Banach's fixed point theorem in perturbed metric spaces, J. Appl. Anal. Comput. 14 (2) (2025), 992--1001], we first introduce a perturbed metric space equipped with a graph and then present new concepts and notions related to this space. Next, we prove some fixed point theorems related to this new space. Several consequences and an example are also presented to demonstrate the effectiveness of the main results. Following the idea of this article, one can continue this new way to obtain fixed points of the mappings that do not satisfy classic contractions in such spaces endowed with a graph or a partial order.
This study introduces the sequence spaces c(S star) and c0(S star), defined as the domain of the matrix S star constructed from a hybrid structure involving Schr & ouml;der and Catalan numbers. A comprehensive investigation is conducted into the fundamental topological and structural properties of these sequence spaces, such as completeness and their relationships and embedding within classical sequence spaces. Furthermore, the dual space structures corresponding to these newly defined spaces are thoroughly characterized. In the final sections, various classes of matrix transformations and compact linear operators acting on these sequence spaces are examined, emphasizing their significance in functional analysis.
This paper studies the scalability of tensor products of several frames, which may come from different Hilbert spaces. Although the scalability of single frames and tensor products of two frames has been explored, the case with more than two frames has not been studied and solved yet. We establish sufficientand necessary conditions under which such tensor products are scalable, and we describe these conditions using operator theory, spectral analysis, and numerical methods. To clarify the issue, we provide examples and counterexamples. Finally, we briefly mention how this can be applied in signal processing and sparse representation.
Boundary and initial value problems, including nonlinear difference equations and nonlinear differential equations, are the mathematical models of many physics and engineering problems and natural phenomena. Usually, due to the lack of a solid theory for solving these types of equations, these equations are solved by using numerical and approximate methods. In this paper, first some elementary and basic definitions and concepts of discrete and continuous multiplicative calculus are given. Next we apply some ideas and methods to obtain invariant functions with respect to their associated derivative. These invariant functions are used to solve several types of nonlinear difference and differential equations that have appeared in natural sciences and physical problems. After that, these methods are expanded for solving nonlinear difference and differential equations through discrete and continuous multiplicative differential equations. Finally, some applications of multiplicative forms of differential equations are given which simplify numerical methods for solving nonlinear biological problems and exponential approximations for nonlinear functions.
This paper investigates the application of the Quasilinearization Method (QLM) for approximating non-linear delay differential equations (DDEs), which are prevalent in fields such as control systems and population dynamics. QLM effectively transforms these complex non-linear problems into a system of linear equations, a key advantage for computational efficiency. Our work provides two main contributions: a rigorous mathematical proof demonstrating the quadratic convergence of the proposed technique and numerical examples that illustrate its practical applicability and reliability. We apply QLM to DDEs with various non-linear forms, including quadratic and exponential types and with fixed, discrete delays. The results confirm that the method is highly accurate, computationally efficient and easy to implement, making it a valuable tool for future research.
In this article, we introduce a new class of convex functions called cti-inverse cosine convex functions (cti-ICCF), which extends the traditional classes. We analyze various algebraic and geometric properties by illustrating the graphs of several significant cti-ICCF via visual representations. Utilizing this novel class, we derive the Hermite-Hadamard (HH) inequality and certain refinements for functions whose first derivative in absolute value is cti-ICCF. The primary tools employed in deriving the main results include H & ouml;lder's inequality, H & ouml;lder-& Idot;& scedil;can inequality and power-mean integral inequality. Our findings demonstrate that the approximations obtained using H & ouml;lder-& Idot;& scedil;can and the improved power-mean integral inequality are superior to those derived from other methods. In particular, when cti = 1 1, the derived results will coincide with those of classical ICCF. This innovative concept of cti-inverse cosine convexity opens new avenues for research, encouraging further exploration of such convexity classes.
