In 2022, the notion of pointwise slant Riemannian maps were introduced by Y. G?nd?zalp and M. A. Akyol (Journal of Geometry and Physics, 179, 104589, 2022) as a natural generalization of slant Riemannian maps, slant Riemannian submersions, slant submanifolds. As a generalization of pointwise slant Riemannian maps and many subclasses notions, we introduce pointwise bi-slant Riemannian maps (briefly, PBSRM) from almost Hermitian manifolds to Riemannian manifolds, giving a non-trivial (proper) example and investigate some properties of the map, we deal with their properties: the J-pluriharmonicity, the J-invariant, and the totally geodesicness of the map. Finally, we study some curvature relations in complex space form, involving Chen inequalities and Casorati curvatures for PBSRM, respectively.

The subject of this paper revolves around fractional differential equations incorporating a ?-Caputo fractional derivative, focusing on the Ulam-Hyers stability, the existence and uniqueness of solutions for nonlinear fractional quadratic iterative differential equation by utilizing Schauder?s fixed point theorem, reinforced by the Ascoli-Arzel? theorem. Additionally, we present two illustrative examples to buttress our analytical findings.

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

In this paper, we further investigate new construction methods for uninorms on bounded lattices via given uninorms. More specifically, we first construct new uninorms on arbitrary bounded lattices by extending a given uninorm on a subinterval of the lattices under necessary and sufficient conditions on the given uninorm. Moreover, based on the resulting uninorms, we can obtain another sufficient and necessary condition under which S*1 is a t-conorm (T*1 is a t-norm) in [32]. Furthermore, using closure operators (interior operators), we also provide new construction methods for uninorms by extending the given uninorm on a subinterval of a bounded lattice under some additional constraints and simultaneously investigate the additional constraints carefully and systematically. Meanwhile, some illustrative examples for the above construction methods of uninorms on bounded lattices are provided.

Let H be a complex infinite dimensional Hilbert space. For T ? B(H), T is said to satisfy property (UW?) if the complement in the approximate point spectrum of the Weyl essential approximate point spectrum coincides with the poles of T. In this paper, we deeply talk about the property (UW?) under some perturbations and property (UW?) for functions of operators. In addition, if T is Drazin invertible, then property (UW?) for functions of T can be transmitted to the functions of its Drazin inverse.

A graph G is induced matching extendable or IM-extendable if every induced matching of G is contained in a perfect matching of G. For a bipartite graph G[U, V] with |U| = n1, |V|=n2, and n1 > n2 > 1, we say G is k-critical-bipartite if deleting at most k = n1-n2 vertices from U yields G? that has a perfect matching. Previously, Yuan (1998) and Laroche (2014) provided the structural characterizations for IM-extendable graphs and k-critical-bipartite graphs, respectively. Since the eigenvalues of a graph are closely related to its structural properties, we now characterize them from the perspective of the spectrum of graphs. In this paper, we first provide a tight spectral radius condition that guarantees a graph with minimum degree is IM-extendable. Furthermore, we present a tight spectral radius condition that ensures a bipartite graph with minimum degree is k-critical-bipartite.

In this note, we define two distinct categories of fuzzy Z-proximal contractions and we use these two fuzzy Z-proximal contractive inequalities as a tool to obtain best proximity point for a non-self mapping which is defined between two distinct non-empty subsets of a strong fuzzy metric space. Further, prove some proximity theorems by using these categories of fuzzy Z-proximal in a complete strong fuzzy metric space. For the support of these innovative results we produce a few validation of examples. At last, we provide a solution of a non-linear second-order ordinary differential equation with the help of fuzzy Z-proximal contractive inequality provided that assumed space is strong fuzzy metric space.

It is of interest to look for the sufficient conditions for the rigidity of a graph. Fan, Huang and Lin (2023) recently studied the rigidity of a graph from the perspective of its spectral radius of the adjacency matrix and established a sufficient condition involving the spectral radius to ensure a 2-connected (or a 3-connected) graph G with a fixed minimum degree to be rigid (or globally rigid). In this note, we establish a similar condition which relates \lambda_1^a(G) , the spectral radius of the matrix A_a(G) := aD(G) + (1 - \alpha)A(G) , where \alpha \in (0, 1) , A(G) and D(G) are the adjacency matrix and the diagonal degree matrix of G, respectively.

This paper discusses the significance of quantum calculus in some mathematical fields. It specifically investigates solutions? existence, uniqueness, and stability for a system of n-nonlinear fractional q-differential equations with initial conditions involving Caputo fractional q-derivatives. The paper utilizes Schauder?s and Banach?s fixed-point theorems and Ulam-Hyers? stability criteria to explore the analytical dynamics inherent in these solutions. Additionally, it provides two illustrative examples to demonstrate the practical applicability of the obtained results.

Using Schauder's fixed-point theorem, we establish sufficient conditions for the existence and uniqueness of solutions to the nonlinear fractional boundary value problem: \begin{cases} {}_{c}D^{\beta}\zeta(x) + f(x, \zeta(x), I^{\gamma}\zeta(x)) = 0, & x \in I = [0, 1], \quad 1 0, \\?(0) = 0, \quad \zeta(1) = \phi(\zeta), \end{cases} {(0.1)} where \phi is a functional defined on C(I, \mathbb{R}) . By constructing an appropriate Green''s function, we derive a Lyapunov-type inequality for a special case of the problem (0.1): \begin{cases} {}_{c}D^{\beta}\zeta(x) + \lambda(x)I^{\gamma}\zeta(x) = \eta(x, \zeta(x)), & x \in I = [0, 1], \quad 1 0, \\?(0) = 0, \quad \zeta(1) = \phi(\zeta). \end{cases} {(0.2)} We further make an analysis for equation (0.2) by applying the inverse operator method and the Mittag-Leffler function with illustrative examples demonstrating applications obtained. Finally, we construct an analytic solution to the following generalized fractional heat equation with an initial condition in n dimensions based on an inverse operator: \begin{cases} {}_{c}D_{t}^{\alpha}u(t, x) = \Delta_{a_{1}(x_{1}), \cdots, a_{n}(x_{n})}u(t, x) + f(t, x), & (t, x) \in \mathbb{R}^{+} \times \mathbb{R}^{n}, \quad 0 < \alpha \leq 1, \\u(0, x) = \psi(x), \end{cases} {(0.3)} where \Delta_{a_{1}(x_{1}), \cdots, a_{n}(x_{n})} = a_{1}(x_{1})\frac{\partial^{2}}{\partial x_{1}^{2}} + \cdots + a_{n}(x_{n})\frac{\partial^{2}}{\partial x_{n}^{2}}.