European Journal of Mathematical Analysis

C-Class Functions and Fixed Points of Weakly Contractive Mappings in Rectangular b-Metric Spaces

2025-08-19T09:26:05+08:00

In this paper, we introduce C class-F-generalized weakly contractive mapping and prove the existence and uniqueness of fixed points of such maps in the setting of rectangular b-metric spaces. We provide an example in support of our result.

Schwarz Boundary Value Problem for Higher-Order Complex Partial Differential Equations on a Triangle

2025-11-20T21:37:24+08:00

In this paper, we consider the Schwarz boundary value problem for higher-order complex partial differential equations on a triangle. We first introduce the poly-Schwarz operator and the T-type operator for the triangle, and then investigate the boundary behavior of these operators. In addition, we discuss the solvability conditions and present an explicit solution to the Schwarz problem for the inhomoheneous polyanalytic equation on the triangle.

Groupoid Characterization of Partial Algebras on Sobolev Spaces

2025-12-19T06:25:16+08:00

The \(L^p\)-spaces, with \(p \not = \infty\), form a partial algebra \((L^p(\Omega), \Gamma, \cdot)\) with pointwise multiplication of functions. The Sobolev spaces \(W^{k,p}(\Omega)\), delineated by weak derivatives as subspaces of \(L^p\)-spaces is shown to contain the partial algebra \((L^p(\Omega), \Gamma, \cdot)\) generalized by the partial action of the smooth algebra \(\mathscr{K}(\Omega)\) by convolution on the Banach spaces \(L^p(\Omega)\). We characterised the Sobolev space \(W^{k,p}(\Omega)\), invariant under \(\mathscr{K}(\Omega)\) partial action, using Lie groupoid framework, and study the partial algebra as defining the partial dynamical systems on the \(L^p\)-space associated with the weak differential operators. The locally convex partial \(^*\)-algebra \((L^p(\Omega), \Gamma, \cdot,^*)\) defines the stable local flows coinciding with local bisections of the Lie groupoid. The unitary representation of resulting Lie groupoid \(\mathscr{W} \rightrightarrows W^{k,p}(\Omega)\) on the associated Hilbert bundle demonstrates the simplification achieved by the characterisation.

Donoho-Stark Theorem for the Second Hankel-Clifford Transform

2025-10-26T06:08:11+08:00

In this work, we obtain an analog of Donoho-Stark theorem for the second Hankel-Clifford transform for functions in \(f \in L^1_{\mu} \cap L^2_{\mu}\), using the properties of this transform.

Multivalued Contractive-Type Extensions with Stability and Well-Posedness in Cone b-Metric Spaces under (λ, s)-Convexity and Applications

2025-08-28T19:30:49+08:00

We introduce new extensions of multivalued contractive fixed point results in complete cone b-metric spaces endowed with a normal cone structure. By developing a λ-iterative scheme combined with an approximate Hausdorff selection technique, we establish original Nadler-type and Berinde-type results with explicit convergence estimates depending on the b-metric coefficient s and the iteration parameter λ.
In addition, we prove a Berinde-type fixed point theorem for weak multivalued contractions, together with stability and well-posedness results under the sharp condition sδ < 1. The stability theorem provides quantitative bounds for perturbations of contractive multivalued operators, while the well-posedness result guarantees convergence of approximate solutions to the unique fixed point.
Applications to vector optimization and Nash-type equilibrium problems are presented within the framework of (λ, s)-convexity. The results extend classical fixed point theorems of Nadler and Berinde to the ordered and relaxed triangle inequality setting of cone b-metric spaces.

New Fixed Point Results for (τ -k)-F-Contraction Mappings in Complete Metric Spaces

2025-12-01T00:46:40+08:00

In this paper, we introduce and study two novel classes of contractions in complete metric spaces, namely the (τ , k)-F-contractions and (τ , k)-F-weak contractions. These notions generalize and unify several well-known contraction conditions in the existing literature. We establish sufficient conditions ensuring the existence and uniqueness of fixed points for such mappings in complete metric spaces. In addition, illustrative examples are presented to verify the applicability and effectiveness of the proposed results. The findings of this work extend and enhance many classical fixed point theorems within the framework of metric spaces.