Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications

Topological Space in Finite Geometry with Variables in Integer Modulo \(d\)

Semiu Oladipupo Oladejo — 2025-10-01

In this paper, a special class of finite geometry is studied. Lines in the geometry are discussed. The existence of a partially ordered relation leads to the emergence of subgeometries via partial order, which by extension leads to the presence of topological spaces between geometry and its subgeometries, with subgeometries embedded in a topological space.

Different Bounds for an Original Double Integral Involving Concave Functions

Christophe Chesneau — 2025-10-01

Establishing bounds for integrals involving concave functions is an important topic in mathematical analysis. In this article, we investigate a class of double integrals whose integrands are given by the ratio of the sum of two concave functions. This form is particularly interesting because of its connection with well-known inequalities of Hilbert integral type. We derive a series of upper and lower bounds using various valuable techniques, leading to elegant and new results. Where appropriate, multiple proofs of the same result are given. Numerical examples are also used to illustrate and support the findings.

Interpolative Reich-Istratescu-type Hybrid Contractions in Modular Metric Spaces

Sirajo Yahaya — 2025-10-01

In this article, some novel contraction mappings pertaining to modular metric spaces are presented. The conditions that must be met for such operators to possess invariant points are described. Through a nontrivial case, the validity of the derived results is proven.

Zero point approximation schemes for monotone vector fields on complete geodesic spaces

Shuta Sudo — 2025-10-18

In this paper, we obtain two convergence theorems to approximate zero points of a monotone vector field defined on a complete geodesic space with curvature bounded above.

On the Rus-Hicks-Rhoades Contraction Principle

Sehie Park — 2025-10-20

Recently the Banach contractions are extended to the weak contractions or the Rus-Hicks-Rhoades (RHR) maps, for which we collected lots of examples and studied in our previous works [18, 20, 21, 22]. Our aim in the present article is to introduce the weak contraction principle or the RHR contraction principle (Theorem P) which is an extension of the traditional Banach contraction principle. We also improve some known theorems closely related to Theorem P.