International Journal of Mathematics And its Applications

Extremal Solutions for Coupled Quadratic Fractional Integral Equations Involving the Generalized Q-Function

2026-08-02T12:21:10+00:00

We study a coupled $2\times 2$ system of nonlinear quadratic fractional integral equations in which each component carries its own fractional order $q_i\in(1,2)$ and its own generalized $Q$-function kernel. Using the Banach contraction principle and a monotone iterative technique in a product partially ordered function space, we prove that the system possesses a unique coupled solution and that the successive approximations starting from a coupled lower solution converge uniformly and monotonically to it. A perturbation and limit argument then shows the system has both a coupled maximal solution and a coupled minimal solution, and two comparison theorems demonstrate that any pair of functions satisfying the corresponding integral inequalities is bounded
componentwise above (respectively below) by the maximal (respectively minimal) solution. Three numerical examples with explicit parameter values and graphical illustrations are provided to validate every result.

Existence of Prime Labeling in Structurally Extended Wheel Graphs

2026-07-08T17:19:47+00:00

A graph with $n$ vertices has a prime labeling if its vertices can be assigned distinct integers from $1$ to $n$ such that adjacent vertex labels are relatively prime. The study of prime labeling for graphs obtained through structural operations has attracted considerable attention in recent years. In this paper, we introduce and investigate a novel family of graphs derived through a systematic structural extension of the standard wheel graph. The construction process initiates with the edge subdivision of the outer cycle of the wheel graph. Subsequently, we focus on the newly inserted subdivision vertices$-$specifically those that are non-adjacent to the central apex vertex. To enhance the structural complexity, a multi-layered expansion is applied: between every pair of consecutive subdivision vertices, we introduce $k$ distinct intermediate vertices. This operation effectively generates $k$ parallel paths of length two bridging these subdivision vertices. In this study, we specifically focus on graphs constructed with $k = 1, 2, 3,$ and $4$ layers. Furthermore, we explore the labeling properties of these extended structures and analytically prove that they admit a prime labeling for every integer $n \geq 3$.

Product Cayley Graph of a Finite Group

2026-08-02T06:05:57+00:00

In this paper, we introduce and study a new graph associated with a finite group, called the Product Cayley graph. Let $G$ be a finite group and let $S$ be a symmetric generating set of $G$. The Product Cayley graph $\Gamma_{pc}(G,S)$ is a graph with the vertex set $G$, and two distinct vertices $x$ and $y$ are adjacent if either $(xy)x^{-1}\in S$ or $(yx)y^{-1}\in S$. We investigate the fundamental structural properties of this graph, including connectedness, regularity, automorphisms, bipartiteness, and spectral properties. Special attention is devoted to finite abelian groups, where the structure of the graph is characterized in terms of the generating set. Furthermore, we study the non-abelian case by considering the dihedral groups $D_{n}$. We first classify symmetric generating sets of small cardinality and determine the conditions under which they generate the whole dihedral group. Based on these classifications, representative families of Product Cayley graphs of dihedral groups are investigated. Several graph invariants, including degree sequence, diameter, clique number, chromatic number, adjacency spectrum, and energy, are obtained.

Generalized Useful Information Generating Function and Applications

2026-06-18T09:47:16+00:00

In this paper, new generalized 'useful' information generating function have been defined with their particular and limiting cases. On the differentiation of this generating function , it gives some well known results vailable in the literature of information theory. Some examples are worked out for discrete and continous distributions like Uniform, Geometric, Normal, Exponential and Pareto distribution.

Conformal Vector Fields With C-Factor on Kropina Metric

2026-06-10T17:01:45+00:00

In this paper, we study the conformal vector fields wit C -factor on a class of Finsler metrics called Kropina metric $F = \frac{\alpha^2}{\beta} $ is defined in Riemannian metric $ \alpha $ and 1-form $ \beta $ and its norm. Then we characterize the PDE's of conformal vector fields on Kropina metric.

Structural Properties of Multiplicative Fractional Integral Inequalities

2026-07-06T06:07:07+00:00

This paper studies four qualitative properties of multiplicative fractional integral inequalities: boundedness, sharpness, additivity, and stability. An auxiliary kernel identity is established to express the error between the multiplicative fractional integral mean and the arithmetic-type mean, which is then used with Hölder's and power-mean inequalities to derive sharp two-sided error bounds for multiplicatively convex, Lipschitz-continuous functions, with the extremal function identified explicitly. A semigroup-type additivity result decomposes the error over $[a,b]$ into errors over $[a,c]$ and $[c,b]$ up to a computable correction term, while stability estimates quantify the error's sensitivity to perturbations of $f$. Corollaries recover known Ostrowski, Simpson, and trapezoid-type results as special cases, and two numerical examples with tables and visualizations confirm all theoretical bounds.

On Lacunary Statistical Convergence in Metric-Like Spaces

2026-08-16T15:09:24+00:00

In the present study, we generalize the notions of lacunary statistical $\sigma$-convergence and lacunary statistical $\sigma$-boundedness of real valued sequences to that of vector valued sequences in an arbitrary metric-like space $(X,\sigma)$. We also explore that a bounded and lacunary statistically $\sigma$-convergent sequence is lacunary strongly $\sigma$-Cesàro summable in a metric-like space. Beside this some inclusion relations are also established between the notion of lacunary statistical $\sigma$-convergence and lacunary strongly $\sigma$-Cesàro summability in $(X,\sigma)$.