Journal of Prime Research in Mathematics

Abstract: Face irregularity strength under ρ−labeling ξ with class (α1, β1, γ1) of plane graphs is a labeling from the set of graph elements into the set of integers, that is, ξ: {V ∪ E ∪ F} → {1, 2, 3, .., ρ}, such that the face weights are distinct at any stage in the graph labeling, that is, Wξ(α1,β1,γ1)(f) ̸= Wξ(α1,β1,γ1)(g), for any two faces f and g of the graph G. The face irregular strength of a plane graph G is the least possible integer ρ such that G admits face irregular ρ−labeling. In this research, authors have examined the exact tight lower bounds for the face irregular strength of generalized plane graphs under ρ−labeling of class (α1, β1, γ1) for vertex (1, 0, 0), edge (0, 1, 0), face (0, 0, 1), vertex-face (1, 0, 1), edge-face (0, 1, 1) and entire (1, 1, 1). Results are verified by examples.

Abstract: This article introduces the concept of translation-factorable surfaces in the isotropic space 𝕀³ and presents classification theorems for these surfaces based on their isotropic mean and isotropic Gaussian curvatures, considering both zero and nonzero values. Furthermore, an additional investigation is conducted to classify translation-factorable (TF) surfaces in 𝕀³ under the condition H²=K

Abstract: The solvability in a closed form of the following three-dimensional system of difference equations of second order with arbitrary powers
$$x_{n+1}=\frac{y_{n}y_{n-1}^{q}}{x_{n}^{p}(a+by_{n}y_{n-1}^{q})},\,y_{n+1}=\frac{z_{n}z_{n-1}^{r}}{y_{n}^{q}(c+dz_{n}z_{n-1}^{r})}
,\,z_{n+1}=\frac{x_{n}x_{n-1}^{p}}{z_{n}^{r}(h+kx_{n}x_{n-1}^{p})},\,n,\,p,\,q,\,r\in\mathbb{N}_{0}$$
where the initial values x_{_i}, y_{_i}, z_{_i}, i=0,1 are non-zero real numbers and the parameters a,b,c,d,h, are real numbers, will be the subject of the present work. We will also provide the behavior of the solutions of some particular cases of our system.

Abstract: In this paper, some open two-point Newton-Cotes type integral inequalities for functions whose first derivatives are convex via Riemann-Liouville fractional integrals are established. Our finding generalize some already known results. In order to illustrate the efficiency of our main results, some applications are given.

Abstract: In this paper, as a generalization of derivation in a residuated lattice, the notion of f-derivation for a residuated lattice is introduced and some related properties of isotone (resp. contractive) f-derivations and ideal f-derivations are investigated. Also, we define principal f-derivation and their properties. Finally, we define the notion of fixed point. In particular, as an application of ideal f-derivation in Heyting algebras, we obtain that the fixed point set is still a residuated lattice.

Abstract: The aim of this paper is to present the convergence results to approximate the fixed points of multivalued mean nonexpansive mappings in CAT(0) spaces. Strong and ∆-convergence results are established for these mappings using F-iterative scheme. Moreover, a numerical example is given to show the convergence behavior of the iterative scheme for multivalued mean nonexpansive mappings. The results which we derived are generalization of many results existing in literature.