A solvable three dimensional system of difference equations of second order with arbitrary powers
JPRM-Vol. 19 (2023), Issue 2, pp. 37 – 59 Open Access Full-Text PDF
M. C. Benkara Mostefa, A. C¸ete, N. Touafek, Y. Yazlik
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.
$$x_{n+1}=\frac{y_{n}y_{n-1}^{q}}{x_{n}^{p}(a+by_{n}y_{n-1}^{q})},\,y_{n+1}=\frac{z_{n}z_{n-1}^{r}}{y_{n}^{q}(c+dz_{n}z_{n-1}^{r})}
,\,z_{n+1}=\frac{x_{n}x_{n-1}^{p}}{z_{n}^{r}(h+kx_{n}x_{n-1}^{p})},\,n,\,p,\,q,\,r\in\mathbb{N}_{0}$$
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.
Open two-point Newton-Cotes integral inequalities for differentiable convex functions via Riemann-Liouville fractional integrals
JPRM-Vol. 19 (2023), Issue 2, pp. 24 – 36 Open Access Full-Text PDF
Hamida Ayed, Badreddine Meftah
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.
On f-Derivations in Residuated Lattices
JPRM-Vol. 19 (2023), Issue 2, pp. 17 – 23 Open Access Full-Text PDF
Mbarek Zaoui, Driss Gretete, Brahim Fahid
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.
Approximation of Fixed Point of Multivalued Mean Nonexpansive Mappings in CAT(0) spaces
JPRM-Vol. 19 (2023), Issue 2, pp. 1 – 16 Open Access Full-Text PDF
Mujahid Abbas, Khushdil Ahmad, Khurram Shabbir
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.
On edge irregularity strength of certain families of snake graph
JPRM-Vol. 19 (2023), Issue 1, pp. 92 – 101 Open Access Full-Text PDF
Muhammad Faisal Nadeem, Murat Cancan, Muhammad Imran, Yasir Ali
Abstract: Edge irregular mapping or vertex mapping β : V (U) → {1, 2, 3, …, s} is a mapping of vertices in such a way that all edges have distinct weights. We evaluate weight of any edge by using equation wtβ(cd) = β(c)+β(d), ∀c, d ∈ V (U) and cd ∈ E(U). Edge irregularity strength denoted by es(U) is a minimum positive integer used to label vertices to form edge irregular labeling. The aim of this paper is to determine the exact value of edge irregularity strength of different families of snake graph.
Milnor Fibrations and Regularity Conditions for Real Analytic Mappings
JPRM-Vol. 19 (2023), Issue 1, pp. 82 – 91 Open Access Full-Text PDF
Khurram Shabbir
Abstract: When ƒ: \((\mathbb{R^n},0)\)→\((\mathbb{R^p},0)\)is a surjective real analytic map with isolated critical value, we prove that the(m)-regularity condition (in a sense we define) ensures that \(\frac{f}{||f||}\) is a fibration on small spheres, ƒ induces afibration on the tubes and these fibrations are equivalent.In particular, we make the statement of [12] more precise in the case of an isolated critical point and weextend it to the case of an isolated critical value.
