# Journal of Prime Research in Mathematics

Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing two issues in June and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year.

Latest Published Articles

### New subclass of starlike functions of complex order

JPRM-Vol. 1 (2006), Issue 1, pp. 157 – 169 Open Access Full-Text PDF
Yasar Polatoglu, H. Esra Ozkan
Abstract: The aim of the present paper is to investigate a new subclass of starlike functions of complex order $$b\neq 0$$. Let $$f(z)=z+a_{2}z^{2}+…$$ be an analytic function in the unit disc $$D=\{z| |z|<1\}$$ which satisfies $$1+\frac{1}{b}(z\frac{f'(z)}{f(z)}-1)=\frac{1+A\omega z}{1+B\omega z}$$, for some $$\omega \in \Omega$$ and for all $$z \in D$$. Then f is called a Janowski starlike function of complex order b, where A and B are complex numbers such that $$Re(1-A\overline{B})\geq |A-B|, im(1-A\overline{B}<|A-B|, |B|<1$$ and $$\omega(z)$$ ) is a Schwarz function in the unit disc D [1], [10], [12]. The class of these functions is denoted by $$S^{∗}(A, B, b)$$. In this paper we will give the representation theorem, distortion theorem, two point distortion theorem, Koebe domain under the montel normalization, and coefficient inequality for this class.

### Vertex-magic total labelings of disconnected graph

JPRM-Vol. 1 (2006), Issue 1, pp. 147 – 156 Open Access Full-Text PDF
Slamin, A.C. Prihandoko, T.B. Setiawan, F. Rosita, B. Shaleh
Abstract: Let G be a graph with vertex set $$V = V (G)$$ and edge set $$E = E(G)$$ and let $$e = |E(G)|$$ and $$v = |V (G)|$$. A one-to-one map $$λ$$ from $$V ∪ E$$ onto the integers $$\{1, 2, …, v + e\}$$ is called vertex magic total labeling if there is a constant $$k$$ so that for every vertex $$x$$, $$λ+\sum λ(xy)=k$$. where the sum is over all vertices $$y$$ adjacent to $$x$$. Let us call the sum of labels at vertex x the weight $$w_{λ}(x)$$ of the vertex under labeling $$λ$$; we require $$w_{λ}(x) = k$$ for all $$x$$. The constant $$k$$ is called the magic constant for $$λ$$. In this paper, we present the vertex magic total labelings of disconnected graph, in particular, two copies of isomorphic generalized Petersen graphs $$2P(n, m)$$, disjoint union of two non-isomorphic suns $$S_{m} ∪ S_{n}$$ and t copies of isomorphic suns $$tS_{n}$$.

### Upper bounds for the size Ramsey numbers for $$P_3$$ versus $$C^{t}_{3}$$ or $$P_{n}$$

JPRM-Vol. 1 (2006), Issue 1, pp. 141 – 146 Open Access Full-Text PDF
E.T. Baskoro, Y. Nuraeni, A.A.G. Ngurah
Abstract: In this paper, we derive an upper bound for the size Ramsey number for a path $$P_3$$ versus a friendship graph $$C_{3}^{t}$$. Furthermore, some minimal Ramsey graph for a combination $$(P_{3}, C_{3}^{t})$$is presented. We also give an upper bound of the size Ramsey number for $$P_3$$ versus $$P_n$$.

### Unsteady MHD oscillating flow with general free stream velocity

JPRM-Vol. 1 (2006), Issue 1, pp. 131 – 140 Open Access
Abstract: Unsteady magnetohydrodynamics viscous problem is solved by Laplace transform technique when fluid at lower plate is oscillating in time and fluid at infinity is assumed as general free stream velocity. Some special cases with their physical significance are also discussed and are compared with already known results.

### An iterative method for nonexpansive mapping in Banch Spaces

JPRM-Vol. 2 (2006), Issue 1, pp. 120 – 130 Open Access Full-Text PDF
Xiaolong Qin, Yongfu Su.
Abstract: In this paper, we establish weak and strong convergence theorems of the three-step iterative sequences with errors for non-self nonexpansive mappings in uniformly convex Banach spaces. Our results extend and improve the recent ones announced by Naseer Shahzad and some others.

### Sum graph based access in a secret sharing scheme

JPRM-Vol. 2 (2006), Issue 1, pp. 113 – 119 Open Access Full-Text PDF
Surjadi Slamet, Kiki Ariyanti Sugeng, Mirka Miller