# 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

### Computation of Topological Indices for Inner Dual Graph of Honeycomb and Graphene Network

JPRM-Vol. 17 (2021), Issue 2, pp. 138 – 148 Open Access Full-Text PDF
FM Bhatti, Iqra Zaman, Sawaira Sikander
Abstract: In QSPR/QSAR study, the molecular structure indices are now standard methods for studying structureproperty relations. Due to the chemical significance of these indices, the number of proposed molecular descriptors is quickly rising in the last few years. A topological index is a transformation of a chemical structure into a real number. In mathematics, honeycomb networks are widely used because of their extreme importance in computer graphics, image processing, cellular phone base stations, and in chemistry to represent benzenoid hydrocarbons. They are formed by recursively using hexagonal tiling in a particular pattern. HC(n) represents the honeycomb network of dimension n, where n is the number of hexagons between boundary and central hexagon. An atomic-scale honeycomb structure composed of carbon atoms is known as graphene. Professor Andre Geim and Professor Kostya Novoselov separated it from graphite in 2004. It is the first 2D material that is one million times thinner than human hair, two hundred times stronger than steel, and the world’s most conductive material. The graph 2D graphene is expressed as G(r, s) where “r” means the number of rows, and “s” is the number of hexagons in a row. This paper uses the inner dual graph of honeycomb networks and 2D graphene network, which are named as HcID(n) and GID(r, s) respectively. We derive some results related to topological indices for these graphs. We compute degree-based indices, first general Zagreb index, general Randi´c connectivity index, general sum-connectivity index, first Zagreb index, Second Zagreb index, Randi´c index, Atom-bond Connectivity (ABC) index, and Geometric-Arithmetic (GA) index of inner dual graphs of honeycomb networks and graphene network.

### A Conceptual Framework of Convex and Concave Sets under Refined Intuitionistic Fuzzy Set Environment

JPRM-Vol. 17 (2021), Issue 2, pp. 122 – 137 Open Access Full-Text PDF
Abstract: Intuitionistic fuzzy set deals with membership and non-membership of a certain element of universe of discourse whereas these are further partitioned into their sub-membership degrees in refined intuitionistic fuzzy set. This study aims to introduce the notions of convex and concave refined intuitionistic fuzzy sets. Moreover, some of its important properties e.g. complement, union, intersection etc. and results are discussed.

### Correction on General Convergence Analysis for Two-Step Projection Methods and Applications to Variational Problems

JPRM-Vol. 18 (2022), Issue 1, pp. 38 – 42 Open Access Full-Text PDF
Abstract: The aim of this study is to illustrate that the main result of the paper [1] is incorrect by giving an counterexample. I also present and study a new algorithm 4.1 to correct the main result of [1]. The possible impact of this study is rather important, it puts a question mark on results in all references that have been cited This publication ( 203 times just in Google Scholar alone).

### Fuzzy L$$^P$$-Spaces

JPRM-Vol. 18 (2022), Issue 1, pp. 28 – 37 Open Access Full-Text PDF
Shams Yousef, Forouzan Farahrooz
Abstract: The purpose of this paper is to introduce the fuzzy L$$^P$$-Spaces. We give some basic definitions and main properties of fuzzy spaces. The fuzzy Holder’s inequality will be proved. Also we show that the dual offuzzy L$$^P$$-spaces is fuzzy L$$^q$$-spaces, where the scalars p and q are conjugate exponents.

### On Metric Dimension of Chemical Networks

JPRM-Vol. 18 (2022), Issue 1, pp.18 – 27 Open Access Full-Text PDF
Muhammad Hussain, Saqib Nazeer, Hassan Raza
Abstract: Metric Dimension of any graph G is termed as the minimum number of basis element in the resolving set. Let G = (V, E) be any connected graph and length of the shortest path between s and h is known as distance, denoted by d(s, h) in G. Let B = {b1, b2, …, bq} be any ordered subset of V and representation r(u|B) with respect to B is the q−tuple (d(u, b1), d(u, b2), d(u, b3), …, d(u, bq)}, here B is called the resolving set or the locating set if every vertex of G is uniquely represented by distances from the vertices of B or if distinct vertices of G have distinct representations with respect to B. Any resolving set containing minimum cardinality is named as basis for G and its cardinality is the metric dimension of G is denoted by dim(G). We investigated metric dimension of Polythiophene Network, Backbone Network, Hex-derive Network and Nylone6,6.

### Fixed Point Approximations of a Family of α-nonexpansive Mappings in CAT(0) Spaces

JPRM-Vol. 18 (2022), Issue 1, pp. 7 – 17 Open Access Full-Text PDF
Sundus Shahzeen, Maqbool Ahmed, Liliana Guran
Abstract: In this article, the results deal with the strong convergence of Halpern iteration in CAT(0) spaces. The study revolves around finding a fixed point for nonexpansive mappings, which are also the metric projection points in CA(0) space.Moreover, the strong convergence of Halpern iteration for α-nonexpansive mapping sequence is also given.Our results extend some known results which appeared in the literature.