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.