Some new estimates of generalized \((h_1, h_2)\)-convex functions

JPRM-Vol. 1 (2019), Issue 1, pp. 129 – 146 Open Access Full-Text PDF
Farhat Safdar, Muhammad Aslam Noor, Khalida Inayat Noor, Saima Rashid
Abstract: In this article, we introduce a new class of generalized convex functions involving two arbitrary auxiliary functions \(h_1, h_2 : I = [a, b] ⊆ R → R\), which is called generalized \((h_1, h_2)\) convex functions. We obtain several new classes of convex functions as special cases. We derive some new integral inequalities for generalized convex functions. Several special cases are also discussed. Results proved in this paper can be viewed as new significant contributions in this area.
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Forgotten index of generalized F-sum graphs

JPRM-Vol. 1 (2019), Issue 1, pp. 115 – 128 Open Access Full-Text PDF
H. M. Awais, M. Javaid, M. Jamal
Abstract: Liu et al. [IEEE Access; 7(2019); 105479-105488] defined the concept of the generalized subdivided operations on graphs and obtained the generalized F-sum graphs. They also calculated the 1st and 2nd Zagreb indices of the generalized F-sum graphs. In the continuation of this work, we study the forgotten index (F-index) of the generalized F-sum graphs in terms of different topological indices (TI’s) of their base graphs. In the end, the results of F-index on the generalized F-sum graphs acquired by the particular classes of alkane are also included.
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Sum divisor cordial labeling for path and cycle related graphs

JPRM-Vol. 1 (2019), Issue 1, pp. 101 – 114 Open Access Full-Text PDF
A. Lourdusamy, F. Patrick
Abstract: A sum divisor cordial labeling of a graph \(G\) with vertex set \(V\) is a bijection \(f\) from \(V\) to \(\{1, 2, ··· , |V (G)|\}\) such that an edge \(uv\) is assigned the label 1 if 2 divides \(f(u) + f(v)\) and \(0\) otherwise; and the number of edges labeled with \(0\) and the number of edges labeled with 1 differ by at most 1. A graph with a sum divisor cordial labeling is called a sum divisor cordial graph. In this paper, we prove that \(P^{2}_{n}, P_n ⊙ mK_1, S(P_n ⊙ mK_1), D_2(P_n), T(P_n)\), the graph obtained by duplication of each vertex of path by an edge, \(T(C_n), D_2(C_n)\), the graph obtained by duplication of each vertex of cycle by an edge, C^{(t)}_{4}, book, quadrilateral snake and alternate triangular snake are sum divisor cordial graphs.
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Similarity measures for picture hesitant fuzzy sets and their applications in pattern recognition

JPRM-Vol. 1 (2019), Issue 1, pp. 81 – 100 Open Access Full-Text PDF
Zeeshan Ahmad, Tahir Mahmood, Muhammad Saad, Naeem Jan, Kifayat Ullah
Abstract: The concept of picture hesitant fuzzy set (PHFS) is a generalization of picture fuzzy set (PFS) and hesitant fuzzy set (HFS). Such kind of idea can be very helpful in problems where opinions are of more than two types i.e. yes, no, abstinence and refusal. The goal of this manuscript is to introduce the concept of similarity measures for PHFSs as a generalization of the similarity measures for PFS. We studied the basic concepts of  PFSs, HFSs and PHFSs. We proposed some similarity measures for PHFSs such as cosine similarity measure, set-theoretic similarity measure and grey similarity measure for PHFSs. Some weighted similarity measures are also proposed where weight of the attributes is considered. Then these similarity measures for PHFSs are applied to a building material recognition problem. Finally, a comparative study of similarity measures of PHFSs is established with similarity measures of PFSs, HFSs, IFSs and IHFSs and the advantages of new work are studied.
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Heat and mass transfer in mhd maxwell fluid over an infinite vertical plate

JPRM-Vol. 1 (2019), Issue 1, pp. 63 – 80 Open Access Full-Text PDF
Nazish Iftikhar, S. M. Husnine, M. B. Riaz
Abstract: The main focus of this article is to investigate the exact solution for MHD flow of Maxwell fluid over an infinite vertical plate with ramped temperature and constant concentration. Plate is moving along a straight line with arbitrary velocity which depends on time. Laplace transform and convolution theorem are used to acquire solutions for temperature, concentration and velocity. Moreover, results already present in literature are acquired as limiting case from these general results.
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Some new inequalities related to \((α, m)\)-convex functions

JPRM-Vol. 1 (2019), Issue 1, pp. 49 – 62 Open Access Full-Text PDF
Farhat Safdar, Muhammad Aslam Noor, Khalida Inayat Noor
Abstract: In this paper, we establish some results for functions whose derivatives in absolute values at certain power is generalized \((α, m)\)-convex function. We derive some new estimates to the right-hand side of HermiteHadamard inequality for functions whose absolute values of second derivatives raised to real powers are m-convex functions. Special cases are discussed as applications of our results. The technique of this paper may stimulate further research in this field.
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Modified beta generalized linear failure rate distribution: theory and applications

JPRM-Vol. 1 (2019), Issue 1, pp. 21 – 48 Open Access Full-Text PDF
Farrukh Jamal, Ibrahim Elbatal, Christophe Chesneau, Mohammed Elgarhy, Amal S. Hassan
Abstract: In this paper we introduce a new comprehensive six-parameter distribution called the modified beta generalized linear failure rate distribution. One of the interest of this distribution is to generalize some well-known flexible distributions discussed in the literature, such as (i) the beta linear failure rate distribution, (ii) the generalized linear failure rate distribution, (iii) the beta exponential distribution, (iv) the beta Rayleigh distribution and (v) the generalized exponential distribution, among others. We derive some of its statistical properties, including the moments, the moment generating function, the quantile function, the order statistics and the mean deviations. We propose the method of maximum likelihood for estimating the model parameters. A simulation study is performed in order to investigate the performance of the maximum likelihood estimators. A real data set is used to illustrate the importance and the flexibility of the new distribution.
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Advanced algorithm for solving a transportation problem with five indicators and fixed cost

JPRM-Vol. 1 (2019), Issue 1, pp. 05 – 20 Open Access Full-Text PDF
Benoumelaz Farouk, Abed Samira, Khelil Nacer, Rebiai Belgacem, Kamal Houam.
Abstract: In this paper, we studied an advanced algorithm for obtaining the best solution to a transportation problem a fixed-charge with five indicators (AATPI5FC) , the procedure itself is very quick; the proposed method solves FCTPI5 by analyze the problem into partial subsections, solution algorithm is coupling between our technique and simplex algorithm (the technique on the fifth index to guarantee improved service), which is novel and can be useful to researchers solved these problems, the advantages of the proposed advanced algorithm are discussed on the existing methods in the context of the application model, the results showed that the proposed advanced algorithm is simple ,accurate and more computational methods found in literature.
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Quasi invo-regular rings

JPRM-Vol. 1 (2019), Issue 1, pp. 01 – 04 Open Access Full-Text PDF
Peter V. Danchev
Abstract: We define the class of quasi invo-regular rings and prove that they curiously coincide with the so-called invo-regular rings, recently introduced and explored by the present author in Ann. Univ. Mariae CurieSklodowska – Sect. Math. (2018).
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