Authors:Abdellatif Moudafi; Muhammad Aslam Noor Pages: 669 - 676 Abstract: Abstract Inspired by some growth conditions used in convex and nonconvex optimization and given a bifunction defined on a nonempty closed subset of a real Hilbert space, we design a Proximal Point Method for finding its equilibria points. Then, we investigate the convergence of this scheme under a regularity metric type assumption and state other metric regularity conditions. The purpose of this short article is mainly to launch new ideas and bring some novelty in this field. PubDate: 2017-09-01 DOI: 10.1007/s13370-016-0474-4 Issue No:Vol. 28, No. 5-6 (2017)

Authors:Dang Van Hieu Pages: 677 - 692 Abstract: Abstract In this paper, we propose two hybrid subgradient extragradient methods for solving common solutions of variational inequalities problems (CSVIP). The first is a parallel algorithm which can be performed simultaneously while the second is a cyclic algorithm which is computed sequentially on each subproblem in the family. The novelty of this paper is that we have designed the algorithms to develop possible practical numerical methods when the number of subproblems is large. The algorithms can be considered as improvements of some previously known results for CSVIPs. Numerical experiments are also performed to illustrate the efficiency of the proposed algorithms. PubDate: 2017-09-01 DOI: 10.1007/s13370-016-0473-5 Issue No:Vol. 28, No. 5-6 (2017)

Authors:T. Panigrahi; R. K. Raina Pages: 707 - 716 Abstract: Abstract In the present paper, we introduce a certain subclass of analytic univalent functions which is defined in terms of a quasi-subordination and we obtain certain sharp bounds of the Fekete–Szegö functional for functions belonging to this class. The results presented give improved versions for this and associated classes involving the subordination and majorization. Special cases of the main results are also mentioned briefly. PubDate: 2017-09-01 DOI: 10.1007/s13370-016-0477-1 Issue No:Vol. 28, No. 5-6 (2017)

Authors:François E. Tanoé Pages: 727 - 744 Abstract: Abstract Let \(K=\mathbb {Q}(\sqrt{dm}, \sqrt{dn})\) be a biquadratic field. In this paper we give a new integral basis for \(\mathbb {Z}_{K}\) , by applying to biquadratic fields a method of D. Chatelain, for building formel integral bases of n-quadratic fields’ ring of integers. We give some examples. We set the monogenesis problem’s equations, and find the same characterizations that we’ve found, when we had used other bases. We give also new expressions for the elements of monogenesis. PubDate: 2017-09-01 DOI: 10.1007/s13370-016-0476-2 Issue No:Vol. 28, No. 5-6 (2017)

Authors:G. N. V. Kishore; K. P. R. Rao; V. M. L. Hima Bindu Pages: 793 - 803 Abstract: Abstract In this paper, we obtain a Suzuki type unique common fixed point theorem by using C - condition with rational expressions in partial metric spaces. Also we give an example which supports our main theorem. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0484-x Issue No:Vol. 28, No. 5-6 (2017)

Authors:A. M. Abd El-latif Pages: 805 - 821 Abstract: Abstract In this paper, we generalize the notion of soft connectedness (Chen, Some Local Properties of Soft Semi-Open Sets, 2013; Kandil et al., J New Results Sci 4:90–108, 2014; Lin, Int J Math Sci Eng 7(2):1–7, 2013) by using the notion of \(\beta \) -open soft sets. Also, the concept of \(\beta \) -irresolute soft functions is introduced, as a generalization of \(\beta \) -continuous soft functions and several properties of it is investigated. Further, we introduce and study the notion of \(\beta \) -connectedness and gave the basic definitions and theorems about it. Finally, we show that, the surjective \(\beta \) -irresolute soft image of soft \(\beta \) -connected space is also soft \(\beta \) -connected. This study is a standard generalization of some notions in classical topological spaces to soft topological spaces. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0485-9 Issue No:Vol. 28, No. 5-6 (2017)

Authors:Thomas McKenzie; Shannon Overbay Pages: 823 - 830 Abstract: Abstract We determine the book thickness of all zero-divisor graphs with genus at most one. We also describe four families of three page embeddable zero-divisor graphs. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0487-7 Issue No:Vol. 28, No. 5-6 (2017)

Authors:A. M. Zahran; A. Ghareeb; A. K. Mousa Pages: 831 - 839 Abstract: Abstract In this paper, we introduce and study the concept of almost continuity in weak structures (Császár in Acta Math Hung 131(1–2):193–195, 2011) and discuss some of its characteristic properties. Finally, we give some applications of this new kind of continuity. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0490-z Issue No:Vol. 28, No. 5-6 (2017)

Authors:Osama Rashed Sayed; Nasruddin Hassan; Ahmed Mostafa Khalil Pages: 887 - 898 Abstract: Abstract Introducing the notions of soft \(\varvec{{\widetilde{t}}}\) -sets, soft \(\varvec{{\widetilde{t}}^{*}}\) -sets, soft \(\varvec{\mathcal {{\widetilde{B}}}}\) -sets, soft \(\varvec{{\widetilde{\alpha }}^{*}}\) -sets and soft \(\varvec{{\widetilde{C}}}\) -sets in the setting of soft topological spaces, we study some of its properties and investigate the relationships between them besides considering some variants of continuous maps on soft topological spaces. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0494-8 Issue No:Vol. 28, No. 5-6 (2017)

Authors:D. G. Prakasha; F. O. Zengin; Vasant Chavan Pages: 899 - 908 Abstract: Abstract We consider \({\mathcal {M}}\) -projective curvature tensor on Lorentzian \(\alpha \) - Sasakian manifolds and show that \({\mathcal {M}}\) -projectively semisymmetric Lorentzian \(\alpha \) -Sasakian manifold is \({\mathcal {M}}\) -projectively flat. Further, it is shown that, \({\mathcal {M}}\) -projectively semisymmetric Lorentzian \(\alpha \) -Sasakian manifold is semisymmetric. Finally, some results related to energy momentum tensor satisfying the Einstein field equation with cosmological constant of the \({\mathcal {M}}\) -projectively semisymmetric Lorentzian \(\alpha \) -Sasakian space-times are investigated. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0493-9 Issue No:Vol. 28, No. 5-6 (2017)

Authors:B. Bhattacharya Pages: 909 - 928 Abstract: Abstract To the best of our knowledge, till date there are only two directions along which fuzzy topology (general topology) can be compared, one is the generalization of fuzzy topology (such as fuzzy supra topology, generalized fuzzy topology etc.) and the other is the stronger form of fuzzy topology which is known as Alexandroff fuzzy topology. It means that a given topology is always linear. This paper aims to propose the third direction that is a new parallel form of fuzzy topology (or a non-linear topology) called fuzzy independent topology which is neither a generalization nor a stronger form of the given fuzzy topology though it is a unique natural offshoot of the given fuzzy topology but very rare in existence and that has been shown by defining fuzzy \(\gamma ^{*}\) -open set in the sense of Dimitrije Andrijevic, by proving that fuzzy \(\gamma ^{*}\) -open set and fuzzy open set are completely independent of each other though the collection of fuzzy \(\gamma ^{*}\) -open sets are themselves a fuzzy topology therein. At the same time we claim that it is beyond the scope of general topology with the existing generalized open sets in literature and consequently we move one more step towards learning the difference between topology and fuzzy topology. To this end, we study the fundamental properties of the new structure. Also we study some of the basic properties and characterizations of fuzzy \(\gamma ^{*}\) -open sets and few of their applications. The investigation enables us to present a new covering property of the given fuzzy topological space and the preservation theory is obtained. Finally to illustrate the advantage of the proposed concept, we compare the obtained results with some already existing ones. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0483-y Issue No:Vol. 28, No. 5-6 (2017)

Authors:Reza Aghayan Pages: 929 - 943 Abstract: Abstract This paper is devoted to GM-sets and their applications in Lie theory from the theoretical and computational points of view. We consider the GM-set of a transformation group G acting on a smooth manifold M as the set of all associated G-equivariant maps and then investigate the relation between the concepts of G-conjugacy and G-invariance in Lie theory with respect to the associated GM-set. We will also have a look at the fundamental and constructive concept of moving frames through the GM-sets and apply this construction to carry out a detailed survey of some basic concepts in Lie algebra theory. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0481-0 Issue No:Vol. 28, No. 5-6 (2017)

Authors:M. Pitchaimani; D. Ramesh Kumar Pages: 957 - 970 Abstract: Abstract The aim of this paper to establish the existence and uniqueness of coincidence and common fixed points of Nadler type set-valued mappings under various generalized contractive conditions in the context of ultrametric spaces. Illustrative examples are provided to support our results. As an application, we have obtained well-posedness of the common fixed point problems. The presented results generalize several existing results in the literature in ultrametric space setting. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0496-6 Issue No:Vol. 28, No. 5-6 (2017)

Authors:Akbar Paad Pages: 971 - 984 Abstract: Abstract In this paper, we introduce the concepts of n-fold integral ideals and n-fold Boolean ideals in BL-algebras. With respect to concepts, we give some related results. In particular, we prove that an ideal is an n-fold integral ideal if and only if is an n-fold Boolean and (prime)maximal ideal. Also, we prove that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal \(\{0\}\) is an n-fold integral ideal. Moreover, we study relation between n-fold integral ideals and n-fold obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between n-fold Boolean ideals and n-fold positive implicative filters in BL-algebras. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0497-5 Issue No:Vol. 28, No. 5-6 (2017)

Authors:Taja Yaying; Bipan Hazarika Pages: 985 - 989 Abstract: Abstract The main purpose of this article is to introduce the concept of arithmetic continuity and arithmetic compactness in metric spaces and prove some interesting results related to these notions. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0498-4 Issue No:Vol. 28, No. 5-6 (2017)

Authors:K. El Fahri; A. El Kaddouri; M. Moussa Pages: 991 - 997 Abstract: Abstract We investigate Banach lattices on which each positive weak Dunford–Pettis operator is semi-compact and conversely. PubDate: 2017-09-01 DOI: 10.1007/s13370-017-0499-3 Issue No:Vol. 28, No. 5-6 (2017)

Authors:Mahmood Bakhshi; Mahdi Izanlou Abstract: Abstract Based on Pawlak’s rough set theory, we study and investigate the roughness in non-commutative residuated lattices, which are generalizations of non-commutative fuzzy structures such as MV-algebras and BL-algebras. We give many theorems and examples to describe the rough approximations. Also, to investigate the properties of roughness of subsets (and of course filters) more closely, we consider some different kinds of filters such as Boolean filters and prime filters. Especially, we prove that with respect to some certain filters, the obtained approximations form a Boolean algebra or a pseudo MTL-algebra. PubDate: 2017-09-16 DOI: 10.1007/s13370-017-0529-1

Abstract: Abstract As extensions of Vandermonde determinant, we establish a general determinant evaluation formula by means of the Laplace expansion formula. Several interesting determinant identities are consequently derived by computing divided differences. PubDate: 2017-09-08 DOI: 10.1007/s13370-017-0527-3

Abstract: Abstract A dominating set D of a connected graph \(G = (V, E)\) is said to be bi-connected dominating set if the induced subgraphs of both \(\langle D \rangle \) and \(\langle V-D \rangle \) are connected. The bi-connected domination number \(\gamma _{bc}(G)\) is the minimum cardinality of a bi-connected dominating set. A \(\gamma _{bc}\) -set is a minimum bi-connected dominating set of G. In this paper, we obtain the Partially Balanced Incomplete Block (PBIB)-designs with m = 1, 2, 3, 4 and \(\lfloor \frac{p}{2}\rfloor \) association schemes arising from \(\gamma _{bc}\) -sets of some special classes of graphs. PubDate: 2017-09-08 DOI: 10.1007/s13370-017-0525-5

Authors:Niovi Kehayopulu Abstract: Abstract The concept of a \(\Gamma \) -semigroup has been introduced by Mridul Kanti Sen in the Int. Symp., New Delhi, 1981. It is well known that the Green’s relations play an essential role in studying the structure of semigroups. In the present paper we deal with an application of \(\Gamma \) -semigroups techniques to the Green’s Theorem in an attempt to show the way we pass from semigroups to \(\Gamma \) -semigroups. PubDate: 2017-09-06 DOI: 10.1007/s13370-017-0526-4