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: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: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: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: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:Nanjundan Magesh; Serap Bulut Abstract: Abstract In this paper, we obtain initial coefficient bounds for functions belong to a subclass of analytic bi-univalent functions related to pseudo-starlike functions by using the Chebyshev polynomials and also we find Fekete-Szegö inequalities for this class. PubDate: 2017-10-14 DOI: 10.1007/s13370-017-0535-3

Authors:Mohammad M. Al-Gharabli Abstract: Abstract In this paper, we consider a porous thermoelastic system with a micro-heat dissipation and a nonlinear frictional damping. We establish an explicit and general decay rate result, using some properties of the convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term. PubDate: 2017-10-14 DOI: 10.1007/s13370-017-0536-2

Authors:Paltu Sarkar; Sukhendu Kar Abstract: Abstract In this paper, our main objective is to introduce and investigate the interval-valued (in short, (i-v)) prime fuzzy hyperideal in semihypergroups in detail. We notice that every (i-v) semiprime fuzzy hyperideal may not be an (i-v) prime fuzzy hyperideal and we produce a counter example to illustrate this result. Moreover, we define (i-v) fuzzy hyper radical of an (i-v) fuzzy hyperideal of a semihypergroup. Finally, we study some interesting properties regarding this radical. PubDate: 2017-10-07 DOI: 10.1007/s13370-017-0528-2

Authors:Nacira Agram; Elin Engen Røse Abstract: Abstract We study methods for solving stochastic control problems of systems offorward–backward mean-field equations with delay, in finite and infinite time horizon.Necessary and sufficient maximum principles under partial information are given. The results are applied to solve a mean-field recursive utility optimal problem. PubDate: 2017-09-30 DOI: 10.1007/s13370-017-0532-6

Authors:Bashir Ali; G. C. Ugwunnadi Abstract: Abstract A new strong convergence theorem for approximation of common fixed points of family of uniformly asymptotically regular asymptotically nonexpansive mappings, which is also a unique solution of some variational inequality problem is proved in the framework of a real Banach space. The Theorem presented here extend, generalize and unify many recently announced results. PubDate: 2017-09-25 DOI: 10.1007/s13370-017-0530-8

Authors:Artem Ostapenko; Galina Bulanchuk Abstract: Abstract In this work, we studied the calculation of the drag coefficient using the lattice Boltzmann method with variable lattice speed of sound. The modified method of calculation the drag coefficient that includes the kinematic viscosity dependence was proposed. Calculations were based on the variable lattice speed of sound values that depend on the kinematic viscosity and the computational grid resolution. Shown the influence of the Reynolds number on the flow pattern and on the drag coefficient. The relation between the lattice Mach number and the computational grid resolution have been shown. The influence of the lattice Mach number on the accuracy of the numerical results was studied in detail. Shown that proposed method is more efficient because the researcher can set the kinematic viscosity of the fluid and the computational grid resolution at the same time. Therefore there is an opportunity to control the accuracy of the numerical results and the modeling time. PubDate: 2017-09-21 DOI: 10.1007/s13370-017-0531-7

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