GENERALIZED NONLINEAR VARIATIONAL INEQUALITIES

Abstract. In this paper, we consider a generalized nonlinear variational inequality problem involving single valued and multivalued nonlinear operators. We also study criteria of its solvability. Iterative methods for approximate solution are also proposed and a convergence result is established. Further, we study iterative methods for finding common element of fixed point set of nonexpansive mapping and solution set of the proposed variational inequality problem. AMS Mathematics Subject Classification (2010): 47J20, 65K10, 65K15, 90C33 Key words and phrases: Generalized nonlinear variational inequality, fixed point problem, relaxed monotone operator, relaxed cocoercive mapping, nonexpansive mapping

IN VITRO ANTIOXIDANT CAPACITY OF THE FERN, DRYNARIA QUERCIFOLIA (L) SM., RHIZOME EXTRACT

Objective: The study was aimed to evaluate polyphenolic composition and antioxidant properties of methanol extract of rhizome of Drynaria quercifolia (L.) Sm. Methods: In this study, assessment of total phenolic and flavonoid contents were performed using Foiln-Ciocalteu and Aluminium chloride methods respectively. Antioxidant capacity of crude methanolic extract of rhizome of D. quercifolia were examined using established 1,1 – diphenyl – 2-picrylhydrazyl stable free radical (DPPH∙) assay, hydroxyl ion radicals (˙OH), nitric oxide (NO), hydrogen peroxide (H2O2)and 2, 2'-Azinobis (3-ethylbenzothiazoline sulphonic acid) ABTS•+ scavenging assays.  Results: The extract yielded total phenolic content (TP) of 240 ± 0.01 mg gallic acid equivalents (GAE)/100g of fresh mass (FM) and total flavonoid content (TF) of 150 ± 0.02 mg quercetin equivalents (QE)/100g of fresh mass (FM). The extract of D. quercifolia rhizome exhibited remarkable scavenging capacity towards DPPH∙ (EC50 18.54 ±0.70 µg mL-1), ˙OH (EC50 37.60±0.41 µg mL-1) NO (EC50 42.40 µg mL-1), H2O2 (EC50 32.80±1.89 µg mL-1) and ABTS•+ (EC50 29.80 ±0.70 µg mL-1). The antioxidant capacities of the extract were comparable and stronger than that of the antioxidant standard, butyl hydroxy toluene (BHT). The findings were also comparable with antioxidant properties of other medicinal ferns which are discussed in the study. Conclusion: Significant and positive correlations (R2 0.999-0.862) were observed between polyphenolic contents and the antioxidant capacities, indicating that the phenolics were major contributors of the antioxidant property. Thus, the methanol extract from the rhizome of D. quercifolia indicated the existence of strong antioxidants and it can be used as tonic

An Improved Proxy Blind Signature Scheme With Forward Security

This paper presents a proxy blind signature scheme with forward security mechanism. The proposed digital signature scheme combines the two special-purpose signature schemes, blind signature and proxy signature. In this signature scheme, the original signer gives authority to another entity which is known as a proxy signer, but without having any idea about the content of the document. This paper, proposes an enhanced proxy blind signature, in which the forward security is incorporated and the security of the signature scheme relies on the discrete logarithm problem (DLP). Forward security mechanism will provide protection to the system from the key leakage or key exposure, because in this mechanism, the private key of proxy signer is updated periodically. In case if the signature key at some stage is compromised, the adversary cannot be able to forge signatures as if they had been generated before the exposure or leakage of key. General Terms: Public key cryptography, Digital signatur

Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces

Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1<p<∞ and k≥0

Weak and Strong Convergence of Multistep Iteration for Finite Family of Asymptotically Nonexpansive Mappings

<p/> <p>Strong and weak convergence theorems for multistep iterative scheme with errors for finite family of asymptotically nonexpansive mappings are established in Banach spaces. Our results extend and improve the corresponding results of Chidume and Ali (2007), Cho et al. (2004), Khan and Fukhar-ud-din (2005), Plubtieng et al.(2006), Xu and Noor (2002), and many others.</p