Journal of Nonlinear Analysis and Optimization: Theory & Applications
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao
<p><strong>Journal of Nonlinear Analysis and Optimization: Theory & Applications</strong> is a peer-reviewed, open access international journal, that devotes to the publication of original articles of current interest in every theoretical, computational and applicational aspect of nonlinear analysis, convex analysis, fixed point theory and optimization techniques and their applications to science and engineering. All manuscripts are refereed under the same standards as those used by the finest-quality printed mathematical journals. Accepted papers will be published in two issues annually in March and September, free of charge.</p><p><span style="font-family: Arial; font-size: x-small;"><span style="font-family: Arial,sans-serif; color: #000000; font-size: x-small;"><span style="font-size: 10pt;"><strong>Reviewing/Indexing:</strong></span></span><span style="font-family: Arial,sans-serif; color: #000000; font-size: x-small;"><span style="font-size: 10pt;"> Papers appearing in JNAO will be reviewed/indexed in <strong>Zentralblatt MATH; <strong>MathSciNet; <strong>Mathematical Reviews; <strong>Google Scholar; <strong>CrossRef.; Directory of Open Access Journals (DOAJ).</strong></strong></strong></strong></strong></span></span></span><span style="font-family: Arial; font-size: x-small;"><span style="font-family: Arial,sans-serif; color: #000000; font-size: x-small;"><span style="font-size: 10pt;"> </span></span></span></p>en-USAuthors who publish with this journal agree to the following terms:<br /><ol type="a"><br /><li>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" target="_new"><span style="color: #337755;">Creative Commons Attribution License</span></a> that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li><br /><li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li><br /><li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See <a href="http://opcit.eprints.org/oacitation-biblio.html" target="_new"><span style="color: #337755;">The Effect of Open Access</span></a>).</li><br /></ol><br /><br />narinp@nu.ac.th (Narin Petrot)wuttipongr@nu.ac.th (Wuttipong Ruanthong)Wed, 20 Nov 2013 14:26:40 SE Asia Standard TimeOJS 2.3.6.0http://blogs.law.harvard.edu/tech/rss60Expanding the Applicability of a Two Step Newton Lavrentiev Method for Ill-Posed Problems
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/242
In [3] we presented a cubically convergent Two Step Directional NewtonMethod (TSDNM) for approximating a solution of an operator equationin a Hilbert space setting. George and Pareth in [13] use the analogousTwo Step Newton Lavrentiev Method (TSNLM) to approximate asolution of an ill-posed equation. In the present paper we show how toexpand the applicability of (TSNLM). In particular, we present a semilocalconvergence analysis of (TSNLM) under: weaker hypotheses, weakerconvergence criteria, tighter error estimates on the distances involved andan at least as precise information on the location of the solution.Ioannis Konstantinos Argyros, Santhosh Georgehttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/242Sun, 07 Jul 2013 10:56:05 SE Asia Daylight TimeSuzuki-type fixed point theorems for two maps in metric-type spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/272
In this paper, we generalize the Suzuki-type fixed point theorems in [N.~Hussain, D.~Dori\'c, Z.~Kadelburg, and S.~Radenovi\'c, \emph{Suzuki-type fixed point results in metric type spaces}, Fixed Point Theory Appl \textbf{2012:126} (2012), 1 - 10] for two maps on metric-type spaces. Examples are given to validate the results.Dung Van Nguyen, Thanh Ly Thi Nguyen, Hieu Trung Nguyen, Thinh Duc Vohttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/272Mon, 12 Aug 2013 17:04:28 SE Asia Daylight TimeExistence of positive periodic solutions for a nonlinear neutral difference equation with variable delay
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/280
In this paper, we study the existence of positive periodic solutions of the nonlinear neutral difference equation with variable delay<br /><br /> x(n+1)=a(n)x(n)+???g(n,x(n-??(n)))+f(n,x(n-??(n))).<br /><br />The main tool employed here is the Krasnoselskii's hybrid fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Raffoul and Yankson <cite>r1</cite>.Abdelouaheb Ardjouni, Ahcene Djoudihttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/280Mon, 12 Aug 2013 16:49:43 SE Asia Daylight TimeGeneralizations of the KKMF principle having coercing families
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/279
In 2005 [1], Ben-El-Mechaiekh, Chebbi, and Florenzanoobtained a generalization of the Ky Fan's 1984 KKM theorem on theintersection of a family of closed sets on non-compact convex setsin a topological vector space. They also obtained a Fan-Browder typefixed point theorem to a set-valued maps on non-compact convex sets.In 2011 [3], Chebbi, Gourdel, and Hammami introduced a generalizedcoercivity type condition for set-valued maps defined on topologicalspaces endowed with a generalized convex structure and extendedFan's KKM theorem. In this paper, we show that better forms oftheorems in [1] and [3] can be deduced from a KKM theorem onabstract convex spaces in Park's sense [11-15].Sehie Parkhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/279Tue, 18 Jun 2013 11:40:21 SE Asia Daylight TimeOn the means of projections on CAT(0) spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/293
We improve a result on approximation a common elementof two closed convex subsets of a complete CAT(0) space appeared asTheorem 4.1 in [2]. New practical iterative scheme is presented andconditions on two given sets are relaxed.Watcharapong Anakkamatee, Sompong Dhompongsahttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/293Thu, 11 Jul 2013 15:02:01 SE Asia Daylight TimeRefinements of $\varepsilon$-Duality theorems for a Nonconvex Problem with an Infinite Number of Constraints
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/252
Some remarks on approximate optimality conditions of a nonconvex optimization problem which has an?? infinite number of constraints are given. Results?? on $\epsilon$-duality theorems of the problem are refined by using?? a mixed type dual problem of Wolfe?? and Mond-Weir type. <br />Ta Quang Sonhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/252Sun, 07 Jul 2013 11:04:53 SE Asia Daylight TimeStrong convergence theorems for a common fixed point of nonexpansive mappings in Banach spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/245
In this paper, we introduce some strong convergence theorems for the problem of finding a common fixed point of a finite family of nonexpansive mappings in Banach spaces by the combination the regularization method and the viscosity approximation method.Truong Minh Tuyenhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/245Sat, 27 Apr 2013 22:46:48 SE Asia Daylight TimeA unifying semi-local analysis for iterative algorithms of high convergence order
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/264
We present a unifying semi-local convergence analysis of two-step Newton-type methods for solving nonlinear equations in a Banach space setting. Convergence order of these methods is higher than two. Our analysis expands the applicability of these methods by providing weaker convergence criteria and a convergence analysis-which is tighter than earlier studies [see 1???4,24???34] ??? is also presented. Numerical examples illustrating the developed theoretical results are also given.Ioannis Konstantinos Argyros, Sanjay Kumar Khattrihttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/264Sun, 07 Jul 2013 10:53:19 SE Asia Daylight TimeOn the computation of fixed points for random operator equations
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/253
We approximate fixed points of random operator equation on a completeprobability space using Newton???s method. Error bounds on the distancesinvolved and some applications are also provided in this study.Ioannis Konstantinos Argyros, Said Hilouthttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/253Fri, 12 Jul 2013 12:28:04 SE Asia Daylight TimeExistence theorems for generalized Nash equilibrium problems
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/241
The generalized Nash equilibrium, where the feasible sets of the players depend on other players' action, becomes increasingly popular among academics and practitionners. In this paper, we provide a thorough study of theorems guaranteeing existence of generalized Nash equilibria and analyze the assumptions on practical parametric feasible sets.Christophe Dutanghttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/241Fri, 12 Jul 2013 12:24:58 SE Asia Daylight TimeAn Embedding Theorem for a Class of Convex Sets in Nonarchimedean Normed Spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/233
In this article we show that the class of all compact convex sets of a real nonarchimedean normed space can be embedded in a real nonarchimedean normed space.<br />Masoumeh Aghajani, Kourosh Nourouzihttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/233Mon, 12 Aug 2013 16:52:56 SE Asia Daylight TimeMinimum-norm fixed point of a finite family of $\lambda-$strictly pseudocontractive mappings
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/301
Let?? $K$ be a nonempty closed and?? convex<br /> subset?? of a real Hilbert space $H$?? and?? for each $1\leq i\leq N$, let $T_i: K\rightarrow K$ be $\lambda_i$-strictly?? pseudocontractive mapping.<br />Then???? for $\beta \in (0,2\lambda]$, where $\lambda:=\min\{ \lambda_i:i=1,2,...,N\}$,?? and?? each?? $t \in (0,1)$,<br /> it is proved that,?? there?? exists a net?? $ \{y_t\} \subset?? K$?? satisfying<br />$ y_t=?? P_K\big[(1-t)(\beta Ty_t+(1-\beta) y_t)\big],$<br />where $T:=\theta_1T_1+\theta_2T_2+...+\theta_NT_N$, for $\theta_1+\theta_2+...+\theta_N=1$,<br /> which converges strongly, as $t\to 0^+$, to the common minimum-norm fixed point?? of $\{T_i: i=1,2,...,N\}$.<br />Moreover, we provide an?? explicit iteration process which?? converges strongly to?? a common<br /> minimum-norm fixed point?? of $\{T_i:i=1,2,...,N\}$. Corresponding results,?? for a common?? minimum-norm solution?? of<br /> a finite family of?? $\alpha-$inverse?? strongly?? monotone mappings?? are also discussed.<br /> Our theorems?? improve?? several results in this direction.Habtu Zegeye, M. V. Thutohttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/301Wed, 20 Nov 2013 15:21:57 SE Asia Standard TimeSome Fixed Point Results for Uniformly Quasi-Lipschitzian Mappings in Convex Metric Spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/109
<span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;"><p>In this paper, an iteration process for approximating common fi<span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;">xed points of two uniformly quasi Lipschitzian mappings in convex metric </span></span><span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;">spaces is defined. Without using "the rate of convergence </span></span><span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;">condition" $\sum_{n=1}^\infty(k_n-1)<\infty$ associated with asymptotically (quasi-)nonexpansive mapings. </span></span><span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;">some convergence theorems are also proved. The results presented gen</span></span><span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;">eralize, improve and unify some recent results.</span></span></p><p><span style="font-family: Dcr10; font-size: xx-small;"><span style="font-family: Dcr10; font-size: xx-small;">??</span></span></p><p><span style="font-family: Dcr10; font-size: xx-small;">??</span></p></span></span>Isa Yildirim, Safeer Hussain Khan, Murat Ozdemirhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/109Sat, 08 Sep 2012 21:26:07 SE Asia Daylight TimeBanach fixed point theorem in application to nonlinear elliptic Systems
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/172
This paper is concerned with some nonlinear elliptic systems.<br />Under suitable conditions on the nonlinearities $f$ and $g$, we obtain weak solution in Sobolev space $H=H_0^1(\Omega)\times H_0^1(\Omega)$ by applying the Banach fixed point theorem.Ghasem Alizadeh Afrouzi, Qihu Zhang, Z. Naghizadehhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/172Thu, 13 Jun 2013 13:09:46 SE Asia Daylight TimePPF Dependent Fixed Point Theorems for Rational Type Contraction Mappings in Banach spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/257
<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In this paper, we prove the existence of the PPF dependent fixed point theorems in the Razumikhin class for rational type contraction mappings in Banach spaces where the domain and range of the mappings are not the same. We also use this result to prove the PPF dependent coincidence point theorems. Our results extend and generalize some results of Bernfeld </span><span>et al. </span><span>in [S. R. Bernfeld, V. Lakshmikatham and Y. M. Reddy, Fixed point theorems of operators with PPF dependence in Banach spaces, Applicable Anal. 6 (1977), 271???280.]. </span></p></div></div></div>Wuriphol Sintunavarat, Poom Kumamhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/257Mon, 13 May 2013 12:53:13 SE Asia Daylight TimeGeneralized mixed general vector variational-like inequalities in topological vector spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/249
<p>In this work, we consider and study new kinds of generalized mixed general vector variational-like inequalities in real topological vector spaces. We use the Ferro minimax theorem to discuss the existence of weak and strong solutions for the generalized mixed general vector variational-like inequality problems.</p>Xie Ping Ding, Salahuddin .http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/249Thu, 05 Sep 2013 15:37:22 SE Asia Daylight TimeMinimax programming with (G, ??)-invexty
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/224
In this paper, we deal withthe minimax programming (P) under the differentiable ??(G, ????)-invexitywhich was proposed in [J. Nonlinear Anal. Optim. 2(2): 305-315]. ??With the help ofauxiliary ??programming problem (G-P), some new Kuhn-Tucker necessary conditions,namely for G-Kuhn-Tucker necessary conditions, is presented for the minimax programming (P). Also ??G-Karush-Kuhn-Tucker sufficient conditions under (G, ??)-invexity assumptionare obtained for the minimax programming (P). Making use of these optimality conditions,we construct a dual problem (DI) for (P) and establish weak, strong and strictconverse duality theorems between problems (P)and (DI).Yuan Dehui, Xiaoling Liuhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/224Sat, 10 Aug 2013 11:50:47 SE Asia Daylight TimeUlam-Hyers stability of a fixed point equation via generalized Picard operators
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/267
<pre>In this paper we introduce new classes of generalized Picard operator??</pre><pre>and obtain some Ulam-Hyers stability results for the operators??</pre><pre>which extend results in [5]. As application, an existence??</pre><pre>and uniqueness result for an integral equation is given.</pre>Narawadee Na nanhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/267Sun, 28 Jul 2013 17:49:04 SE Asia Daylight TimeWeak convergence of fixed point iterations in metric spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/239
<span style="font-family: CMR10; font-size: x-small;"><span style="font-family: CMR10; font-size: x-small;"><p>The concept of convergence in normed spaces is extended to</p><p>metric spaces; and weak convergence of fixed point iterations of</p><p>contractions on metric spaces is obtained in this article.</p></span></span>Ganesa Moorthy, Iruthaya Rajhttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/239Sat, 10 Aug 2013 11:56:19 SE Asia Daylight TimeLavrentiev Regularization of Nonlinear Ill-Posed Equations Under General Source Condition
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/186
Analogues to the procedure adopted by Scherzer et.al (1993) for choosing the regularization parameter in Tikhonov regularization of nonlinear ill-posed equations of the form F(x) = y, Tautenhahn (2002) considered an a posteriori parameter choice strategy for Lavrentiev regularization, and derived order optimal error estimates under Holder type source conditions. In this paper, we derive order optimalerror estimates under a general source condition so that the results are applicable for both mildly and exponentially ill-posed problems. Results in this paper generalize results of Tautenhahn (2002) and also extend results of Nair and Tautenhahn (2004) to the nonlinear case.M. Thamban Nair, Pallavi Mahalehttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/186Sun, 27 Oct 2013 08:50:04 SE Asia Standard TimeExistence of Nonlinear Neutral Impulsive Integrodifferential Evolution Equations of Sobolev type with Time Varying Delays
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/265
In this paper, we prove the existence of solutions for nonlinear neutral impulsiveevolution integrodifferential equations of Sobolov type with time varying delays. Theresults are obtained by using semigroup theory and the Monch???s fixed point theorem.An application of the same problem is discussed. An example is provided to illustratethe theory.Radhakrishnan Bheeman, Mohanraj Aruchamy, Velu Vinobahttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/265Thu, 17 Oct 2013 15:48:25 SE Asia Daylight TimeRecent Fixed Point Theorems for T-contractive Mappings and T-weak (almost) Contractions in Metric and Cone Metric Spaces are not Real Generalizations
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/246
The purpose of this research article is to show that recent fixed point theoremsobtained in metric and cone metric spaces for T-contractive mappings and TW-contractions areequivalent to previously existing theorems in the literature; hence are redundant. We also showthat Proposition 2.5 of [4] is invalid.Tadesse Bekeshie Gerbaba, Naidu G. Appalahttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/246Wed, 06 Nov 2013 14:50:12 SE Asia Standard TimeGeneralized minimax fractional programming problems with generalized nonsmooth $(F, alpha, rho, d, theta)$-univex functions
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/256
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-fareast-font-family: PMingLiU; mso-ansi-language: EN-US; mso-font-kerning: 1.0pt; mso-fareast-language: ZH-TW; mso-bidi-language: AR-SA;">The aim of this paper is to establish the sufficient optimality conditions for a class of nondifferentiable multiobjective generalized minimax fractional programming problems involving <span style="top: 5pt; position: relative; mso-text-raise: -5.0pt;"> </span>univex functions. Subsequently, we apply the optimality condition to formulate a dual model and prove weak, strong and strict converse duality theorems.</span>Anurag Jayswal, Ioan Stancu Minasian, Izhar Ahmad, Krishna Kummarihttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/256Fri, 09 Aug 2013 16:44:01 SE Asia Daylight TimeFixed point theorems for some generalized nonexpansive mappings in CAT(0) spaces
http://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/243
In this paper, at rst we introduce C condition, which is weaker than -nonexpansivityand present some xed point theorems for mappings satisfying this condition, in CAT(0) spaces.Our results extend and improve some results in [6]. In the sequal, we introduce fundamentalynonexpansive mapping which generalizes the Suzuki's generalized nonexpansive mapping and con-sequently we give some xed point results for this kind of mappings.Hero Salahifard, Seiyed Mansour Vaezpour, Sompong Dhompongsahttp://www.math.sci.nu.ac.th/ojs234/index.php/jnao/article/view/243Fri, 11 Jan 2013 16:08:08 SE Asia Standard Time