Applied General Topology
https://polipapers.upv.es/index.php/AGT
<p style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 6.0pt; margin-left: 0cm; text-align: justify; text-justify: inter-ideograph;"><span>The international journal <strong>Applied General Topology</strong> publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications.</span></p>Universitat Politècnica de Valènciaen-USApplied General Topology1576-9402The works published in this journal are subject to the following terms:<br /><ol><li>The journal conserves the patrimonial rights (copyright) of the works published, and encourages and allows the reuse of the same under the license specified in point 2.</li><li>The works are published in the online edition of the journal under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0. You can copy, use, distribute, transmit and publicly display, provided acknowledgment of the authorship, the url, and the journal, and not used for commercial purposes.</li><li>The authors agree with the license used by the journal, with the conditions of self-archiving and the open access policy.</li><li>It allows authors to spread electronically (e.g., in institutional repositories or on their own website) the published version of his works, as it encourages its circulation and diffusion earliest and thus a possible increase in its citation and scope between the academic community.</li></ol>Sheaf cohomology on network codings: maxflow-mincut theorem
https://polipapers.upv.es/index.php/AGT/article/view/3371
<p>Surveying briefly a novel algebraic topological application sheaf theory into directed network coding<br />problems, we obtain the weak duality in multiple source scenario by<br />using the idea of modified graph. Furthermore,we establish the<br />maxflow-mincut theorem with network coding sheaves in the case of multiple source.</p>Miradain Atontsa NguemoCalvin Tcheka
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218221923010.4995/agt.2017.3371A decomposition of normality via a generalization of $\kappa$-normality
https://polipapers.upv.es/index.php/AGT/article/view/4220
A simultaneous generalization of $\kappa$-normality and weak $\theta$-normality is introduced. Interrelation of this generalization of normality with existing variants of normality is studied.In the process of investigation a new decomposition of normality is obtained.Ananga Kumar DasPratibha Bhat
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218223124010.4995/agt.2017.4220An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces
https://polipapers.upv.es/index.php/AGT/article/view/5185
We construct a $b$-metric from a given $C^*$-algebra-valued $b$-metric and prove some equivalences between them. Then we show that not only fixed point results but also topological properties on $C^*$-algebra-valued $b$-metric spaces may be deduced from certain results in $b$-metric spaces. In particular, every $C^*$-algebra-valued $b$-metric space is metrizable.Nguyen Van DungVo Thi Le HangDiana Dolicanin-Djekic
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218224125310.4995/agt.2017.5185Oriented components and their separations
https://polipapers.upv.es/index.php/AGT/article/view/5868
<p>There is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spaces and reaches and derive associated systems of oriented components that generalize connected components in a natural manner. The main result is a characterization of generalized reaches in terms of equivalent separation spaces.<br /><br /></p>Baerbel M R StadlerPeter F. Stadler
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218225527510.4995/agt.2017.5868Existence of common fixed points of improved F-contraction on partial metric spaces
https://polipapers.upv.es/index.php/AGT/article/view/6776
Following the approach of $F$- contraction introduced by Wardowski \cite{DW}, in this paper, we introduce improved $F$-contraction of rational type in the framework of partial metric spaces and used it to obtain a common fixed point theorem for a pair of self mappings. We show, through example, that improved $F$-contraction is more general than $F$- contraction and guarantees fixed points in those cases where $F$-contraction fails to provide. Moreover, we apply this fixed point result to show the existence of common solution of the system of integral equations.Muhammad NazamMuhammad ArshadMujahid Abbas
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218227728710.4995/agt.2017.6776Generalized open sets in grill N-topology
https://polipapers.upv.es/index.php/AGT/article/view/6797
The aim of this paper is to give a systematic development of grill N-topological spaces and discuss a few properties of local function. We build a topology for the corresponding grill by using the local function. Furthermore, we investigate the properties of weak forms of open sets in the grill N-topological spaces and discuss the relationships between them.M. Lellis ThivagarIvan L ReillyM. Arockia DasanV. Ramesh
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218228929910.4995/agt.2017.6797Quasi-uniform convergence topologies on function spaces- Revisited
https://polipapers.upv.es/index.php/AGT/article/view/7048
Let X and Y be topological space and F(X,Y) the set of all functions from X into Y. We study various quasi-uniform convergence topologies U_{A} (A⊆P(X)) on F(X,Y) and their comparison in the setting of Y a quasi-uniform space. Further, we study U_{A}-closedness and right K-completeness properties of certain subspaces of generalized continuous functions in F(X,Y) in the case of Y a locally symmetric quasi-uniform space or a locally uniform space.Wafa Khalaf AlqurashLiaqat Ali Khan
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2017-10-022017-10-0218230131610.4995/agt.2017.7048Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance
https://polipapers.upv.es/index.php/AGT/article/view/7067
<p>We introduce and study a general concept of multiple fixed point for mappings defined on partially ordered distance spaces in the presence of a contraction type condition and appropriate monotonicity properties. This notion and the obtained results complement the corresponding ones from [M. Choban, V. Berinde, A general concept of multiple fixed point for mappings defined on spaces with a distance, Carpathian J. Math. 33 (2017), no. 3, 275--286] and also simplifies some concepts of multiple fixed point considered by various authors in the last decade or so.</p>Mitrofan M ChobanVasile Berinde
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218231733010.4995/agt.2017.7067A study of function space topologies for multifunctions
https://polipapers.upv.es/index.php/AGT/article/view/7149
<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>Function space topologies are investigated for the class of continuous multifunctions. Using the notion of continuous convergence, splittingness and admissibility are discussed for the topologies on continuous multifunctions. The theory of net of sets is further developed for this purpose. The (</span><span>τ,μ</span><span>)-topology on the class of continuous multifunctions is found to be upper admissible, while the compact-open topology is upper splitting. The point-open topology is the coarsest topology which is coordinately admissible, it is also the finest topology which is coordinately splitting. </span></p></div></div></div>Ankit GuptaRatna Dev Sarma
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218233134410.4995/agt.2017.7149Convergence theorems for finding the split common null point in Banach spaces
https://polipapers.upv.es/index.php/AGT/article/view/7257
<p>In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.</p>Suthep SuantaiKittipong SrisapNatthapong NaprangManatsawin MamatVithoon YundonPrasit Cholamjiak
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2017-10-022017-10-0218234536010.4995/agt.2017.7257Uniform reconstruction of continuous functions with the RAFU method
https://polipapers.upv.es/index.php/AGT/article/view/7263
<pre><span>The</span> <span>RAFU</span> (radical <span>functions</span>) <span>method</span> can be <span>used</span> to <span>obtain</span> <span>the</span> uniform</pre><pre><span>reconstruction</span> <span>of</span> a <span>continuous</span> function from <span>its</span> <span>values</span> <span>at</span> <span>some</span> <span>of</span></pre><pre><span>the</span> <span>points</span> <span>of</span> <span>partitions</span> <span>of</span> a <span>closed</span> <span>interval</span>. In this <span>work</span> <span>we</span> <span>will</span></pre><pre><span>prove</span> <span>that</span> <span>we</span> can <span>reconstruct</span> a <span>continuous</span> function from <span>average</span> <span>samples</span></pre><pre><span>of</span> <span>these</span> <span>points</span>, from linear <span>combinations</span> <span>of</span> <span>them</span> and from local <span>average</span></pre><pre><span>samples</span> <span>given</span> <span>by</span> <span>convolution</span>. Uniform error <span>bounds will be </span><span>established</span>. <span>If</span> <span>these</span> data are unknown <span>but</span> <span>approximate</span> <span>values</span> <span>of</span> <span>them</span> are known, uniform <span>reconstruction</span> <span>will</span> be also <span>possible</span>. Error <span>estimates</span> in these cases will be given. <span>The</span> case <span>of</span> a non-uniform <span>net</span> <span>will</span> be <span>treated</span>. <span>Examples</span> and <span>algorithms</span> <span>will</span> be also <span>shown</span>.</pre>Eduardo Corbacho Cortés
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2017-10-022017-10-0218236137510.4995/agt.2017.7263Some fixed point theorems on non-convex sets
https://polipapers.upv.es/index.php/AGT/article/view/7452
<span style="color: #000000;">In this paper, we prove that if </span><span style="color: #008000;">$K$</span><span style="color: #000000;"> is a </span><span style="text-decoration: underline; color: #000000;">nonempty</span><span style="color: #000000;"> weakly compact set in a </span><span style="text-decoration: underline; color: #000000;">Banach</span><span style="color: #000000;"> space </span><span style="color: #008000;">$X$</span><span style="color: #000000;">, </span><span style="color: #008000;">$T:K\to K$</span><span style="color: #000000;"> is a </span><span style="text-decoration: underline; color: #000000;">nonexpansive</span><span style="color: #000000;"> map satisfying </span><span style="color: #008000;">$\frac{x+Tx}{2}\in K$</span><span style="color: #000000;"> for all </span><span style="color: #008000;">$x\in K$</span><span style="color: #000000;"> and if </span><span style="color: #008000;">$X$</span><span style="color: #000000;"> is </span><span style="color: #008000;">$3-$</span><span style="color: #000000;">uniformly convex or </span><span style="color: #008000;">$X$</span><span style="color: #000000;"> has the </span><span style="text-decoration: underline; color: #000000;">Opial</span><span style="color: #000000;"> property, then </span><span style="color: #008000;">$T$</span><span style="color: #000000;"> has a fixed point in </span><span style="color: #008000;">$K.$ <br /></span>Mohanasundaram RadhakrishnanS. RajeshSushama Agrawal
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218237739010.4995/agt.2017.7452Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results
https://polipapers.upv.es/index.php/AGT/article/view/7673
<p>The aim of this paper is to present fixed point results of contractive mappings in the framework of cone b-metric spaces endowed with a graph and associated with a generalized c-distance. Some corollaries and an example are presented to support the main result proved herein. Our results unify, extend and generalize various comparable results in the literature.</p>Kamal FallahiMujahid AbbasGhasem Soleimani Rad
Copyright (c) 2017 Applied General Topology
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2017-10-022017-10-0218239140010.4995/agt.2017.7673Generalized Normal Product Adjacency in Digital Topology
https://polipapers.upv.es/index.php/AGT/article/view/7798
We study properties of Cartesian products of digital images for which<br />adjacencies based on the normal product adjacency are used. We show<br />that the use of such adjacencies lets us obtain many "product properties"<br />for which the analogous statement is either unknown or invalid if, instead,<br />we were to use c_u-adjacencies.Laurence Boxer
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2017-10-022017-10-0218240142710.4995/agt.2017.7798