The purpose of this paper is to prove Boyd-Wong and Matkowski type fixed point theorems in orthogonal metric space which was defined by M.E. Gordji 2017 an extension the space. Some examples are established support our main results. Finally, we apply results establish existence a unique solution periodic boundary value problem.

[1] Nemirovski and Yudin. Problems Complexity and Method Efficiency in Optimization. Wiley-Interscience series in discrete mathematics. Wiley, 1983. [2] W. Krichene, A. Bayen and P. Bartlett. Accelerated Mirror Descent in Continuous and Discrete Time. NIPS 2015. [3] W. Su, S. Boyd and E. Candes. A differential equation for modeling Nesterov's accelerated gradient method: theory and insights. NI...

In this note we prove the two formulae conjectured by D. W. Boyd [Experiment. Math. 7 (1998), 37-82], m(y(x + 1) + y(x + 6x + 1) + (x + 1)) = 8 3 L ′ (χ−4,−1), m(y(x + 1) + y(x − 10x + 1) + (x + 1)) = 20 3 L ′ (χ−3,−1), where m denotes the logarithmic Mahler measure for two-variable polynomials.

In this paper, we study the minimum size 2-edge connected spanning subgraph problem (henceforth 2EC) and show that every 3-edge connected cubic graphG = (V,E), with n = |V | allows a 2EC solution for G of size at most 7n 6 , which improves upon Boyd, Iwata and Takazawa’s guarantee of 6n 5 .

We proved that a finite commuting Boyd-Wong type contractive family with equicontinuous words have the approximate common fixed point property. We also proved that given X Ă R, compact and convex subset, F : X Ñ X a compact-and-convex valued Lipschitz correspondence and g an isometry on X, then gF “ F g implies F admits a Lipschitz selection commuting with g.

This article presents results from a multiple-year project concerned with the involvement of foreign (non-U.S.) entities in U.S. patent litigation. A comparison of data from 2004 and 2009 that cover 5,407 patent cases filed in U.S. federal district courts in those two years evidences an increase in the number of cases involving foreign defendants, and thus an increasing potential for cross-bord...

An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.

Radiographic demonstration of the internal structures of the knee is not new, having been first described by Werndroff and Robinson (1905). it was not, however, until much later that more detailed papers on arthrography were published (Boyd 1934: Bircher and Oberholzer 1934: Simon, Hamilton and Farrington 1936: Quaintance 1938). Most papers describe its use in the diagnosis of ligamentous injur...

Several reports have demonstrated biotransformation of tetrachloroethylene at low concentrations under strict anaerobic conditions by sequential reductive dechlorination (Fathepure and Boyd, 1988a; Freedman and Gosset, 1989). During this biodegradation, trichloroethylene (TCE), 1,1dichloroethylene, vinylidene chloride (DCE), and vinyl chloride (VC) are the intermediate products ; ethene or etha...

The purpose of this paper is to describe experience with four children who presented with bowing or pseudarthrosis of the fibula. These children demonstrate a gradation in the severity and significance of this condition. There may be : 1) fibular bowing without fibular pseudarthrosis (Case 1); 2) fibular pseudarthrosis without ankle deformity (Case 2); 3) fibular pseudarthrosis with ankle defor...