In this paper, we presented the results for extended nonlinear contraction defined on S-left complete topological spaces. Our results generalize earlier results in literature. Also, we obtain the fixed point theorem for extended nonlinear contraction defined on quasi b-metric spaces. This result extended recent results of Pasicki, obtained for dislocated metric spaces.

Abstract It is known that Fourier’s heat equation which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte was proved that such process can be describe by Heaviside’s telegraph equation. In this paper has been shown that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that equation of heat conduction with finite velocity propagation of the thermal disturbance, can be obtained as solution of one variational problem.

The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.

In this paper, we present fixed point theorem for mappings defined on b-metric spaces, which satisfies extended quasi-contractive inequality with nonlinear comparison function. Our result generalizes and improves several recent results from fixed point theory.

In this paper, we present some results on the existence and uniqueness of common fixed points on d*-complete topological spaces. Our results generalize and improve upon earlier results in the literature. Finally, we give some examples in lp spaces, (p∈(0,1)), where we use the obtained results.

In this study, we establish the convergence of Ishikawa iterates defined by nonlinear quasicontractive mappings on TVS-cone metric space. Further, our results generalize many existing results in the literature.

In this paper we shall introduced the class of $d-CS$ spaces and so we shall obtained topological approach to large Kasahara spaces. This class include complete symmetric spaces, complete quasi $b$-metric spaces and complete $b$-spaces, but not include $d^*$-complete topological spaces and $d$-complete topological spaces. Further will be presented fixed theorem for nonlinear extended-contraction defined on this spaces, which generalize earlier results obtaned by Browder, Matkowski, Jachymski, Matkowski and \'Swiatkowski, Aran{\dj}elovi\'{c} and Ke\v{c}ki\'{c} and Alshehri, Aran{\dj}elovi\'c and Shahzad. Also, we obtain the fixed point theorem for nonlinear extended-contraction defined on quasi-metric spaces which extended recent result's of Pasicki, obtained for pseudo-metric spaces.

In this paper influence of ventilation system availability and effectiveness is evaluated by applying standardized analytical methods for classification of areas of explosive atmospheres with the aim to obtain high dilution for non-hazardous zone or to reduce Zone 2 area within hydrogen storage room and transportation pipeline corridors in industrial applications. Several leakage cross section areas are taken into consideration from 0.025 mm2 at flanges with compressed fiber and spiral wound gasket, 0.25 mm2 at ring type joint connections up to 1 mm2 at small bore connections. Hydrogen storage pressures were varied from typical spherical tank at 50 bar to vertical tube storage at 100 bar. In this case the release rate of gas from a container or pipeline is with choked gas velocity - sonic releases case. Dimensionless discharge coefficient that accounts for the turbulence and viscosity is typically from 0.50 to 0.75. Safety factor was varied from 0.5 to 1, due to uncertainty related to lower flammability limit (LFL) because of possibility of existence of hydrogen background concentrations. Grade of release as estimated as secondary leakage due to a seal rupture. In the case of a pressure of 100 bar and an opening diameter of 0.25 mm2, the air velocity due to the operation of the ventilation system should be at least 6 m/s, which can be achieved by the proper selection of the ventilation system in a closed space. In all other cases considered in the paper, except for the leakage cross section of 1 mm2, calculated ventilation air speeds are lower, so conventional ventilation systems (such as mechanical supply and extraction ventilation or local extraction ventilation) can be applied in order to prevent hydrogen explosive atmospheres.

In this paper, we obtain the results of coincidence and common fixed points in b-metric spaces. We work with a new type of multivalued quasi-contractive mapping with nonlinear comparison functions. Our results generalize and improve several recent results. Additionally, we give an application of the obtained results to dynamical systems.

We present a fixed point result in quasi b -metric spaces. Our result generalizes recent fixed point results obtained by Aleksić et al., Dung and Hang, Jovanović et al., Sarwar, and Rahman and classical results obtained by Hardy, Rogers, and Ćirić. Also, we obtain a common fixed point result in b -metric spaces. As a special case, we get a result of Ćirić and Wong.

Significant limitation of the methodology for determining the class of fire resistance, defined by the group of standards DIN 18230, is its inapplicability to industrial facilities in which energy is produced or distributed. The aim of this paper is to define new methodology for determining the necessary fire resistance of the building structure of a boiler room where liquid or gaseous fuels are used.

In this paper, we introduce the concept of d*-complete topological spaces, which include earlier defined classes of complete metric spaces and quasi b-metric spaces. Further, we prove some fixed point results for mappings defined on d*-complete topological spaces, generalizing earlier results of Tasković, Ćirić and Prešić, Prešić, Bryant, Marjanović, Yen, Caccioppoli, Reich and Bianchini.

In this paper we obtain non compact versions of the best approximation theorem for set valued maps in hyperconvex spaces. Our results generalize the results obtained by Khamsi, Kirk, Park, Sims and Yuan. Acknowledgments. The second author was supported by the Ministry of Education, Science and Technological Development of Serbia, Grant no. 174002.

Statistical regularity of random mechanical failures of the bucket wheel excavator will be considered based on dispatcher’s reports about excavator-conveyors-spreader (ECS-III) on the Tamnava - West Field Open Cast Mine in Lazarevac (Serbia) system failures in the period from 2003 to 2011. This kind of failures happens suddenly due to undetectable defects, unexplainable causes, and unavoidable failures. Reliability functions R(t), failure rate λ(t) and failure density f(t) of the bucket wheel excavator will be empirically determined. It was concluded that the random failures could be well approximated by the Exponential distribution. Below, serial reliability configuration of the BWE subsystem was analysed and the failure frequency as well as the values of the failure rate by subsystems were determined. Finally, proactive maintenance approach, which represents the latest innovation in the field of maintenance, will be presented. This approach to maintenance utilizes various technologies in order to achieve extension of operational life and elimination of reactive maintenance.

In this paper, we present a new theorem on the existence of solutions for a three-function scalar equilibrium problem. Compactness is expressed in terms of the existence of feasibility sets of arbitrarily small measures of non-compactness, in addition to the completeness of the domain. Hereby we present some new results on the best approximations and coupled best approximations. We propose the generalized coupled coincidence problem and present a theorem on existence of its solution.

Biće prikazano nekoliko pristupa analizi požarnih rizika, i najvažnije metode će biti ukratko opisane. Te metode imaju slične osnovne komponente parametara, vrednosti i međusobnih odnosa. Biće razmatrana ograničenja zapažena u primeni tih komponenti. U okviru ovog rada opisaćemo, u kratkim crtama, neke od najčešće primenjivanih postupaka za procenu rizika od požara: Euroalarmov postupak, Gretenerov postupak, TRVB 100, FRAME, DIN18230, SRPS-EN1991-1-2:2012 i DOW index. Takođe biće data i uporedna analiza rezultata dobijenih navedenim postupcima.

Professor Ljubomir B. Ciric, one of the pioneers in the study of fixed point theory and nonlinear analysis in Serbia, died on Saturday, 23th July 2016. Here, we present his brief biography, some comments on main streams of his research work and complete bibliography.

A negative answer to an open problem is provided.Fixed point results for α-ϕ-contractive mappings in semi-metric spaces are proved.To show the generality of our results, examples are given.Finally, an application of our result to probabilistic spaces is derived.