In this framework, a pair of Mond–Weir type third order symmetric nonlinear programming problems are introduced. Appropriate duality theorems are established for the newly formulated third order ...symmetric dual problems under the assumptions of boncavity and bonvexity. Different counterexamples are also provided in order to justify the present findings. It is also verified that some of the previously published results in the literarue are particular cases of the findings of the paper.
Third order dual of a primal nonlinear programming problem is established which involves the third order derivatives of the functions constituting the primal problem. Desired duality theorems are ...provided for the pair of primal and the corresponding third order dual problem. Numerical examples are illustrated to justify the efficiency of the proposed method. It is also observed that some of the existing results are obtained as special cases.
The present investigation introduces the third order duality in variational problems, as because, in certain situations, first and second order duality do not yield solutions but it succeeds in ...finding the desired results. The duality results for the pair of variational primal problems and their corresponding third order dual problems are demonstrated. Counterexamples are provided to justify the importance of the current research work. It is found that many reported results of the literature are particular cases of this paper.
We have performed optimization of (5,0) zigzag and (5,5) armchair single-walled carbon nanotube and SiC nanotube using density functional theory at zero spin and high spin values. Further, Infrared ...and Raman spectra, highest occupied and lowest unoccupied molecular orbitals and their gap and natural bond orbital analysis were carried out at optimized structures of these materials. Three different exchange and correlation functionals PBE, LSDA and HCTH along with cc-pVDZ basis set were used. For conspicuous normal modes assignments of both the (5,0) zigzag and (5,5) armchair single-walled carbon nanotube and SiC nanotube, potential energy distributions of the normal modes were calculated using normal coordinate analysis. The diameter of carbon nanotube and SiC nanotube in (5,0) zigzag form were optimized at 4.0 Å and 5.0 Å respectively and in (5,5) armchair form were optimized at 7.0 Å and 8.0 Å respectively at all the three level of theories.
•(5,0) zigzag and (5,5) armchair single-walled carbon nanotube and SiC nanotube were optimized at density functional theory.•Three exchange functionals namely, generalized gradient approximation, local spin density approximation and extended generalized gradient approximation were used.•Minimal energy obtained at extended generalized gradient approximation.•Infrared and Raman spectra were computed and normal mode assignment was carried out.•Highest occupied and lowest unoccupied molecular orbitals and their gap, orbital occupancies and energies were computed.
The notion of rational F-contractions using α -admissibility of type-S in b-metric-like spaces is introduced and the new fixed and periodic point theorems are proved for such mappings. Numerical ...examples are illustrated to check the efficiency and applicability of our fresh findings. It is also observed that some of the works reported in the literature are the particular cases of the present study.
In this paper we present a pair of Wolfe and Mond–Weir type higher-order symmetric dual programs for multiobjective symmetric programming problems. Different types of higher-order duality results ...(weak, strong and converse duality) are established for the above higher-order symmetric dual programs under higher-order invexity and higher-order pseudo-invexity assumptions. Also we discuss many examples and counterexamples to justify our work.
We introduce a higher-order duality (Mangasarian type and Mond-Weir type) for the control problem. Under the higher-order generalized invexity assumptions on the functions that compose the primal ...problems, higher-order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems. Also, we establish few examples in support of our investigation.
In this paper, we introduce the concept of second order duality for the variational problems using
ρ
−
(
η
,
θ
)
-invexity type conditions. Weak, strong and converse duality results of Mangasarian ...and Mond–Weir type of variational problems are established under
ρ
−
(
η
,
θ
)
-invexity assumptions. Many examples and counterexamples are illustrated to justify our work.
In this paper, we introduce the concept of second order duality for the variational problems using Ie a degree ( I. , I ) -invexity type conditions. Weak, strong and converse duality results of ...Mangasarian and Mond-Weir type of variational problems are established under Ie a degree ( I. , I ) -invexity assumptions. Many examples and counterexamples are illustrated to justify our work.
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