Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
In this paper, a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow&g...
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| Format: | Article |
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MDPI AG
2019-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/8/3/97 |
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| author | Ramu Dubey Lakshmi Narayan Mishra Clemente Cesarano |
| author_facet | Ramu Dubey Lakshmi Narayan Mishra Clemente Cesarano |
| author_sort | Ramu Dubey |
| collection | DOAJ |
| description | In this paper, a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>F</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity, <i>C</i>-convex etc.). We consider Mond−Weir type fractional symmetric dual programs and derive duality results under <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity assumptions. Our results generalize several known results in the literature. |
| first_indexed | 2024-12-21T16:36:42Z |
| format | Article |
| id | doaj.art-4fbbc8487fe2456593e00daa180f3be1 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-21T16:36:42Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4fbbc8487fe2456593e00daa180f3be12022-12-21T18:57:12ZengMDPI AGAxioms2075-16802019-08-01839710.3390/axioms8030097axioms8030097Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity AssumptionsRamu Dubey0Lakshmi Narayan Mishra1Clemente Cesarano2Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, IndiaSection of Mathematics, International Telematic University UNINETTUNO, C.so Vittorio Emanuele II, 3900186 Roma, ItalyIn this paper, a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>F</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity, <i>C</i>-convex etc.). We consider Mond−Weir type fractional symmetric dual programs and derive duality results under <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity assumptions. Our results generalize several known results in the literature.https://www.mdpi.com/2075-1680/8/3/97symmetric dualitymultiobjectivefractional programming(<i>C</i>,<i>G<sub>f</sub></i>)-invexity |
| spellingShingle | Ramu Dubey Lakshmi Narayan Mishra Clemente Cesarano Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions Axioms symmetric duality multiobjective fractional programming (<i>C</i>,<i>G<sub>f</sub></i>)-invexity |
| title | Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions |
| title_full | Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions |
| title_fullStr | Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions |
| title_full_unstemmed | Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions |
| title_short | Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions |
| title_sort | multiobjective fractional symmetric duality in mathematical programming with i c i i g sub f sub i invexity assumptions |
| topic | symmetric duality multiobjective fractional programming (<i>C</i>,<i>G<sub>f</sub></i>)-invexity |
| url | https://www.mdpi.com/2075-1680/8/3/97 |
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