{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T04:53:26Z","timestamp":1767588806706,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T00:00:00Z","timestamp":1565654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, a new class of     ( C ,  G f  )    -invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as,     ( F ,  G f  )    -invexity, C-convex etc.). We consider Mond\u2013Weir type fractional symmetric dual programs and derive duality results under     ( C ,  G f  )    -invexity assumptions. Our results generalize several known results in the literature.<\/jats:p>","DOI":"10.3390\/axioms8030097","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T04:31:21Z","timestamp":1565670681000},"page":"97","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions"],"prefix":"10.3390","volume":"8","author":[{"given":"Ramu","family":"Dubey","sequence":"first","affiliation":[{"name":"Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7774-7290","authenticated-orcid":false,"given":"Lakshmi Narayan","family":"Mishra","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University UNINETTUNO, C.so Vittorio Emanuele II, 3900186 Roma, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/0022-247X(81)90123-2","article-title":"On sufficiency on the Kuhn-Tucker conditions","volume":"80","author":"Hanson","year":"1981","journal-title":"J. Math. Anal. 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