{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,11]],"date-time":"2023-02-11T05:35:50Z","timestamp":1676093750357},"reference-count":0,"publisher":"Politechnika Wroclawska Oficyna Wydawnicza","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:p>As a generalization of convex functions and derivatives, in this paper, the authors study the concept of a symmetric derivative for preinvex functions. Using symmetrical differentiation, they discuss an important characterization for preinvex functions and define symmetrically pseudo-invex and symmetrically quasi-invex functions. They also generalize the first derivative theorem for symmetrically differentiable functions and establish some relationships between symmetrically pseudo-invex and symmetrically quasi-invex functions. They also discuss the Fritz John type optimality conditions for preinvex, symmetrically pseudo-invex and symmetrically quasi-invex functions using symmetrical differentiability.<\/jats:p>","DOI":"10.37190\/ord220406","type":"journal-article","created":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T07:10:57Z","timestamp":1676013057000},"source":"Crossref","is-referenced-by-count":0,"title":["Optimality conditions for preinvex functions using symmetric derivative"],"prefix":"10.37190","volume":"32","author":[{"given":"Sachin","family":"Rastogi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akhlad","family":"Iqbal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sanjeev","family":"Rajan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23140","container-title":["Operations Research and Decisions"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/ord.pwr.edu.pl\/assets\/papers_archive\/ord2022vol32no4_6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T07:11:15Z","timestamp":1676013075000},"score":1,"resource":{"primary":{"URL":"https:\/\/ord.pwr.edu.pl\/assets\/papers_archive\/ord2022vol32no4_6.pdf"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.37190\/ord220406","relation":{},"ISSN":["2081-8858","2391-6060"],"issn-type":[{"value":"2081-8858","type":"print"},{"value":"2391-6060","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]}}}