In this article, we introduce a new notion of generalized convex fuzzy mapping known as strongly preinvex on the invex set. Firstly, have investigated some properties mapping. particular, establish equivalence among mapping, and monotonicity. We also prove that optimality conditions for sum G-differentiable mappings non-G-differentiable can be characterized by mixed variational-like inequalitie...

†Department of Mathematics, Statistics and Computer Science, College of Basic Sciences and Humanities, G.B. Pant University of Agriculture and Technology, Pantnagar-263 145, India ‡Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China §Department of Management Sciences, City University of Hong Kong, Tat Chee Avenue, Kowloon...

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.