Fuzzy mixed variational-like and integral inequalities for strongly preinvex fuzzy mappings
Date
2021
Authors
Khan, Muhammad Bilal
Srivastava, H.M.
Mohammed, Pshtiwan Othman
Guirao, Juan L. G.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
It is a familiar fact that convex and non-convex fuzzy mappings play a critical role in
the study of fuzzy optimization. Due to the behavior of its definition, the idea of convexity plays
a significant role in the subject of inequalities. The concepts of convexity and symmetry have a
tight connection. We may use whatever we learn from one to the other, thanks to the significant
correlation that has developed between both in recent years. Our aim is to consider a new class of
fuzzy mappings (FMs) known as strongly preinvex fuzzy mappings (strongly preinvex-FMs) on the
invex set. These FMs are more general than convex fuzzy mappings (convex-FMs) and preinvex fuzzy
mappings (preinvex-FMs), and when generalized differentiable (briefly, G-differentiable), strongly
preinvex-FMs are strongly invex fuzzy mappings (strongly invex-FMs). Some new relationships
among various concepts of strongly preinvex-FMs are established and verified with the support of
some useful examples. We have also shown that optimality conditions of G-differentiable strongly
preinvex-FMs and the fuzzy functional, which is the sum of G-differentiable preinvex-FMs and
non G-differentiable strongly preinvex-FMs, can be distinguished by strongly fuzzy variational-like
inequalities and strongly fuzzy mixed variational-like inequalities, respectively. In the end, we
have established and verified a strong relationship between the Hermite–Hadamard inequality and
strongly preinvex-FM. Several exceptional cases are also discussed. These inequalities are a very
interesting outcome of our main results and appear to be new ones. The results in this research can
be seen as refinements and improvements to previously published findings.
Description
Keywords
preinvex fuzzy mappings, strongly preinvex fuzzy mappings, strongly invex fuzzy mappings, strongly fuzzy monotonicity, strongly fuzzy mixed variational-like inequalities
Citation
Khan, M. B., Srivastava, H. M., Mohammed, P. O., & Guirao, J. L. G. (2021). “Fuzzy mixed variational-like and integral inequalities for strongly preinvex fuzzy mappings.” Symmetry, 13(10), 1816. https://doi.org/10.3390/sym13101816