Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction fractional has prompted another direction in different branches mathematics applied sciences. First, we investigate prove equality. Considering this equality as the auxiliary result, attain some estimations a Hermite–Hadamard type inequality involving s-p...

For generalized variational-like inequalities, by combining the auxiliary principle technique with the bundle idea for nonconvex nonsmooth minimization, we present an implementable iterative method. To make the subproblem easier to solve, even though the preinvex function may not be convex, we still consider using the model similar to the one in [R. Mifflin, A modification and extension of Lema...

Sufficient optimality conditions are obtained for a nonlinear multiple objective fractional programming problem involving η-semidifferentiable type I-preinvex and related functions. Furthermore, a general dual is formulated and duality results are proved under the assumptions of generalized semilocally type I-preinvex and related functions. Our result generalize the results of Preda [V. Preda, ...

In this paper we consider some classes of α-preinvex and α-invex functions. We study some properties of these classes of α-preinvex (α-invex) functions. In particular, we establish the equivalence among the α-preinvex functions, α-invex functions and αη-monotonicity of their differential under some suitable conditions.

In this paper, we derive several weighted Hermite-HadmardNoor type inequalities for the differentiable preinvex functions and quasi preinvex functions. AMS (MOS) Subject Classification Codes: 26D15, 26D20, 26D07

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.

In this paper, we present weighted integral inequalities of Hermite-Hadamard type for differentiable preinvex and prequasiinvex functions. Our results, on the one hand, give a weighted generalization of recent results for preinvex functions and, on the other hand, extend several results connected with the Hermite-Hadamard type integral inequalities. Applications of the obtained results are prov...

In order to show novel generalizations of mathematical inequality, fractional integral operators are frequently used. Fractional used simulate a broad range scientific as well engineering phenomena such elasticity, viscous fluid, fracture mechanics, continuous population, equilibrium, visco-elastic deformation, heat conduction problems, and others. this manuscript, we introduce some notions gen...

In this paper, we define and introduce some new concepts of strongly φ-preinvex (φ-invex) functions and strongly φη-monotone operators. We establish some new relationships among various concepts of φ-preinvex (φ-invex) functions. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previous...